a modell of the fire-workes to be presented in lincolnes-inne fields on the 5th. of novemb. 1647. before the lords and commons of parliament, and the militia of london, in commemoration of gods great mercy in delivering this kingdome from the hellish plots of papists, acted in the damnable gunpowder treason. with their present statues and proportions. browne, george, gunner. this text is an enriched version of the tcp digital transcription a77668 of text r210669 in the english short title catalog (thomason 669.f.11[92]). textual changes and metadata enrichments aim at making the text more computationally tractable, easier to read, and suitable for network-based collaborative curation by amateur and professional end users from many walks of life. the text has been tokenized and linguistically annotated with morphadorner. the annotation includes standard spellings that support the display of a text in a standardized format that preserves archaic forms ('loveth', 'seekest'). textual changes aim at restoring the text the author or stationer meant to publish. this text has not been fully proofread approx. 4 kb of xml-encoded text transcribed from 1 1-bit group-iv tiff page image. earlyprint project evanston,il, notre dame, in, st. louis, mo 2017 a77668 wing b5114 thomason 669.f.11[92] estc r210669 99869444 99869444 162744 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a77668) transcribed from: (early english books online ; image set 162744) images scanned from microfilm: (thomason tracts ; 246:669f11[92]) a modell of the fire-workes to be presented in lincolnes-inne fields on the 5th. of novemb. 1647. before the lords and commons of parliament, and the militia of london, in commemoration of gods great mercy in delivering this kingdome from the hellish plots of papists, acted in the damnable gunpowder treason. with their present statues and proportions. browne, george, gunner. 1 sheet ([1] p.) printed for george lindsey, and are to be sold at his shop over against london-stone, london : 1647. signed at end: per george browne gunner, to bee performed in lincolns-inne fields before the lords and commons of parliament, and the militia of london. with decorative border. annotation on thomason copy: "nouemb: 4th". reproduction of the original in the british library. eng fireworks -england -early works to 1800. great britain -history -civil war, 1642-1649 -early works to 1800. london (england) -social life and customs -17th century -early works to 1800. a77668 r210669 (thomason 669.f.11[92]). civilwar no a modell of the fire-workes to be presented in lincolnes-inne fields on the 5th. of novemb. 1647. before the lords and commons of parliament browne, george, gunner. 1647 528 0 0 0 0 0 0 0 a this text has no known defects that were recorded as gap elements at the time of transcription. 2008-07 tcp assigned for keying and markup 2008-07 spi global keyed and coded from proquest page images 2008-08 john pas sampled and proofread 2008-08 john pas text and markup reviewed and edited 2008-09 pfs batch review (qc) and xml conversion a modell of the fire-workes to be presented in lincolnes-inne fields on the 5th . of novemb. 1647. before the lords and commons of parliament , and the militia of london , in commemoration of gods great mercy in delivering this kingdome from the hellish plots of papists , acted in the damnable gunpowder treason . with their perfect statues and proportions . the actors good will to this kingdome , and city of london . jn a description of his fire-workes to be performed novem the 5th . 1647 , in commemoration of the great deliverance from the powder plot by popish conspiracie against englands then king and parliament , and by consequence , the enslaving the whole kingdome to popery . 1 fire-bals burning in the water , and rising out of the water burning , shewing the papists conjuration and consultation with infernall spirits , for the destruction of englands king and parliament . 2 fire-boxes like meteors , sending forth many dozen of rockets out of the water , intimating the popish 〈◊〉 coming from below to act their treasonous plots against englands king and parliament . 3 faux with his darke lanthorne , and many fire-boxes , lights , and lamps , ushering the pope into england , intimating the full plot to destroy englands king and parliament . 4 pluto with his fiery club , presenting himselfe malitiously bent to destroy all that have hindered the pope from destroying englands king and parliament . 5 hercules with his fiery club , who discomfiteth pluto , and suffers him not , nor any of his infernall spirits to hurt englands king and parliament . 6 runners on a line , intimating the papists sending to all parts of the world , for subtill , cunning , and malitious plotters of mischiefe against englands king and parliament . 7 a fire wheele , intimating the display of a flag of victory over the enemies that would have destroyed englands king and parliament , in the time of which motion , a payre of virginals musically playing of themselves . 8 rockets in the ayre , shewing the thankfulnesse of all well willers to true religion , for the deliverance of englands king and parliament 9 balloones breaking in the ayre , with many streames of fire , shewing gods large and bounteous goodnesse towards englands king and parliament . 10 chambers of lights , shewing englands willingnesse to cherish the light of the glorious gospell therein to bee continued . 11 a great bumber-ball breaking in pieces , and discharging it selfe of other its lights , holding forth the cruelty of papists to englands king and parliament . 12 fire boxes among the spectators , to warne them to take heede for the future that they cherish none that are enemies to englands king and parliament . per george browne gunner , to bee performed in lincolns-inne fields before the lords and commons of parliament , and the militia of london . london , printed for george lindsey , and are to be sold at his shop over against london-stone , 1647. at the court at whitehall this sixth day of november 1685 present, the kings most excellent majesty. his royal highness prince george.... mr. chancellour of the dutchy. for the preventing tumultuous disorders, which may happen hereafter upon pretence of assembling, to make bonfires, and fire-works,... orders in council. 1685-11-06 england and wales. sovereign (1685-1688 : james ii) 1685 approx. 3 kb of xml-encoded text transcribed from 1 1-bit group-iv tiff page image. text creation partnership, ann arbor, mi ; oxford (uk) : 2008-09 (eebo-tcp phase 1). a84492 wing e799 estc r223032 99896125 99896125 153924 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a84492) transcribed from: (early english books online ; image set 153924) images scanned from microfilm: (early english books, 1641-1700 ; 2390:4) at the court at whitehall this sixth day of november 1685 present, the kings most excellent majesty. his royal highness prince george.... mr. chancellour of the dutchy. for the preventing tumultuous disorders, which may happen hereafter upon pretence of assembling, to make bonfires, and fire-works,... orders in council. 1685-11-06 england and wales. sovereign (1685-1688 : james ii) james ii, king of england, 1633-1701. 1 sheet ([1] p.) printed by the assigns of john bill deceas'd: and by henry hills, and thomas newcomb, printers to the kings most excellent majesty, london : 1685. "a reissue of previous orders in council, nos. 3711, 3734, 3754, q.v., forbidding bonfires and fireworks without permission having been previously obtained." -steele. title from caption title and first lines of text. arms 102a; steele notation: may fires, persons. reproduction of original in the henry e. huntington library. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng fireworks -law and legislation -england -early works to 1800. riots -england -early works to 1800. broadsides -england -london 2007-09 tcp assigned for keying and markup 2007-11 aptara keyed and coded from proquest page images 2008-01 emma (leeson) huber sampled and proofread 2008-01 emma (leeson) huber text and markup reviewed and edited 2008-02 pfs batch review (qc) and xml conversion royal blazon or coat of arms j2 r diev et mon droit at the court at whitehall this sixth day of november 1685. present , the kings most excellent majesty . his royal highness prince george . lord arch-bishop of canterbury . lord chancellor . lord treasurer . lord privy seal . duke of ormond . duke of beaufort . duke of queensbery . lord chamberlain . earl of huntingdon . earl of peterborough . earl of sunderland . earl of craven . earl of nottingham . earl of perth . earl of middleton . lord viscount fauconberg . lord viscount preston . lord viscount melfort . lord dartmouth . lord godolphin . mr. chancellour of the exchequer . lord chief justice herbert . mr. chancellour of the dutchy . for the preventing tumultuous disorders , which may happen hereafter upon pretence of assembling , to make bonfires , and fire-works , and disappointing the evil designs of persons disaffected to the government , who commonly make use of such occasions , to turn those meetings into riots and tumults : it is this day ordered by his majesty in council , that no person or persons whatsoever , do presume to make or encourage the making any bonfires , or other publick fire-works , at or upon any festival day , or at any other time or times whatsoever , without particular permission , leave , or order first had from his majesty , or this board , or signified to them by the right honourable the lord mayor of london , or by the justices of the peace in their respective limits , upon pain of his majesties displeasure , and being prosecuted with the utmost severity of the law ; whereof all persons whom it may concern , are to take notice at their perils . w. bridgeman . london , printed by the assigns of john bill deceas'd : and by henry hills , and thomas newcomb , printers to the kings most excellent majesty , 1685. the making of rockets in two parts, the first containing the making of rockets for the meanest capacity, the other to make rockets by a duplicate proposition, to 1000 pound weight or higher / experimentally and mathematically demonstrated, by robert anderson. anderson, robert, fl. 1668-1696. 1696 approx. 55 kb of xml-encoded text transcribed from 33 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2003-11 (eebo-tcp phase 1). a25366 wing a3105 estc r1638 12306204 ocm 12306204 59261 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a25366) transcribed from: (early english books online ; image set 59261) images scanned from microfilm: (early english books, 1641-1700 ; 198:12) the making of rockets in two parts, the first containing the making of rockets for the meanest capacity, the other to make rockets by a duplicate proposition, to 1000 pound weight or higher / experimentally and mathematically demonstrated, by robert anderson. anderson, robert, fl. 1668-1696. [17], 48 p. : ill. printed for robert morden ..., london : 1696. reproduction of original in british library. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng fireworks -early works to 1800. 2003-07 tcp assigned for keying and markup 2003-07 aptara keyed and coded from proquest page images 2003-08 marika ismail sampled and proofread 2003-08 marika ismail text and markup reviewed and edited 2003-10 pfs batch review (qc) and xml conversion the making of rockets . in two parts . the first containing the making of rockets for the meanest capacity . the other to make rockets by a duplicate proposition , to 1000 pound weight or higher . experimentally and mathematically demonstrated , by robert anderson . london : printed for robert morden , at the atlas in cornhil . 1696. to the right honourable henry earl of romney . vicount sidney of sheppy , baron of milton , master general of his majesty's ordnance , constable of dover castle , lord warden of the cinque ports , and one of the lords of his majesty's most honourable privy council . well knowing my most noble lord , that these things will easily receive perfection in your hands , which for many reasons are beyond my reach . this treatise ( if it may deserve that name ) is the least in bulk , and seemingly relating to the sleightest subject i have met withal in pyrotechnia . but in the many volumns great and small that i have read relating to these matters in our own and other languages ; i do not find the least pretence or thought of doing that which here is undertaken , viz. to raise so great a heap of fire , and to confirm the fact by the greatest proofs that can be had or wish'd for , which are experiments and demonstrations mathematical . yet this alone is not the matter aim'd at , the problem is universal , and applicable to the fortifications of all sorts of guns and other engines with their carriages , &c. and is to increase or decrease the strength of materials according to the effects and services required . but the greatest skill in this undertaking being to adjust the instrument and means in a due and proper proportion to the effect sought for ; i do with all humility and profound respect make offer of this small essay . it is your lordships great abilities and merit , that has enabled you to tread the intricate and painful steps of greatness ; and by the well discharging so many eminent employments , to add , ( if any thing can be added ) to the great name of your renowned ancestors . an ardent zeal for the welfare and honour of your country , has always been the inbred vertue of your family , and which is brought to its perfection in your self . the name of master general of the ordnance , lays claim to all my ( more than 25 years ) experience and studies about the art of shooting in all sorts of great artillery amounts to : but the adding something ( according to my poor sphere and capacity ) to the defence , safety and reputation of my native country , has at all times so intirely govern'd me , that upon this account also , and indeed chiefly , i am emboldned to lay this mean attempt of mine before your lordship ; trusting that it may at some time or other undergo a trial , and by your lordships favour receive a meet incouragement , and procure your lordships pardon , &c. to my lord , your lordships most obedient , humble servant , robert anderson . to the young pyrobolistes . rockets are the most artificial piece of fire-work yet used amongst the pyrobolistes , and hath been more used of late years than formerly , and that the young artists may not spend their time and money unnecessarily , i have given easie , plain , and ready rules for making of rockets to two inches and half diameter , which is sufficient for all private occasion , viz. of the mould of a rocket . of the rouler and case . of the compositions . of the receipts of rockets . of the driver . of the boring of the rocket . of the stars and other matter to be put in the head of a rocket . to head a rocket . of the sticking of a rocket . and lastly , to fire the rocket . and some observations about the management of a rocket in general ; all which i hope will prove casie and beneficial to the ingenious , and those that are willing to learn : and what you do , endeavour to do it well , and do not be conceited ; which if so , i have my ends . and from these little beginnings greater matters may be obtained , and you may become serviceable to your country ; in which be sure to be careful , honest and faithful . to the other pyrobolistes . about fifteen years since i considered of a method to increase or decrease the strength of the metal of guns , which is this that i intend to discourse of . and at the close of a small treatise to hit a mark published in the year 1691. i proposed that problem in print ; since that time there has been more than ordinary occasion for it , by reason of the new casting of the mortar-pieces . about two years since i put that problem into a method , and made a draught of the whole matter to increase or decrease the strength of the metal of a gun in any possible proportion assigned . but when i saw the mortar-pieces brought from sea broke , it was thought to be a good time to shew it , which was done , and the whole matter discoursed of at large , but it signified 00. but now i apply that problem to the making of rockets for the young artist , as you see in its proper place . and it is manifest that the young rocket-makers of this city are very careful and artificial in their rockets of 8d . 12d . or 18d . value , otherwise they may break and so lose their labour and discredit themselves . seeing these mathematical rules are so applicable to the greatest nicety of the rising of all sizes of rockets ; is it not more valuable to be applied to those chargeable instruments of war , viz. guns of all sorts , with their carriages , and all other their furniture ? as to the doctrine of shooting by the increase and decrease of powder , this way of making of rockets proves it to be absurd ; for all rocket makers to this time weaken the composition of their rockets , as their rockets are in greatness , or having greater quantities of composition ; and that by chance , and without any mathematical demonstration . and also by experience , in table june 1. 1691. and in the first column experiment 4 , against that in column 2 you will find 4 ounces of powder , and in column 3 , 3377. again , in column . 1 , against experiment 1 in column 2 , you find ½ an ounce of powder , and against that in column 3 , you find 213 ; now because the requisite of powder are as 8 to 1 , therefore i multiply 213 by 8 , and it makes 1704 , much short of 3377 , which indeed should have been equal to the said 3377. that is the ranges upon the plain of the horizon are not as the requisites of powder which projected those ranges ; the like may be done in all the other experiments . i. have made hundreds of experiments in several sorts of mortar-pieces , and am ready to make as many more , all which will manifestly confute the doctrine of shooting by the increase and decrease of powder , and have often invited the first promoter of that doctrine to see his invention confuted ; and i do here invite all the practitioners in that science of shooting by the increase and decrease of powder , to come and see their doctrine confuted . i do hear assert it is impossible ever to bring that way of shooting to be so exact and ready for use , in all or any sorts of guns , as the common or usual way is , by keeping the requisites of powder constant , and elevating the piece . in the complicating of rockets , whose diameters are at any great distance ; we make use of experiments of shooting made upon another occasion , and those experiments serves sufficiently well ; but if we were to do them justly according to art , there should be two even chased guns of the same proportion as the rockets are of , that is the diameter of the exposed rocket 2½ inch multiplied by 6 is 15 inches , and those should be the diameter and length of one of the guns : 4 inches the diameter of the other rocket , multiplied by 6 is 24 inches , which 4 inches for the diameter , and 24 inches for the length should be the other gun , or any two guns in that proportion . for the requisite of powder take the cube of 4 , which is 64 , as also the cube of 2½ , which is 15.625 , divide the greater cube number by the lesser , and the quotient is 4 , sufficiently near ; so the requisites of powder of these two pieces are as 4 to 1 , then take any reasonable requisite of powder for the 4 inch gun , then take the fourth part of that requisite for the requisite of powder for the lesser gun , discharge them both at one degree of elevation , and note their ranges . their bullets are to be of the same metal , and of the same likeness , and both exactly fit . in a mathematical sence these ranges should be equal ; but by combination the greater quantity of powder aggitates more upon the great bullet , than the lesser requisites doth aggitate upon the lesser bullet , and that causes those differences , the like when two quantities of powder aggitate upon one bullet ; it is experience only that determines the matter . although strange things sometimes happens ; yet this we will assert , and endeavour to maintain that mathematical knowledg , join'd with faithful experiments , will do greater matters than most men commonly conceive . rob. anderson . rocket moulds are made by mr. cuggley just without cripplegate . taper bits for rockets , are made by mr. goode just within cripplegate . rods for rockets , are made by mr. stateham in token-house-yard , lothbury . all three right good workmen . proposition i. of a rocket-mould . let e m r d d h l e be a rocket-mould , a b the diameter of it , viz. one inch and half ; z k 4 diameters , that is 6 inches the height to be filled with composition , b e half a diameter an overplus , z c the height of the boring 4 inches and ½ , or ¾ of the height of the mould , g f the orifice one third of the diameter of the rocket half an inch , z y one sixth of the diameter of the rocket a quarter of an inch , the thickness of the case , d y z g c f z y d the bottom of the rocket-mould with the needle to be put in and taken out ; r h a pin of iron to fix the mould and bottom together . proposition . ii. of the rowler and case of a rocket . make the body of the rowler nine diameters in length , and in diameter two thirds of the diameter of the rocket , and the head of the rowler of the rocket the same diameter ; let the diameter of the neck of the rowler be a little less than one third of the diameter of the rocket , because when opened with a cone of wood the orifice of the rocket may be just one third smooth and hard to endure the fire . then the thickness of the case will be one sixth of the diameter of the rocket , which being well rowled and choaked , the case may be finished . proposition iii. of the composition for rockets . the ingredients which rockets are composed of are saltpetre , sulphur , and wood-coal mealed , and passed through a fine sieve . first , take the largest of small-coal made of birch-wood . secondly , chuse the yellowest roch sulphur . thirdly , take saltpetre put in a brass vessel , to which put so much fair water as will dissolve it , put that vessel upon the fire , when it boils scum it clean ; when the water evaporates and consumes , stir it with a spatula of wood to meal it , what remains of the saltpetre upon the spatula , and sides of the vessel , rub off with your spatula of wood ; then meal it , and pass it through a fine sieve . a second way to clarifie saltpetre ; take a crucible , set it in the fire , put saltpetre thereunto , increase the fire till the saltpetre be reduced to a liquid quality like water ; when it boils take mealed sulphur upon a spatula of iron , and put it into the boiling saltpetre ; so often repeated , the flegmy quality of the saltpetre will be burnt away , and the flame will remain as white as the body of the sun. then pour it into some very smooth vessel , which being cooled , you may reduce it into meal . these ways i have done for my recreation ; but i usually take the cleanest saltpetre to be found in drugsters shops , and it does as well . proposition iv. the receipts for rockets . for an inch , an inch and half , and two inch rocket , and for a white fire , take 2 drams of antimony , 1 ounce of sulphur 2½ ounces of coal-dust , 6 ounces of saltpetre , and 8 ounces of powder dust , [ casimer du grand art d' artillerie , partie 1. livre 3. pag. 145. ] fill 4 diameters and bore 2½ . for an inch and half , and two inch , and two inch and half rocket , and a yellow fire , take 1 ounce of sulphur , 1 ounce of coal-dust , 4 ounces of saltpetre ; or take 1 ounce of sulphur , 1½ ounce of coal-dust , and 4 ounces of saltpetre . [ casimer du grand art d' artillerie , partie 1. livre 2. pag. 99. ] fill 4 diameters , and bore 3 , or a little more . and daniel elrich der grossen kunst artillerie zweiter , thei l . pag. 54. at . 19. advises to take 1 ounce of sulphur , one ounce of coal dust , 4 ounces of saltpetre . again , take 1 ounce of sulphur , 2 ounces of coal , and 6 ounces of saltpetre ; also take 1 ounce of sulphur 2½ of coal , and 6 of saltpetre . johann . sigmund . buchner in theoria praxis artilleria andere thei l , pag. 28. weigh the ingredients single , put them into a wooden bowl , mix them very well together , and pass them through the sieve , then your composition is fit for use . in filling rockets of one or two inches diameter ; let them be filled at 6 , 8 , or 10 times charging , and to every charge 10 , 12 , or 14 blows with a mallet , and betwixt every three blows turn the driver a little in your hand , so the composition about the needle will be preserved . some of our rocket-makers cry up the compositions of woolverman and nelson , as though there was no composition to be found like theirs , and they are thus : that falsly called woolverman's is 1 of sulphur , 1 of coal , and 4 of saltpetre : and that of nelson , 1 of sulphur , 1½ of coal , and 4 of saltpetre , as they stand in the remains of mr. francis deane , sometime gunner of the tower. these compositions are old and common , as you see , they are good , strong , and dull compositions , and easily mannaged . those compositions where powder is judiciously mixed are more lively , and so more difficult to mannage . proposition v. of the driver of a rocket . let y a f g h e b y be the driver of the rocket , a f e b a piece of a gun barrel , f g h e o l a piece of box or hard wood , r l o q a hole for the needle to pass through , a c d b y a piece of box to drive upon ; this we call a hollow driver , it dispatches business quickly , and does right well . or you may fasten a piece of brass in the end of your iron driver with a hole in it to receive the needle . if any will use a solid driver , let them have the bottom of the mould as d y z z z y d with a hole passing through the bottom , as z r , for a strait piercer to pass through which bottom will be a guide to the piercer to be just in the middle of the rocket , make a mark in your piercer to be a guide to bore always an equal depth , then take your rocket out of the mould , open the hole with a taper bit , and your work is done , thus you may do for all sizes of rockets . proposition vi. of the boring of a rocket . make the diameter of your borer one third of the diameter of your rocket , not for any necessity , but for conformity to the other parts of the rocket ; from that diameter let it be exactly taper to a point . further , there being an entrance made by the needle , it is very easie to bore the rocket very exactly , by holding the rocket in the left hand , and the borer in the right , moving the rocket in the left hand , keeping the borer fast in the right hand . if you make the diameter of the needle one third of the diameter of the rocket , and so taper , you need no borer ; here you shall find the rocket will rise swifter than when bored , the composition lying looser about the needle than if it were bored , takes fire easier , and this is most necessary in large rockets , viz. of 3 , 4 , or 6 inches diameter ; for such will hang too long time upon the nails before they rise . those rockets whose compositions are composed of mealed powder , saltpetre , coal and sulphur , fill four diameters , bore two and half . those composed of saltpetre , coal , and sulphur fill four diameters , bore three or a little more . this will hold in rockets of 1 inch , 1½ and 2 inches , but in larger rockets there must be less solidity to the hollow cone of fire . i used for many years to drive my rockets solid , and to bore them after , but that way did no better than these i now use and deliver ; but this is most certain that any one may drive and bore 3 rockets with those hollow drivers which i now use , whilst one many finish the driving and boring of one rocket with a solid driver ; when the rocket is near filled , use a shorter driver with a smaller hole . proposition vii . of stars for rockets . 1 , 1 , 2 , 2. sulphur . 2 , 3 , 3 , 2. antimony . 4 , 6 , 8 , 6. saltpetre . meal these ingredients fine , pass them through a sieve , mix them with water in which some glue , or gum araback , or gum dragon hath been dissolved , make them of the bigness of a hazle nut , or small wallnut ; roul them in meal powder , when dryed they are fit for use . rockets are headed with small serpents , their orifices washed with mealed powder and brandy wine , to take fire . of rain and hail . take any of those receipts for stars , viz. 1 sulphur , 2 antimony , and 4 saltpetre ; if you moisten that composition with oil of petre only made well into paste , formed into little globes , rowled into mealed powder ; such stars will have red colour : the same composition moistned with linseed oil will have a red mixed with white : the same composition mixed with oil of petre and linseed oil mixed together , will make an amethist fi●e . all these will require a long time a drying , the best time is to make them in the summer . the same composition mixed with gum araback water , and colophone , gives a red yellowish fire . the former composition moistned with brandy and oil of petre , or linseed oil , mixed together , requires less drying powder of glass , powder made of sawdust mixed with the former composition gives different fire ; coal dust instead of antimony , all which you may govern by your own reason . take the old proverb , so many men , so many minds . proposition viii . to head a rocket . turn a piece of wood just so big as your rocket is , with a cone at one end thereof , paste a piece of strong paper about the wood , then paste another piece of paper about the cone , and paste both papers together ; then put your stars into this paper vessel , with some rocket composition to break the vessel , then put a little paste a little within the sides of this paper vessel , then draw it upon your rocket , and paste it to the rocket , so your work is done . proposition ix . of the sticking of rockets . the stick of a rocket ought to be seven times the length of the rocket or more , viz. a rocket of an inch and half , six diameters thereof , the length of the rocket , is nine inches , seven times nine is sixty three inches , that is five foot three inches . the breadth of the stick at the head , three quarters of an inch or less , the thickness half an inch or less , the small end of the stick three eighths of an inch and square , and to be made of light deal ; such a stick will do very well , and may be counted custom without demonstration . in the winter 1695. there were two sets of fire works , in the first of which the wind was northward , and the rockets in their rising worked into the wind. in the second the wind was westward , and had the same effect as the first ; the reason was because the stick was to heavy at the upper end , and too light at the lower ; and so the center of gravity of the rocket and stick was too near the rocket : when indeed the center of gravity should be in the middle , betwixt the lower end of the stick and upper end of the rocket ; and to do which the bigger end of the stick ought to be downward ; by this means a lighter stick would serve , and if the wind did drive the rocket , the rocket would move less , and yet perpendicular to the horizon . nature it self has taught us the same ; for all birds , especially birds of a swift flight , spread their tails for their guide . sticks of rockets ought to be one to another as the length and diameters of the respective rockets ; that is , as the diametre 1½ inch is to the thickness of its stick , so is 4 inches the diameter of a 4 inch rocket to the thickness of its respective stick . as the length of one rocket is to its stick ; so is the length of any other rocket to its stick : and as the weight of one rocket is to the weight of its stick ; so is the weight of any other rocket to the weight of its respective stick . proposition x. to fire the rocket . place the rocket perpendicular to the horizon by four nails , make a port-fire , about half an inch in diameter , with single paper , viz. 1 sulphur , 2 saw-dust sifted fine , or rather logwood beaten and sifted fine , 4 of mealed powder , and 8 of saltpetre ; or make the port-fire with rocket composition : fire the port-fire , move it gently towards the orifice of the rocket till it takes fire . observations concerning rockets . ( 1. ) if a rocket be driven not hard enough it either consumes or breaks ; if just hard enough it rises well ; if two hard it turns a loft , and breaks not at the just turn . ( 2. ) if a rocket be bored not deep enough it will not rise well ; if just deep enough it rises well ; if too deep it often breaks . ( 3. ) if a rocket be bored with too great a borer it will not rise well ; if with a fit borer it rises well ; if with too small a borer it breaks , or rises not well . ( 4. ) if the composition be too moist it will not rise well ; if too dry it rises too fast or breaks . ( 5. ) if a rocket be made , and kept in too dry or too moist a place , it will have the same effect as at the ( 4. ) ( 6. ) the velocity of a rocket is caused by the boring , or in the hollow cone ; the time of its flight is in the solid part above the boring , which solid part ought to be less in a great rocket than in a little one . from these observations a youth may take any composition ( in reason ) and make a good rocket . proposition xi . the weight of the mallets for rockets . the weight of the mallets which rockets are driven with , ought to be as the cube of the respective diameters of their bores , viz. if the weight of the mallet for an inch rocket be twelve ounces , the weight of the mallet for an inch and half rocket ought to be two pounds and half , and for a two inch rocket six pounds , &c. proposition xii . how rockets are estimated . rockets are estimated either by measure or by weight ; if by measure , then by the common standard by inches or by feet ; if by weight , then they are estimated by cast iron , that is , by the gunners rule , viz. an inch rocket weigheth two ounces and a quater : an inch and half rocket weigheth half a pound : a two inch rocket weigheth a little above a pound : a three inch rocket weigheth almost four pounds : a four inch rocket weigheth nine pounds : an eight inch rocket weigheth seventy two pounds , which may be called a rocket royal. proposition xiii . of the cause of the rockets rising . let a c b be the hollow cone for the the fire , a y c z b the superficies of that cone , all the lines o z at right angles with b c , and all the lines o y at right angle with a c ; now all the angles z o y being towards r , whether the angles z o y are obtuse or acute , but the more acuter the better . the rays of fire z o and y o issuing from the sides of the cone b c and a c , and continually agitating with greater force one upon another at o , forcing the whole cone b c a upward from the point r ; ( and the wider the bore is ( in reason ) the rocket will rise with the greater velocity ; if the composition and deepness of boring be sutable . ) by the rays z x , and y z of fire , crossing , each other at the center of the cone r , and the point r , as it were , remains fixt ; and here the similitude of guns and rockets appears plainly , a gun remains fixt upon the center of motion of the trunnions , and projects its burden forth ; but a rocket flys from its burden , leaving it at r , as it were fixt . part ii. to our pyrobolistes . a duplicate proposition . having one rocket well proved in all its parts , viz. a three inch rocket . then , to decrease the velocity of the composition of the aforesaid rocket , to make it fit for a 4 inch 4½ and 5 inch rocket . and to increase the velocity of the aforesaid composition , to adapt it to a 2 inch 1½ and 1 inch rocket , keeping the same kind of boring . secondly , from the exposed rocket of 3 inches , to increase the diameter of the orifice of the rockets of 4 : 4½ and 5 inches diameter ; and to decrease the diameter of the orifice of the rockets of 2 : 1½ and 1 inch diameter , to adapt them to the exposed rocket , keeping the composition of the same velocity . from experimental and mathematical demonstration . the resolution of this problem will manifestly shew , the invalidity of the doctrine of shooting by the increase and decrease of powder ; and that weak and narrow scantling it pinfolds in , too mean for this lofty engine . it also tells the gun-founder how to give his guns their due fortification ; otherwise they may become useless instruments of war. it teacheth our pyrobolistes to direct their work so that it may rise well , and not break nor fall . it teacheth artificers to increase and decrease the force or strength of their materials in any possible proportion assigned . this proposition was publickly proposed three months before the publication of this book , but no resolution given by any . proposition xiv . the complication of rockets in relation to their borers . from a 2 inch and half rocket , we complicate other rockets , viz. a four inch rocket thus , we take the cube of 4 , which is 64 , also we take the cube of 2½ , which is 15.625 , with which we divide 64 , the quotient is 4 ▪ and so many times the lesser rocket is contained in the greater , that is as 4 is to 1. then i look into the tables of ranges for the year 1691. iune 1 , and in the second column i find the requisite of powder 1 and 4 , and against the 4 in the third column i find the range 3377 ; and in the third column against 1 i find the range 652 , which i multiply by 4 , the ratio of the rockets , and it is 2608 : now if this last number had been equal to 3377 , the range with the quadruple of powder , it would have confirmed the shooting by the increase and decrease of powder ; but as it is short , it is a visible demonstration of the error of that doctrine : and if the doctrine of shooting by the increase and decrease of powder were true , there would be no need for our pyrobolistes to give different velocities of compositions to different sizes of rockets , but one composition would have served all sizes ; which every youth knows the contrary . in the parabola a h z let a g be 2608 , and a h 3377 ; then g z and h z are the velocities of the equal and unequal ranges . toricellius 22. prop. de motu projec . lib secund . then as g z the velocity of the equal range ; is to one third of the diameter of the four inch rocket 1. 333 ; so is h z the velocity of the unequal range , to a larger diameter of the 4 inch rocket , to keep the same composition . or as the equal range 2608 , is to the unequal range 3377 ; so is the square of the diameter of the orifice of the 4 inch rocket , to the square of the diameter of the orifice of the rocket inlarged , keeping the same composition . or as the equal range 2608 , is to the unequal range 3377 ; so is the area of the orifice of the rocket of 4 diameter , when taking ⅓ of the diameter ; to the area of the orifice of the same rocket when enlarged , to bare the composition that would serve a rocket of two inches and a half , taking ⅓ of the diameter of the rocket for the diameter of its orifice . example . 2608 the equal range 3 . 4′6308 3377 the unequal range 3.028531 the square of 1.333 , &c. the diam . of the equal oriffice .249660 take the half .361883 the diam . of the new orifice 1.516 one inch and half .180941 take another example . august 24. 1691. i look in column 2 , and find the requisites of powder half an ounce , and 2 ounces , and against those requisites in column 3 i find 1482 the unequal range , and 236 the equal range ; which i multiply by 4 , and it makes 944. 944 the equal range 2.974972 1482 the unequal range 3.170848 the square of 1.333 , &c. the equal orifice .249660 .445536 the diameter of the new orifice 1.67 .222768 here may be seen the concurrence of experiments made upon another account , not then thinking to apply it to the complication of rockets . i made 2 rockets of 4 inches diameter , and a taper bit according to this method , and bored three diameters , and left 2 inch●s solid , and they rose well . an example of a rocket of 6 inches diameter , keeping the same composition . take the cube of 6 , which is 216 , divide that cube by the cube of 4 , which is 64 , the quotient is 3 , that is the composition in the rocket of 4 inches , is to the composition in the rocket of 6 inches , is as 1 to 3 ; then i look in the table of aug. 24. and find in the second column the requisites of powder half an ounce , and an ounce and a half ; and against these requisites in column three 800 , the unequal range , and 236 the equal range , which i multiply by 3 , and it makes 708 : then as 4 is to 6 , so is twelve half quarters of an inch , the diameter of the new orifice of the four inch rocket , to eighteen half quarters of inches ; that is 2 inches and 1 quarter : or as 4 is to 6 , so is 1½ , that is 3 halfs , to 4½ half inches , that is 2¼ . then i had no such ranges , that their requisites of powder were in proportion as the cube of 6 is to the cube of 2½ ; therefore was i forced to help my self by proportion , which is the same in substance . 708 the equal range 2.850033 800 the unequal range 2.903089 the square of 2¼ , or 18 half quarters 2.510544 the half of this logarithm 2.563600 half quarters of inches 19.13 that is 2.2 is 1.281800 a second example , april 21 ▪ 1692. i look in column 2 , and find the requisites of powder 12 drams , and 36 drams ; and against these requisites in the third column i find 1176 the unequal range , and 303 the equal range , which i multiply by 3 , and it makes 909. 909 the equal range 2.958564 1176 the unequal range 3.070407 the square of 18 half quarters 2.510544 2.622387 20.47 , that is 2 inches and a half , and 47 / 100 1.311193 here may be seen one example makes the diameter a little more than two inches and a half , and in the other a little less , therefore we make the taper bores just two inches and a half for a 6 inch rocket . to work from a two inch and a half rocket to an inch , put the unequal range in the first place , and the work is done . the composition these 4 and 6 inch rockets were made of , were 1 sulphur , 1½ coal , and 4 saltpetre ; but i believe 1 sulphur , 1 coal , and 4 salt-petre would do better , there being no great danger of the rocket breaking , by reason of the large diameter of the bore , and tapering to a point ; and by the same reason , a lesser solid head is required , that is about 2 inches in a 4 inch , and 1¼ in a 6 or 8 inch rocket , will suffice . proposition xv. the complication of rockets in relation to their composition , with some cautions and limitations . to decrease the velocity of the composition of 1 , 1½ , and 4 , which served to a 2½ inch rocket , to make it fit for a 4 inch rocket : remember the ratio of the rockets are as 1 to 4. look in the table of ranges , and find the requisites of powder in the second column , as 1 to 4 , and against them in the third column the ranges , viz. 3377 and 652 , then multiply the equal range by 4 , and it is 2608 , ( in fig. 1. ) in the parabola z a h , let a h be equal to 3377 , and a g equal to 2608 ; then h z , and g z will be the velocity of the powder , which projected those ranges , and we increase or decrease the velocity of the salpetre by the ratio of g z to h z : then let a c in fig. 2 , be equal to h z in fig. 1 , and a b in fig. 2 , be equal to g z in fig 1 ; then draw the ordinate c h and b g in fig. 2 , and by these two lines , viz. c h and b g we increase or decrease the velocity of the coal . further , let d f in fig. 3 , be equal to c h in fig. 2 ; and d e in fig. 3. be equal to b g in fig. 2 : draw the ordinates f k and e i , and by these 3 lines we increase or decrease the velocity of the sulphur . then if we take the logarit●m of ( 0 ) ( 1 ) ( ● ) ( 4 ) ( 8 ) 3377 3.518531 1.759265 0.879632 0.439816 and is 26●8 3.416308 1.708154 0.854077 0.427038 that is , the ranges under ( 0 ) , their logarithm under ( 1 ) the half of the log. under ( 2 ) , the numbers answering those logarithms are the lines h z and g z in fig. 1. the logarithm under ( 4 ) is the fourth part of the logarithm under ( 1 ) : the numbers answering these logarithms , are the lines c h , and b g in fig. 2. further , the logarithm under ( 8 ) is the eighth part of the logarithm under ( 1 ) ; the numbers answering those logarithms , are the ordinates f k and e i in the parabola f d k. or you may take the difference of the logarithms under ( 1 ) viz. 102223 half 51111 quarter 25555 eighth 12777 by adding or subtracting these log. to or from the logarithm of the salt-petre , coal , and sulphur , you have your desire , viz. their velocities either increased or decreased : or thus , take the difference of the logarithm of the two ranges 102223 , and subtract it from the logarithm of the square of the number of drams , ounces , or pounds of salt-petre , or from the logarithm of the fourth power of the numbers of drams , ounces , or pounds of coal . and lastly , that difference being subtracted from the logarithms of the eighth power of the number of the drams , ounces , or pounds of sulphur , there will remain three logarithms , the first being divided by 2 , the second by 4 , and the third by 8 ; there will remain three logarithms , the numbers answering to which , will be the number of drams , and tenths of the salt-petre , coal , and sulphur desired . to weaken the velocity of the composition of 1 , 1½ , and 4. 3377 the unequal range 3.518531 2608 the equal range 3.416308 the square of 64 drams of saltpetre 3.612360 take the half 3.510137 drams 56.9 nine tenths of saltpetre 1.755068 the fourth power of twenty four drams of coal 5.520844 the difference of the logarithm of unequal , and equal ranges subtract .102223 is the logarithm of the fourth power , which being divided by fourth 5.418621 22 drams 63 / 100 of coal 1.354655 the eighth power of fix 〈…〉 drams of sulphur 9632960 the difference of the logarithm .102223 subtract .102223 is the logarithm of the eighth power which being divided by 8 9.530737 15 drams 54 / 100 of sulphur 1.191342 the composition will be sulphur 15½ , coal 22½ , and saltpetre 57 ; but if you quicken the velocity , the equal range will be in the first place of the proportion . proposition xvi . tables of ranges made with mortar-pieces . june 1. 1691. on wimbleton-heath at 15 deg . of elevation , with a four inch mortar-piece , and a turned iron ball. 1 2 3 experiments . powder . chain . 1 ½ 213 2 1 652 3 2 1640 4 4 3377 august 24. 1691 : at 15 deg . of elevation , with a 3½ inches mortar-piece , and a turn'd iron ball. 1 2 3 4 5   the chamber of this mortar-piece a frustum of a cone . the chamber of this mortar piece a frustum of a sphere .   powder chain . powder chain . 1 ½ 236 ½ 144 2 1 496 1 304 3 1½ 800 1½ 1258 4 2 1482 2 3394 ● april 21. 162. at 15 deg . of elevation , with a 3½ inch mortar-piece , and a turn'd iron ball. 1 2 3 experiment . powder . chain . 1 12 303 2 24 746 3 36 1176 4 48 1820 5 60 2698 thus have i given plain and easie rules to the young pyrobolistes for the making of small rockets ; and also for the making of great rockets , to them of a greater knowledge and purse , even such as was reputed impossible ; for a 4 inch rocket was given in by our ablest pyrobolistes to be out of size , and therefore impossible to rise . now , if that 4 inch rocket was thought so , what will they say to them of 6 , 8 , 10 or 12 inches diameter ; for certainly this rule takes in all sizes to 500 or 1000 weight , or higher . necessary tables for rockets . inches and half inches . pounds of rockets . ounces ounces of compos . for rockets . pounds of the mall . ounces 1 2 3 4 5 6 1 02 0●01 12 1½ 08 0004 0002 08 2 001 02 0010 0006 0● 2½ 002 04 0018 0011 11 3 003 12 0032 0020 04 3½ 006 00 0051 0032 04 4 009 00 0076 0048 00 4½ 012 13 0108 0068 08 5 017 09 0148 0093 12 5½ 023 06 0197 0120 12 6 030 06 0256 0162 00 6½ 038 10 0326 0206 06 7 048 04 0407 0251 00 7½ 059 05 0500 0316 06 8 072 00 0607 0384 00 8½ 086 06 0728 0460 09 9 102 08 0864 0546 12 9½ 120 09 1016 0643 00 10 140 10 1285 0748 04 10½ 162 13 1372 0868 03 11 187 02 1578 0998 04 11½ 213 14 1805 ●40 10 12 423 00 2048 1296 ●0 the use of these necessary tables . in the first column you have the inches and half inches , to 12 inches . in the second and third columns you have the weight of pounds and ounces of the rockets , when six diameters in length . in the fourth column you have the ounces of composition to fill those rockets 4 diameters . in the fifth and sixth columns you have the weight of the mallets to drive those rockets in pounds and ounces . an example in the whole , for a three inch rocket . i find 3 in the first column under inches and half inches ; in the second and third column , under pounds and ounces of rockets . i find three pounds and 12 ounces the weight of the rocket when finished , being 6 diameters . in the fourth column i find 32 ounces of composition to fill 4 diameters . in the fifth and sixth columns i find 20 pounds 4 ounces for the mallet to drive that rocket . when rockets are of a great weight , the mallet will be too heavy to manage , therefore do thus . the mallet of a three inch rocket , viz. 20 pounds weight is of a good size ; and we will make an example of a 3 inch and 7½ rockets , and we will take it as useful that all rockets to 3 inches diameter , may be filled with eight charges , but further not , then against 7½ in the first column . in colum 4 i find 500 ounces of composition for that rocket , which i divide by 8 , and the quotient will be 62.5 . in the parabola a h z , let a h be the number of ounces 5062 5 in the mallet for the 7½ rocket , and a g the number of ounces 324 in the mallet for a 3 inch rocket ; then the ordinates h z and g z will be the forces of those mallets ; then as h z is to g z , so is 62.5 to 15.811 , that is 15 ounces and ●●●1000 shall be your charge of composition . further , divide 62.5 by 15.811 , the quotient will be 3.2●22 / 10000 the number of charges in the eight part of the composition ; then multiply 39529 by 8 , there will be 31. ●●31000 charges in that rocket . lastly , give about eighteen blows to every charge , with that mallet for the 3 inch rocket , so your work will be done , by two men , in two hours . 324 2.510545 62.5 squared 3.591760 5062.5 sub. 6.102305 3.704364 ½ 2.397941 15.811 is sub. 1.198970 62.5 is from 1.795880 3.9529 rest 0.596910 8. log. 0.903090 31.623 sum of 2 logarithm 1.500000 15811 add 1.198970 500. the sum of logarithm 2.698970 iune 26. 1696. then was fired a 4 and 6 inch rocket , mr. ayres junior fired them both off a hand , mr. dandridge , mr. rodway , my self , and several other being present : the 6 inch rocket had 3 inches solid head , that is about the double of what it ought to have had , the reason of that was to hold fire ; it moved off the nails at about 78 deg . of elevation , and the horizontal range was just 15 chains , that is 330 yards , by which we may find the altitude of that parabola it moved in , and the greatest range , and consequently the greatest perpendicular altitude it could have reached . in the parabola a b c , let a c be equal to 330 yards , a d equal to 165 the angle d a e 78 degrees , then in the right angled triangle e d a. radius 90 10.000000 tangent 78 10.672525 a d 165 2.217484 d e 776.22 2.889989 d b 388.11 as the sine of the double of the elevation 407 2.609594 is to radius 1000 3.000000 so is the horizontal distance at 78 deg . 330 2.518514 to the greatest range in the parabola 810.8 2.908920 half of the greatest range is the perpend ▪ hight desired 405.4 so then the greatest height of that 6 inches rocket in its flight was three hundred eighty and eight yards , had it been put perpendicular , its height would have been four hundred and five yards . the flight of rockets does sufficiently well agree with that of the parabola at each end of the quadrant ; but towards 45 degrees it differs more . a rocket of an inch and half diameter , filled 5 diameters , and bored two and a half , and a little more , with this composition , viz. 8 powder-dust , 6 salt-petre , 2½ coal , and 1 sulphur , and layed to 30 degrees of elevation ; ranged the rocket 880 yards , that is half a mile . to make rockets to swim upon the water , dive into the water , and keep above the water . an example of an inch rocket . make the case 12 diameters , which will be in this example 12 inches , fill it with two compositions , viz a weaker and a stronger ; fill 2 inches with the weaker compsition , then 1½ with the strong , then 2 with the weak , 1½ with the strong . lastly , 2 inches with the weak , then there will remain 3 inches for corn powder , for the report . the weak composition to swim above water ; take 3 of meal powder , 1 of coal . the strong composition to dive under the water , and leap above the water ; take 8 of mealed powder , 1 of saltpetre , and 1 of coal . to divide the driver . from the lower end of your driver set off 3 inches , then 2 inches , then 1 ● , then 2 inches , then 1½ ▪ lastly , 2 inches ; make the rockets of a just length , and so you may see the divisions of the driver appear above the case as you fill . the use. fire the rocket in your hand with with your port-fire , through it into a deep water , ( otherwise it will stick in the mud ) it will swim a little while ; but when the strong composition takes fire it will dive , and when the strong composition is spent it will jump up , &c. the weak composition being the last , the rocket for some time will swim upon the water , and then give a report . this rocket is all solid . to make a rocket charger . let the length of the charger e g , be one diameter and half , the breadth of the charger h z , one diameter and one third , the length of the neck of the charger that slippeth upon the handle b c , two diameters ; the breadth of that ferril a b , one third of the diameter of the rocket : betwixt eight or nine of these charges will fill a rocket 4 diameters . you may cut the charger a b c d h g z a in paper , then it may be made in copper , close a to d , and b to c , sodder both ends together ; bring h g z into more than half a round , and a b and c d in a round , put it then upon a handle , then it is fit for use . to make good coal for rockets . take pieces of a light dry deal board about 12 inches in length , and about the thickness of 2 fingers or less ; put them into an oven , put fire to the wood ; when they are burned enough take them out , and put them into an iron , brass , or eathern pot , close it well with a cover , that it takes no air , the fire being extinguished , beat it and pass it through a fine sieve , then it is fit for use . if the wood be not well burnt , put it into the oven again , and so repeat your work : such coal will make a rocket fly very lively , if not with two much life . compositions for reports .   a b c d 〈…〉 saltpetre 9. 4. 3. 2. salt of tartar 3. 3. 2. 1. sulphur 1. 2. 1. 1. take sulphur 1 , tartar 3 , and salt-petre 9 , grind these well together , and dry them . a few grains of this powder being fired , will give as great a clap as a musket when it is discharged . dr. french , pag. 171. take any of these ingredients under a b c or d , mix them well together , put a little quantity of that mixture into a fire-pan , set it upon the fire , and in a little time it will give a great report . a further use of the tables . what is done in the 14 and 15 propositions , by taking the cubes of the diameter of the bores of the rockets , may be done by the tables in 2 and 3 , or tab 4. thus , look in the first column for the diameters of the rockets , viz. 2½ and 4 , and against them , in column 2 and 3 , i find 2 pounds and 4 ounces , and 9 pounds , divide the greater number by the lesser , the quotient will be 4 , near enough , so the ratio of these two rockets are as 4 to 1 , and this is by the weight of the rockets . in the other example i find 4 and 6 in the first column , and against them 〈…〉 column 4 , i find 76 and 256 ounces of composition for these two rockets ; then divide the greater by the lesser , the quotient will be 3 and more , which is the same thing as if you made use of the cubes of their diameters ; for indeed these tables are made by the cubes of the respective diameters . a conclusion . if any one presumes to say they have resolved the 14. proposition before the publication of this , they might have been so kind as to put it into practice for the defence of the nation . if any say they can do it , i desire them so to do , that i may see my desires accomplished , viz. great guns and their carriages truly fortified and neatly made , which would be great satisfaction ; however this may shew to the next age what has been offered to this . iuly 25. 1696. finis . a treatise of artificial fire-vvorks both for vvarres and recreation with divers pleasant geometricall obseruations, fortifications, and arithmeticall examples. in fauour of mathematicall students. newly written in french, and englished by the authour tho: [sic] malthus. traité des feux artificiels pour la guerre, et pour la recreation. english malthus, francis. 1629 approx. 157 kb of xml-encoded text transcribed from 146 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2003-11 (eebo-tcp phase 1). a06780 stc 17217 estc s109781 99845426 99845426 10323 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a06780) transcribed from: (early english books online ; image set 10323) images scanned from microfilm: (early english books, 1475-1640 ; 851:11) a treatise of artificial fire-vvorks both for vvarres and recreation with divers pleasant geometricall obseruations, fortifications, and arithmeticall examples. in fauour of mathematicall students. newly written in french, and englished by the authour tho: [sic] malthus. traité des feux artificiels pour la guerre, et pour la recreation. english malthus, francis. cecil, thomas, fl. 1630, engraver. [18], 172, 171-261, [11] p. : ill. (metal cuts, woodcuts) printed [by w. jones] for richard havvkins, and are to be sold at his shop in chancerie lane neere to serieants inne, [london] : 1629. a translation of: traité des feux artificiels pour la guerre, et pour la recreation. printer's name from stc. with an additional title page, engraved, "a treatise: of artificiall fireworkes by f. malthus", signed: t. cecill sc: [?fe:]. the first leaf and the last leaf are blank. with four final contents leaves. variant: engraving on c7v also printed on c5v; mistake rectified by a cancel pasted onto c5v. reproduction of the original in the british library. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng fireworks -early works to 1800. 2003-05 tcp assigned for keying and markup 2003-06 spi global keyed and coded from proquest page images 2003-08 jonathan blaney sampled and proofread 2003-08 jonathan blaney text and markup reviewed and edited 2003-10 pfs batch review (qc) and xml conversion a treatise of artificial fire-vvorks both for vvarres and recreation : with divers pleasant geometricall obseruations , fortifications , and arithmeticall examples . in fauour of mathematicall students . newly written in french , and englished by the authour tho : malthvs . printed for richard havvkins , and are to be sold at his shop in chancerie lane neere to serieants inne . 1629. a treatise of artificiall fireworkes by f malthus london for richard hawkins in chancery lane. 1629 the preface apologetique to the reader . although that warres haue beene authorized by the diuine powers , as witnesseth the new and old testament , yet me thinkes i heare many nice , peeuish , and ignorant braines blaming me for setting downe to the view of the world ( at a few leisurely houres ) so many wayes and inuentions how to corrupt and destroy what nature and art striue to make , edifie and conserue , to whom i answer they haue the same reason to exclaim against iustice which hath found and ordained many meanes to abolish and exterminate wicked offenders : for my intention is here but onely to finde inventions to confound and ruinate rebells and their habitations ; that afterward empires , kingdomes , and common-wealths may the better liue in peace and tranquilitie : and what more is i haue set downe perspicuously this treatise of fire-workes , which many heretofore haue written with confusion and great danger , having pend large volumes with most ample and idle discourses touching this subiect , whose names for modesties sake i will not here set downe with an infamous character to posteritie ( as master robert norton hath done some few slight offenders names in the preface to his translation of vianos works , which he calleth his owne , hauing onely added seuen figures taken out of thybourels booke , and transposing the authours workes to disguise it ) that i bee not accounted amongst the calumniators of this age , who write with serpents tongues spitting their venome vpon the silent and sleepi●g innocents gone before vs. but i will onely shew their errors in generall , that the learners may the better auoyde them : for in some you shall see prescribed all sorts of apothecaries drugges for the compounding of fire-workes , which are no more capable of fire then stones , earth , or mettle , as adamant-stone , verdigrease , cristall , vitrioll , salarmoniacke , sublime , mercurie , with a number of the like , which in the iudgement of ignorants may produce in fire-workes wonderfull effects . in others you shall finde the coniunctions of combustible materials in such a sort or manner disposed and ordered to such strange ends , that you would say they were set downe to make the reader laugh , rather then for seruice of fire-workes eyther for warres or recreation , as the meanes how to poyson an armie in the wide field by the smoake of an artificiall ball , is it not to be thought a very prettie imagination , or else that the ball ought to bee somewhat bigge ; and afterward which is more ridiculous , you shall finde in the same authours the same ingredients and mixtures prescribed for fireworks for pleasure and recreation : which to mee seemes strange , that the fire-workes whose smoakes are so venemous even as to poyson armies in the open fields , shall bee also fit to burne in the middle of a cittie or towne amongst thousands of people for recreations : now all these idle conceites with a number of the like are printed in many new and recent bookes , the authours whereof doubtlesse haue set downe all these ridiculous inventions by ignorance , ( thinking them good ) and not of purpose for spight ; and therefore they doe deserue pittie rather then blame ; as well as master robert norton , ( who hath erred onely in attributing another mans workes , and faults to bee his owne ) and what is it that giues mee cause to thinke that all these haue erred by ignorance , is because that all their workes are alike where that they doe speake of fire-workes . but reading these absurdities with a great quantitie of others , which made mee take resolution to set my penne to paper , and shew to posteritie how and what way to auoyde their errours , having heere set downe the true rules and mixtures required for fire-workes , both for vvarres and recreation , with some few geometricall obseruations necessarie for the practise of fireworkes in warres ; and also i haue added vnto it certaine rules and maximes of fortifications , very requisite for enginiers to haue in their memorie , with a compendious arithmetike , hauing written the whole first in french at some broken houres whilest i followed the warres ; and bringing certaine coppies from the presse to my speciall and very good friends ; at whose requests i haue translated the same into english , that others might not translating it , mistake my meaning ; and the worke being already but of small commendations , they to make it of lesser . adiew . london the 22. of may. 1629. to the authour . thy archimedean hand hath learnt to frame celestiall meteors out of nitrous flame : and represents strange fires of differēt sorts suted to martiall vse , & courtly sports : so pleasing that great kings haue spar'd some houres to be spectators of thy golden showres . the thames and seyne haue seen thy balons fly , from their affrighted bosomes to the skye : swift beyond all beliefe ; as if thy ayme were , to restore prometheus theft againe . were , when their force seems spent , breaking asunder they rain down stars , or els outroar the thunder . the roman apotheosis i deeme , would still haue had a reuerent esteeme , if they had vs'd these miracles of fire , to mount their caesars soules , & beare thē higher then eagles flight , but now they serue to raise , the pyramis and trophe of thy praise . and sure thou hast attain'd sufficient glory , in perfecting the pyrotecnique story : which some tooke vpon trust , & by concealing their creditors ; made borowing to seem stealing . but their fire 's out , now thine hath pass'd the presse . for greater fires do extinguish lesse . william bastian studious in mathematicks . a treatise of fire-workes . for warre . chap. i. to imitate nature , our first and chiefest teacher , who far from error seemes to haue produced and brought forth all things ●y a curious and speciall order ; without whose beautifull disposi●●on on the whole world had still con●●nued in the most prodigious con●●sion of caos , which displeased the ●●●ure aspect of the highest , eternall and divine powers , being but a cloud or mixture of darknesse . my intention is here to institute and obserue an order , treating of euery thing one after another in his proper and conuenient place : beginning with artificiall fire-workes , as the chiefest and principall cause which hath vrged me to take my penne in hand , the description of those which belong to warres , shall obtaine the first place , and next the fire-workes for recreation or pleasure , passing from these to many pleasing geometricall obseruations , aswell of mecanical obseruation , as by the sines , tangents , & succents , ioyning to them a most easie & succent method to fortifie all places regularly and irregularly . and to conclude i will adde many briefe and instructiue arithmeticall examples . now to begin with the fire-workes for warres , i will first describe the morter-peece , and the vse thereof : that being an instrument , the most noble , the most vniuersal , the best of greatest effect , and of most wonderfull operation of all the instruments , the practise wherof may be vsed amongst fire-workes for warres , for this instrument may serue for a petard to split , breake and hurle down dores , gates or walles , likewise to massacre , teare in pieces , ouerthrow and confound assailants of any place or breach : and for diuers other most worthy offices , and accidentall occasions , which happen in the troubles of warres : whereof i will not here make a long , weary , and tedious discourse , but in few words cleerely set downe the vse of this instrument for the shooting of diuers sorts of granads , stones , or other weighty burthens to ruine rebels , their habitations and dwelling places . then first of all i will treat of the mettle , whereof this instrument ought to be made , and measures appertaining thereunto . chap. ii. the manner how to make the morter-peece . this instrument may bee made of diuers sorts of mettle or stuffe , according to the means , times and occasions which shall offer themselues to those who would make them , or cause them to bee made . the first and chiefest matter of all , is red copper , brasse and tinne , but very little of the two last , such as canons are made of , without any other brickle or harsh met●●● mingled with it , and beeing made of this stuffe , let the measures following be observed . if the diameter of the calliber or bore be one foot , let the morter be two foot of length , & let the sack or hole for the powder be the third part of a foot broad , and halfe a foot deep , and let the mortar beare in thicknes an inch and a halfe , about one foote high , and the rest onely one inch thicke , the foot shall bee one inch and a halfe thicke , and made square whether the instrument be for the seruice of warres , or recreation , as doth plainely demonstrate the figure a following . the second mettle is yron , such as commonly ordnance for ships are made of : and being cast of this stuffe , the rules prescribed shall be found fit , onely let the mettle be somewhat ●hicker in euery place . the third ●nd fourth , and most common materialls are past-boards and can●as , or pastboords and chord , and either or these materialls must bee ioyned together with glue , and being to bee made of either of these materialls there must be had a woden foot , with the powder sacke or hole made hollow below in the wood , as is represented by the figure b. the precedent measures being obserued which is the third part of the diametre , &c. but if the instrument be to bee made of either of the two first mettalls , that belongs to the founders office , but of the two last materials euery man at his owne pleasure may compose it of what size he please , and to begin he must haue a wodden rowler of such bignesse as he shall desire to make the diametre of his morter-peece , and vpon that rowler let the pastbords and canuas with good store of glue be rowled : which being done , let them dry a while vpon the rowler , and another while off from the ●owler , and when this kinde of truncke is very dry , let the woden foot be ioyned to the one end with glue and nailes very fast ; and then couer the whole with chord and glue againe ; which being well dryed , the instrument may bee of long service , provided that it bee not over-charged , and as for the length , the longest carry furthest , and the thickest dure longest , by the figure c. precedent the instrument is represented perfect , with the touch-hole in the right place required . chap. iii. the manner how to make granades or mettle for the morter , or hand . all granads being made to breake , ought to be composed of the most brickle mettle that may be found , as of brasse , adding the third part of tin to it . ( as the founders know right well ) they may be also made of yron , or of glasse to cast out of mens hands , so that the glasse bee made very thicke , and these will worke wondrous effects , especially in any throng of horsemen or footmen . and as for the thicknesse of those which are made of brasse , if the diameter be one foot , let the mettle be one inch thicke , and let them be somewhat longer then they are round as doth demonstrate the figure a. leauing at the one end , as it were a handle , and on the other , a screwed hole ; by which meanes the granad may be charged , also , let there be made a hollow vice fitting for the former screw , which vice shall be filled with a slow composition made with gunpowder well ●ruised and culled , and then made ●nto past with oile of petrole : but if the powder be excellent good and strong , then mingle with a pound of powder , one ounce of charcoale dust , to make it vveaker , then let ●he composition bee vvell beaten ●nto the hollovv vice , vvhich is represented by the figure b. and the granad shal be filled with fine gun-powder , which being full , let the vice be screwed into the hollow hole of the granade , onely it is to be noted that the vice must not be open at the lower end , but haue a bottom sodered strongly , wherein shall bee made three or ●●ure little holes about the bignes of a tag of a point to giue fire to ●●e powder when the granad hath f●owne the space required . for the performance wherof it is needfull that you know the quicknesse o● slownesse of the mixture wherwith the hollow screw is to be fill●d . and for the better experience , it shall bee conuenient to make of all of one with a granade made 〈◊〉 wood , cloath , pastboord , or a●y other stuffe filled with earth , ●ut let it be neere to the weight of ●●ose which you desire to make vse of , afterward , and by that meanes you may know how long ●ou ought to make your hollow vices , which are called by their ●roper tearmes port-fires , and ●hus much of your granade being performed , novv let it bee all covered over , vvith either chord , canuas , or pastboord , and dipped in glue or in pitch ; this covering may be neere halfe an inch thicke : to the end that the granade going out of the morter vvith violence it breake not , and vvorke his execution vpon your selfe or your company instead of your enemies ; of vvhat mettall soever the granad is made , these rules are to be observed , and by the figure c , is represented a granade quite finished ; and dipped into pitch , by vvhich meanes it may bee conserved many yeares : these sorts of granads vvorke great effects falling vpon houses ; they cast downe the vvalles and coverings , likewise they vvorke vvonderous operations amongst either horsemen or footmen , tearing both man and beast in pieces , sparing nothing . chap. iv. the manner how to make granads of canuas for the morter . the operation or execution of these sorts of granads made of canuas is quite contrary to those prescribed : these are onely fit to set a towne on fire , the houses whereof are most couered with reede , straw , or broome , they are not of so violent execution as the precedent , yet notwithstanding of as great cost , and for the making of them , you must haue a wooden ●owler , which is represented by the ●igure a , of the bignesse you desire ●o make the granad ( which alwaies ought to be lesse then the calliber or bore of your morter , to the end ●hey may bee covered afterward ) ●nd vpon the rowler make a sacke of ●uch cloth as you please , as doth re●resent the figure b , cutting a piece to ●ouer the vpper end , when the sacke ●hall be full of the composition fol●owing . take foure pound of salt●eter , two pound of gunpowder-●ust , two pound of brimstone , all ●hese being well pulverised , let them ●e moystened with oyle of petrole , ●nd then fill your sackes with the ●ame , and cover them with chord , which done , pierce the sacke full of holes with a great bodkin , as representeth the figure e , and in euery hole , place a little yron barrell charged like a pistoll barrell , these little barrells are represented by d , which must be driuen into the sacke vp to the head , and the granad being thus disposed , let there be made at the one end a hole about one inch deepe , which shall serue to prime it with powder-dust , moystened with oyle of petrole , onely it is to be noted that the touch-holes of the little barrells be made somewhat large , to the end ●hat the rust stop them not , being ●ong time kept amongst the salt-pe●er , and so they may be conserved many yeeres , and ready for service ●n all occasions , the figure c. doth ●emonstrate the granad perfect and ●urning . chap. v. how to make fiery arrowes . to avoyde all confusion , i will treat first of all the fires which are cast with violence , and afterward of those which may be cast out of mens hands . and first it is to be observed , that fiery arrowes are of great effects and noysome at sea , specially if the ships approach any thing neere , so that they may bee 〈◊〉 or cast into the sayles chording 〈◊〉 of the ships , either by cros-bowes , long bowes , or any other meanes , for so much as a ship being once a fire , hardly can it be extinguished . and thus the arrowes ought to be made : first a long shaft of wood , ●nd ioyned to it an yron head made after the manner of the figure a , and about the middle of that head , make fast a linnen bag in the forme of an oliue , leauing open a hole at ●he end before , as may be seene by the figure b , that it may bee filled with the composition following . ●ake one pound of saltpeter , halfe a ●ound of gunpowder-dust , and ●alfe a pound of brimstone in ●ovvder : all these ingredients ●eeing well mingled , and min●ed with oyle of petrole , then fill ●e bagge round about the arrow ●ead , noted by b , and then let all be well bound about with wyre . and ●r the priming of these arrowes , dip cotten weeke into gunpowder , wet with water , but let the cotton be wel dried again before it be applied to the arrow head . now for the ioyning of your arrow head , to the wodden shaft it ought to be so slightly fastned to it , that being shooke into any sayle , cordage , or wood , so that if any one would plucke it backe , the shaft should slip out of the head , and so continue burning in the place pretended , and to hinder that one may not pluck out the head with their hands , there may be made ● small hole quite through backeward , and so the fire will hinder a man from touching any part thereof , al●hough it should sticke in other of his fellowes clothes . there may ●e made little arrows of the same fa●hion , to be cast out of mens hands in ●ny meetings , assaults , breaches , or ●ther occasions ; and if there shall be ●reat hast for the making of them , ●esse fashion may serue , hauing onely ●●ttle stickes of wood , about a foote ●nd a halfe long , and in stead of the ●ead prescribed , a pyke ( like a ●reat nayle ) and in lieu of feathers , pieces of past-boord , stucke into the ends of the wood being slit , but the former composition shall be required . chap. vi. how the granads are to be charged into the morter . although it seeme to be but a small difficulty to charge the granads into the morter , yet it is the greatest mastery and most curious worke which hath beene found amongst fireworks , and the most industrious enginers that ever i yet saw , haue after beene deceived therein , and shor ●ut their granads , they not taking ●ire , which is absolutely one of the greatest faults that may be commit●ed . then to avoyde such great er●ors it shall be needfull to note ma●y obseruations following , whereof the first is that you put not too much powder in your morter , marmarked a , but onely the powder-●ckefull ; secondly , that the priming ●f your granad be firme , not spoy●ed with dust or dyrtie moistnes , or other like thing , that it bee not also too dry , least all breake about your selfe going out of the morter taking ●re too quicke , which all fire-works ●re very subiect to doe , then take ●eed that the granad enter not too ●ardly into the morter , which will cause it to breake in the discharging , also it is not needful that it enter too loosely . all these things being well obserued , you must haue alwaies ready port-fires for your morter , which may be made about the bignesse of your litle finger , and hollowed within about the bignes of a quill , even to the bottome , noted b , this portfire is to enter with a vice into the touch-hole of the morter , about half ●n inch , and to turne the vice without any key : there may be made 4 , buttons at the out-side of the vpper ●nd , and let this portfire be charged with a slow composition , mingling 4. ounces of charcoale with a pound of powder-dust , this being done , and your granad placed in your morter , ●o that it shake not , close vp the ●hinks round about your granade , within the morter , with grease , waxe , ●itch & grease , or any such like thing you may so cover the granad with ●ome such stuffe ; that in any weather wet or dry , you shal find no difficul●y to shoote off the granad in any place wheresoever you please . chap. vii . the manner how to shoot the granads . there is no lesse difficultie well to discharge the granads then to charge them , but the contrary will easily appeare , for it is there where the hazards and dangers most great , doe meet together . and the first of all are the aduersaries canons from whose dangers the enginier shall easily conserue himselfe , as followeth , causing to be made a trench like vnto an halfe moone , the connexity thereof being towards the enemy , as appeareth by the figure a , this trench shall be of such bignesse ●s the enginier may conueniently place all such things as shall be need●ull for his present vse . the second difficulty following , is how to shoot ●hem right to the places of any fort ●or towne desired , being not possible ●o see the places to take leuel at them without eminent danger of their canon and musket-shot : which difficultie shall be thus auoyded , and ●et leuel right , and send the granads ●o the places required : let there bee ●e two staues set vpright , betweene ●he towne , fort , or cittadell and the trench , the one of these staues shal be somewhat long , the other may be ●hort , and that , planted vpon the ●rim of the trench ; but the longest ●omewhat distant in a right line towards the place pretended , as doth demonstrate the figures bc , these staues shall be so disposed that you may see the extremities of each , being in the trench out of the enemies sight , and by the sight of these two extremities , you may direct your granads at your pleasure inclining your ●orter-piece vpon either side , as shal 〈◊〉 needfull without danger of the e●●mie , having onelie knowne the di●●●nce betwixt the trench and the ●wne , or place of the towne which ●●u shal desire to destroy . the third ●●d last difficultie is to know the true ●●ngth or distance that your morter ●oth beare , of which to be certaine , ●●u must trie it before , shooting gra●●ds of the same weight , & with one ●●rt of powder , and with a leuel , take ●●vers sorts of elevations , & so may ●ou know such an elevation doth oa●e so far , and such carie so far with ●●ch powder such a weight , being ●●arged , the maner of taking these ●●●vations is represented by the figure 〈◊〉 , & the level in a bigger volume by ●●e figure e , this leuel being placed ●pon the mouth of the morter piece , vnder the foot thereof : wedges , yo● may giue to the morter what incli●nation shall be required : and to b● sure from all harme of your own● granads , which by chance may brea● going out of the morter-piece , le● there be made in the trench a little corner hollow into , or behind the which you may alwayes retyre , ha●ving given fire to the morter . it shal be also needful that some one watch where the granad doth fall whethe● too short or too farre ; that you may the better direct the next shot : thi● method is to bee observed in shooting all sorts of granads , stones , o● other like things . chap. viii . a most violent method to set a towne on fire . hitherto there hath not been found any means or inuention more certaine or violent , whereby one might convey fire for the destruction of the e●emies habitations then by the helpe of the precedent granads , which very hardly cause any disorder or combustion , vnlesse amongst houses covered with straw , whereof few are to bee found in goodly townes . and therefore i will here prescribe a ●ew way much different from the others before written ▪ against which hardly or not at all may be made any resistance or possibilitie for defence , the violence , rage , and order being of such a fearfull power and execution , prouided that the enginier doe but meanly effect his purpose & designe , and for the practise hereof , let there be made a kind of well in the ground but sloping , as doth demonstrate the figure a , of such deepenesse as shall be thought fit , but it is to bee noted , that the neerer you are to the towne , the lesser slooping will be best , and most easie for the performance . the hollow pit or well being made , let there be placed in the bottome thereof one or two barrells of gunpowder , as shall be seen needfull , according to the proximite or ●●stance betweene the place and ●●wne , & these barrels may be places ●●●ry conueniently placed with good ●ore of straw about them to keepe ●●em from the moystures of the ●●rth . and in one , or else in both , 〈◊〉 shall place a gunlocke , making 〈◊〉 to the clicket thereof a chaine of sufficient length to reach out of the hole vpon the plaine ground , but this chaine shall be curiouslyy lodged in a small gutter , which afterward shall be covered with earth , to the end that the fire doe not ouer-heate it , then cover the barrells of powder with strong woodden planckes , or broade stones , covering them againe with earth , and then lay good store of fresh straw and bauins , and fagots , and in the midst of these let there be placed a great fagot , made of peeces of timber , of a reasonable length , be●ng well bound together with chains of yron in three or foure places , as doth appeare by the figure b , and then set fire on the straw wood , and all that shall be in the pit ▪ giving the great wood time to kindle , and this great fagot being in a great arder , let the chaines be drawn which are tyed to the latches of the gunne lockes , and doubtlesse you shall see braue sports ; and if there be many pieces of ordnance about the towne or place thus besiedged , let them be all disposed ready to shoote where this great fagot fals , and whosoeuer would hut this inuention in practise , ought to make many of these pats about a towne , giuing fire to them all at once : but the inginier to know iustly how far these great flaming fagots may flye , the hollow pit declining so many degrees , hee ought to make tryall before in some large place , where he may haue room for his experience : now resteth only to explicate how a man may giue fire to the stra● in the pit without danger , for so much that euery man would not least all should take fire together . then to be free from this perill , it may be fired by a traine of powder , by a gunlocke , a piece of match , a candles end , or other like inuention : peradventure , you may thinke that there may be danger in drawing the chaine when all is on fire ; to which i answer these may be ioyned to it , a chord of such length as shall seeme necessarie ; the enginier who shall put this in practise , may adde of his inuention what hee thinkes fit , facilius est enim addere invento quam in venire . chap. ix . how to make granads to cast with mens hands . having taught how to make granads for the morter , which by the violence of that most wonderfull instrument may be transported very farre over waters , walls , or bulwarks , working strange and rude executions or effects , i will now shew how it shall bee easie to make two or three sorts of granads to bee cast out of mens hands , the effects whereof are no lesse to bee esteemed then the other , chiefly in assaults , whether it be for the offendants or defendants . the chiefest and of greatest operation is made of any kind of brickle mettle as the precedents ▪ and their fabrication is not much different from the other , onely more rounder and lesser , and the single ones hauing a long neck to seem for the port fire , as doth appeare by the figure a , and first of all the granad is to be filled with fine gunpowder , and afterward fill the neck with a slow composition as followeth . take 1. pound of gunpowder dust , two ounces of charcoale d●ust three ounces of saltpeter , al these well mingled together , fill the portfire required , but this mixture must be well beaten into the port-fire , and the granads being thus finished , they may be kept a yeare , ten yeares , yea twenty if need be . it is to be noted that ●hese granads must not be freed vntill a man is ready to cast them away even in the same instant , because the port-fire being consumed , the granad breaks in divers pieces , and each piece sufficient to kill eyther man or beast , and therefore the handling of them is somewhat dangerous . the second manner of granad to bee cast out of the hand , is made also of brickle mettle , but hath no necke for a portfire , but is onelie round , hauing in one side a hole as appears by the figure b , and at this hole it is to be filled with drie powder , and then is to bee put into this hole to stop it , cotten wieke made as followeth . take good gunpowder and steepe it in faire water , and being dissolved , take the cotten wieke and steep it in the gunpowder dissolued , which done , hang it out to drie ; but let it be doubled eight or ten times , to the end that it may the better receiue the powder , and being drie , cut it in such pieces as you shal need , putting the one end into the granad at the hole , and then put that granad into another pot a little bigger then the granad , as appeareth by the figure c , so that you may put a little drie powder round about the lesser granad betweene the pots and granad , then cover the mouth of the last earthen pot either with leather or such like stuffe ; and bind it round about with wyre , but first put the wire through pieces of match about halfe a foot of length as may appear by d , and when you desire to make vse of this sort of granad , set on fire euery end of these pieces of match , and cast the pot away , which falling either vpon the ground , or anie souldiers armour , you shall see the earth-pot breake , the granad split , and worke such furious effects , eyther at a breach or anie approch . the third sort of granad is made much like to either of those precedent , except onely it may bee made double or single , of glasse or of earth onely shall be needfull to be made very thicke , and if it be to be made single , the portfire ought to be either of wood or of pastboord , and well glued in , and this last sort may work great effects . now having somwhat largely treated of the morter , granads , and of their vse , i will speake a little of other oyly fireworkes very pernicious and noysome to all assailants . chap. x. how to make fiery wheeles to be cast with mens hands . for as much as euery souldier wil not meddle with making nor casting out of his hands granads , the handling of them being somewhat dangerous , i will here teach another manner of fireworkes , which is not much lesse offensiue , which being well compounded and compacted , and for the making thereof , these are more ingredients required , then for the precedents , and is more difficultie in making of them as followeth , take foure pound of gunpowder in dust , one pound of charcoale dust , two pound of tarre , two pound of salt-peter , and one pound of rosin . all these ingredients being well mingled and heat ouer the fire , steepe tow or flaxe in the same , ●n● then wrap the tow or flax about ●● whope , which is represented by a , and then cover all this againe with gunpowder dust , & in time of need giue fire to them , and cast hem amongst your enemies ; onelie is to be obserued that the whops or circles ought not to be to large , but falling vpon a many of souldiers they may there stay and sticke , and to make them more troublesome and intangling , two may be tied a crosse on another , and then falling vpon anie man , he cannot choose but be much astonished with such a fearefull eleme●t , and put his company in great disorder . chap. xi . how to make a shippe of wilde fire . after a sufficient discourse of all manner of granads , fierie arrowes and burning wheeles , i cannot thinke it extravagant or amisse to lay open to the industrious or curious , a method how to make a fiery ship at sea , which shall not begin to burne till it hit against some other vessell , rocke , or such like obstacle , or be hooked or grapled on the inside to be drawne a shore . hee that will vndertake to build one of these must spare no reasonable cost to put his intentions or designes in execution , and first of all must be had one ship or many , according to the times and occasions wherein they shall be required ; and within the shippe shall bee disposed great store of broken canons well charged with bullets , and from one canon to another shall be ioyned a port-fire , so that the first , having taken fire , all the rest must neede doe the same ; these canons shall haue their mouthes put out of the gun-ports ready to bee discharged ; this done , let there bee good store of dry straw , small dry wood , and tow and flaxe steeped in pitch , turpentine , rosine , and tarre ; mingle and wrap the tow thus steeped , about and amongst the wood and straw , and place it betweene all the canons ; the straw and small wood shall be so disposed , that it may take fire when the best part of the canons are discharged , and the peece of canon which is to giue fire to the straw , shall be set with the mouth vpward to blow part of the decke away , and at the same time giue fire to great store of granads of all sorts , to adde musket-barrells to barrells of gunpowder ranged in order aboue the deck , to blow out these things by order , now one , then another by the helpe of slow portfires , but the beginning of this sport ought to be very violent and furious , to frighten and also teare in pieces the enemies at once , & that the rage hereof be the more furious , let the greatest part of the canons ●●oot off thick one after another e●●n with the water , and at the same 〈◊〉 the granads shall flye the one ●●re off , the others fall neere , now a ●●rrell of gunpowder blowes out a ●●rt of the flaming ship here , and a●n another barrell caste out a quar●●● of the vessell ardent there , casting ●●uers sorts of fire here and there as ●ls , arrowes , granads , double and ●●gle ones , made of the compositi●● prescribed in the 5. and 10. chap●●●s , but to hinder all the barrells of ●●wder from taking fire together , ●hich is no small difficultie , euery ●●rrell ought to be plastered over , ●●d then covered with glue and a ●●re-cloth , and then put into another ●●rell ; but to make them take fire e●●●y one at your pleasure , put a port●● vnto thē , of such length , & slow composition , as you shall thinke fit●ting . now to begin this mad spor● fasten three or foure good strong gunlockes within the ship , at one en● of the traine , which is to giue fire to the first canon , and to every clicke or tackit of the locks , fasten an yro● rod , and let the other end of the 〈◊〉 rod passe through the ship , and ●ee made fast to peeces of strong wood , in the manner of a gyrdle on ●he outside of the ship , which is re●resented in the figure by the points ; ●o that touched vpon the outside a●y thing rudely , the locks must needs ●trike fire , and set going all the rest ; ●nd to make it give fire being hooked in the inside , to draw it ashore , 〈◊〉 out of the way , let there be made ●ast to each clicket of the locks , long wyers , and the other ends of the wyres may be fastned to pieces of wood in the inside of the ship , round about the edge , so that the first thing that shall touch it , sets all going as vpon the outside , but the pieces of wood vpon the outside ought to be very neere the water , as doth demonstrate the figure with the points , and so to conduct this ship as neere to t●● place as may bee , without dang●● there may be fast ioind to the stern piece of timber noted a , b , to the en● whereof may bee fastned two lon● ropes , and to them two little boats , i● which men shall be for the condu●cting therof . this here is but a spar● of inuention , to which the industri●ous enginier shall adde of his wha● he please , and take this but for an entry of such workes ; for although haue here set downe gunlockes ▪ t● giue fire to the canons , my meaning is that they bee made like gunlocks but ten times stronger , and harder i● going off , leauing to the iudgemen● of the discreet enginier , the true disposition of his owne designes . chap. xii . how to make a petard . diego vsan , a spaniard , francis tibourele a loreine , and master robert norton an english man , hauing al written of fireworks , and neither of them all vnderstanding how to charge a simple petard , i thought fit to end these fireworkes for wars by the description of the same , that being of great violence to make entries & breaches into towns castles , or houses , the morter prescribed , may serue to petard a place as hath beene sayd already : but whosoeuer would make exactly a petard , ought to cast a morter much like vnto an apothecaries morter , as doth represent the figure a , observing the rules following , if you make it , to weigh sixe pound of mettle , let the calliber or bore be of such bignesse to containe one pound of powder ▪ or one pound and a halfe : if you adde or diminish more or lesse mettle , augment or diminish the calliber likewise , to hold the fourth part of powder which the mettle doth weigh ; and for the charging of the petard , fill it only with the best gunpowder you can , almost to the brim ; and then couer it with a round bord made fit for the purpose , leauing aside all frivolous directions , written by others aforenamed ; and for the ●riming of the petard , make a port-fire of slow composition , as for the precedent fireworkes of what length you please ; and to breake open the place you desire if it bee accessible , then with the heele or breach of the petard vpon the ground or some great stone or piece of wood , and the mouth against the part of the dore , gate , or elsewhere , which you shall iudge fittest , but if the place bee vnaccessible , then make a kinde of a little cart with two or foure wheeles , as doth appeare by the figure b with a long forke very strong to beare the petard , and also support the requile of the petard shooting off : this forke is represented by c , but the backer end of this forke must bee stayed either in some hole , or against a stake , or other meanes ; now here in this treatie not intending to imitate these late authours , who writing of artifi●iall fire-workes ; have prescrbed natures and compositions of almost all manner of drugges , the meanes whereof may bee found in anie apothecaryes shopppe , doubtlesse eyther to perswade the curious readers that they had profound knowledge , many rare secrets , or else the better to hide their ignorance , by that great confusion and expence , whereunto few or none would extend and vse their purses to make proofe and experience of . i will finish this treatie of artificiall fire-workes for warres , and goe forward to the second treatie of fire-workes for pleasure and recreation , and explaine in the preface apologitike , for what vse all these vnknowne dregges are fit for , which seemes to those that are ignorant of such rare and wonderfull effects . as salarmoniake , antemonie , arseneeke , vitrioll , stonelime , thutie , adamant stone , not forgetting quick siluer . the second treatise of artificiall fire-workes for pleasure . chap. i. perspicuous & plain shall be the method to make all manner of fire-workes for pleasure , ( which heare i will set downe for the contentment of all curious and ingenious artists ) without such a number of vnknowne dregges for mixtures , as many heretofore haue prescribed more fittest for some prodigious actions , then to mingle for artificiall fireworkes ; and principally for those which are invented for pleasure , for these haue no need of venemous smoaks to poison the spectatours , making mirth turne to mischiefe ( which notwithstanding cannot be done in an open ayre ) neither haue they need of such a continuing , ardent and violent flame , as to consume cities or habitations , but onely of a gentle and pleasing flame to the eyes of the spectactors ; and thus they are divided into three sorts ; the first are those which ascend and mount into the ayre ; the second are such as consume vpon the earth ; the third and last sort , are those which swim and burne in the water . those which worke their effects in the ayre , are ●●kewise divided into three sorts , the ●hiefest and most noble of all are the ●allouns ; the second the rockets ; ●nd the third are flying saucissouns , ●hose which stand fixt vpon the ●round are also distinguished into ●hree sorts ; the first are the rockets ●or the ground , the second the fierie ●nces and the third saucissouns : the ●res for the water , may haue their ●iple diuision ; globes or balls make ●he first , double rocket ; the second , ●nd single ones the last ; and to treate ●f euery one in particular , i wil begin ●ith the rockets for the ayre ; and ●●rst of all describe their moulds , and ●he measures which must be obser●ed in making of them . chap. ii. a method to make moulds for rocket for the ayre . although that ballou● are absolutely th● most noble sort of fir● workes , yet for so muc● as all great fireworkes are compose● rather of rockets , then of balloun● i thinke it conuenient , to begin th●● second treatise with these : first of a●● making the description of the moulds , which may bee made eith●● of brasse or wood , the one being 〈◊〉 good as the other for vse , if the mea●sures following be obserued ; whic● ●●all be conuenient for all sorts of ●●gnesses , because they depend one●● vpon the calliber or bore , and that ●eing enlarged , the other parts will ●e all enlarged also , that being dimi●●shed , all the rest will be diminished ●●kewise . then to make a mould , the ●●lliber wherof shall be suppored an ●●ch of diamer , and is represented 〈◊〉 the figure a , then the mould ●ight to be sixe inches in length ; 〈◊〉 the breech which is represented ●y the figure c , must enter into the ●ould one inch and a halfe , and the ●och noted with o , should be three ●●ches and a halfe long , and a quar●●r of an inch in bignesse , and the ●●wler d , which is to rowle the ●artoush or coffins of paper vpon , ●●all be three quarters of an inch in ●●gnesse , & the rammer e , to charge and ram the rocket , shall be some what lesse then the rowler , to the en● that it may enter easily into the ca●●toush or coffins . also it shall be made hollow , 〈◊〉 deepe as the broch is long , as dot● appeare at p , because the rocket mu●● be loaded , the broch being in it , 〈◊〉 ●●r the massif marked with f , shal be 〈◊〉 the same bignesse as the charger . ●he 2. other ●owlers noted g , g , or 〈◊〉 make serpents , as shall be instru●●ed hereafter , and the bodkin h , is 〈◊〉 make holes through your starres , 〈◊〉 shall follow , the lanterne i , is pro●er to charge the composition into 〈◊〉 rockets . the figure noted k , is 〈◊〉 cartoush or coffin ready to bee ●harged , and by the figure l , is re●resented a rocket quite made . this ●ethod prescribed may be obserued 〈◊〉 all sorts of moulds , for if you ●ould make one lesser , as of halfe an ●●ch , the calliber or bore , then the ●●ngth must be 3. inches , which is 6. ●alfe inches , the breech shall enter 3. ●uarters of an inch , the broch shall be 〈◊〉 inch 3. quarters long , & the rowler ●●r the cartoush shall be half a quarter of an inch ; but if you make the calliber of two inches of diameter , 〈◊〉 the mould be 12. inches in length the breech shall be 3 inches , and th● broch 7. inches of length ; and so fo● all the other parts appertaining to th● mould . now followes the descript●●on and manner how to make a ro●●ket . chap. iii. how to make a flying rocket for the ayre . for to make the mixture or composition of all middle-sized rockets , take a pound of gunpowder finely ●uised and boulted with two oun●●s of charcoale-dust , mingle these ●ell together , and try one rocket , ●hich if it breake , adde more char●●ale dust to the composition ; but the rocket doe not ascend , beeing ●●eak , adde more powder dust boul●●d as before said ; and so shall you make your composition stronger 〈◊〉 weaker according to your desire ; ●●stead of charcoale , you may put se●●coal● , saw-dust , or any other lik● thing , so that you keepe a medium not putting too much nor too little which thus you shall know if th● rocket mount not , you haue adde● too much coledust ; but if it break● you haue not put coledust enough for the charcole-dust which you p●● into the powder dust , is onely to m●derate the violence of the powder and to make the rockets tayle appe●● more beautifull ; which sea-coa●● doth as well as charchoale , and 〈◊〉 charge the rocket with this comp●sition as it ought to be many rul● are required or to be obserued ; and 〈◊〉 of al that in charging the rocket , yo● put not too much cōposition at on●● in the cartoush or coffin ; 2. , that 〈◊〉 ●e beaten with a mallet 3. or 4. good ●●rokes ; and then put new composi●●on thereupon , beating it again with ●●lowes as before ; and thus putting 〈◊〉 at seuerall times the quantity of ●ne or two spoonefulls , at each time ●eating it well with a mallet , and let ●ot the cartoush bee filled higher ●hen the mould , but being iust full ●hereto , then double downe halfe of ●he paper with the bodkin beating it ●as ●he composition before ) & at last ●ierce 2. or 3. holes with the same ●odkin to the powder to giue fire , to ●ither stars , serpents , or faucessous , as ●hall be taught following ; and these ●oles are represēted by c , let the rest of the cartoush be cut even with the mould , and thus must be made all ●orts of rockets , great or little ones . ●t is to be noted , that the composition prescribed is fit ; for all sorts of rockets , great or little , but onely it must be made weaker for great one● then for little ones , adding more charcoale to it , for the whole secret is in making the composition neither to strong , nor to weake , and not as al writers hitherto haue thought , following each one the others errors , thinking that the true manner of making excellent rockets , is to put many ingredients into their compositions , wherein they haue all erred absurdly ; and last of all master norton , for absolutely the best composition is , that which is made of fewest ingredients ; and the rockets made thereof may be kept many yeares , and good at all times . chap. iv. how to make moulds for rockets for the ground . the mould must bee otherwise made then the precedent , because such violence is not required in these , as in those which moūt into the ayre , but onely of somewhat longer continuance ; and therefore these measures following shall serve at all times , neuer being made bigger nor lesser , but alwaies the same for all occasions . let the calliber behalf an inch , the diameter ; and 5. or 6. inches of length ; and the rowler for the cartoush shall be foure lines in diameter which is the third part of an inch , and the rowler to charge withall somewhat lesser to enter without spoyling the cartoush : next let not the broch be longer then 3. quarters of an inch ; and the breech shall enter halfe an inch into the mould ; and the cause of this great alteration is , that the rockets which mount into the aire , haue need of great and violent strength ; and by consequence last not long , but wee desire that those vpon the ground may dure a long while , with a gentle motion , which shall be easily performed , the rules following being obserued . chap. v. how to make the composition for rockets vpon the ground . this is the easiest composition of all others , for in this shall be nothing required , but onely gunpowder well beaten and boulted , so that it be as fine as flower , and then fill your rockets by little and little , well beating it into the cartoushes or coffins with a mallet , as the rockets for the ayre , and being full within an inch of the brim of the mould , double downe one quarter of the paper , or cartoush , beating or pressing it with 3. or 4. good strokes of the mallet , and then with your bodkin , pierce a hole to the composition ; which done ; put into the cartoush about the charge of a pistol , of good gunpowder , and then double down the one halfe of the cartoush , giuing a gentle blow or two with the mallet , & with a smal cord , or big line , choke the rest , and what shall rest aboue the choaking , cut it off , leauing a piked point , as appeareth by the figure e , in the 3. chapter of this treatise ; and your rocket being thus finished , and primed with a little wet powder , and layd a drying , shall be ready for all occasions . chap. vi. the manner how to make serpents . the serpents are to bee made eyther of the composition for rockets on the ground , or of that for the ayre ; for being filled with the composition fitting for the grouund ; they will spreade and sparkle liuely in the ayre , but if filled with the other composition , they will fall weaving neerer together ; notwithstanding eyther sort will shew divers pleasing actions in the ayre , being made as followeth . let the cartoush be about foure inches long and rowled vpon a rowler , somewhat bigger then a goose quill , as is represented by the precedent figure g , in the third chapter , the paper ought to goe about the rowler nine or ten times , and then choaked almost in the middle , yet leaving a little hole to see through , and the longest part shall be filled with the composition , but the shorter with fine grayned powder , and choaked close ; also the longest end must bee halfe choaked close ; as doth appeare by the figure f , chapter third but if you desire not to haue them wamble in the ayre , then let them not bee choaked after the composition , but as doth represent the figure g , both which figures , f , g , represent serpents quite finished . chap. vii . how to make golden rayne . many there are ( specially in france ) who make rockets , yea and boast that they are perfect therein , who know not what golden raine is , but thinke it to be some other thing then it is ; wherefore to put them out of doubt , and to teach all others who desire the knowledge thereof , i will here set downe the description and maner how to make it . take goose quils , and cut off the hollow ends , leaving them as long as may be , as the figure k , doth demonstrate third chap. and fill these quils with the composition of rockets for the ayre , at the last stopping euery one with a little wet powder to keepe in the dry powder , & crowning a rocket with these ( as shall be taught following , chap. 12. in its true place ) will shew a most glorious & pleasing raine , which some hauing in times past seen , haue called it golden rayne for the beauty thereof , but of later times it is more commonly called golden hear : many beautifull and strange figures may be represented in the ayre , with this maner of rayne , as shall follow in the 13 chap. treating how to represent many sorts of figures in the ayre with rockets . chap. viii . the manner how to make starres . although that there bee many sorts of compositions for stars , yet i will set downe here but two of the best ; all the rest being nothing worth , but friuolous and expensiue : the fi●st and best sort , is to be made of dry powder , and the other of moystened powder as followeth . for the ●●sort take 1. pound of saltpeter , halfe a pound of brimston , and a quarter of a pound of gunpowder dust , al these being plu●ri●ed & mingled together , wrap the quantity of a nutmeg in tow in a linnen rag , or in paper , and bind it fast , as appeareth by the precedent figure h , chap 3 ▪ and to prime them , you must pierce them with the bodkin , and put stoupell or cotten wieke dipt in powder through them ( which shall be made as followeth in the 11. chap. ) and to make the second sort , take 1. pound of salt-peter , and halfe a pound of powder-dust , and halfe a pound of brimstone all these wel pulverised and mingled together , moysten them with eyther oyle of petrole , or els wi●h fair water onely , to make a past of them , wherof make little balls about the bignes of a musket bullet , and whilest they are moist , rowle them in dry powder dust , then let them dry , and then may you employ them at your pleasure , without further trouble ; for the last powder in which they are rouled , doth serue for their priming . this last sort of starres doth not make so beautifull a shew in the ayre as the others , for falling downe , the flame of them takes the forme of a lampe , hauing no force to expel it like wings as the others doe , for the flame of the others blowing out of the two sides pierced , make it stretch in length , and by that meanes shew greater in the ayre . chap. ix . how to make starres giuing great reports . to make starres , that each one shall giue a report like a pistoll or bigger gunne , you must first make little saucissons ( as i taught in the chapter following , but the saucisson need not to bee couered with chord ) and being made and pierced , take as much of the former dry composition , and bind it to the end of the saucisson which is pierced , making a hole through the composition , and passe a piece of stoupell or cotten-wieke as in the other starres ; but if you take of the moyst composition , you may onely leaue the paper hollow at the end of the saucisson , fitting to contain the quantity of composition required , putting a little grained powder before , and prime these starres as the others , of the same composition ; these starres are very troublesome and little in vse , because that a great rocket can carry but few vp into the ayre , and by consequence worke but a small effect , and moreouer they are very long in making . one may make starres in the same manner , which ending , turne to serpents and others as shall please the workeman . chap. x. the manner how to make saucissons . in this chapter , my intention is not to treate of the saucisson which flyes into the ayre , but only of that which stands firme in great workes , or else which is applyed to rockets , which thus is made as followeth ; you must haue a rowler of such bignes as you desire to haue the concauity of your saucisson , wherupon rowle as much paper as you please , and then choake it at the one end ; which done , fill it with grayned powder , & choake the ●ther end also , and cover all the sau●isson from the one end to the other , with small chord , as doth represent ●he figure i. chap. 3. and glue that ●ord with strong glue all ouer , and when you would make vse of these ●aucissons , pierce them at the end with your bodkin , and put into the ●ole a quill filled with fine powder dust , which shall serue for a portfire , and the other end of the quill shall passe through a board , whereupon you meane to fasten them , and shall enter into a portfire in the other side of the wood , which shall be fastned all along the wood , and so may you fasten what store you please neere together , or farre asunder , this quill is represented by the figure l , and by this meanes one end of the 〈◊〉 fire beginning ; all the whole ran● of saucissons will giue their repor● one after the other . but if your sa●●cisson is to be applied to a rocket , shall onely be pierced at one end , a●● primed with a little grained powde● and fasten it to the top of the rock● either with paper , parchment , or an● thing else , so that the rocket , endi● the saucissō , may take fire ; so shal yo● not faile of your intent or designe . chap. 11. how to make stoupel or preparing of your cotten wieke . to make stoupell , not the meanest , but the best that may be made to giue fire ( which in ●per tearme is called estoupel●●g ) to all manner of fire-workes . 〈◊〉 cotten-wieke , and double it ●oft as shall bee needfull for your 〈◊〉 , as if it were to estoupel your fie●ances ; then double it eight or ten ●●es , and also for the stoupeling of great rockets ; but if it bee to 〈◊〉 through your starres , then 4. 〈◊〉 threds shall suffice ; so hauing do● led your cotten wieke fitting for yo● purpose , steepe it in faire water , 〈◊〉 then wring it betweene your han● and take gunpowder dust , witho●● other mixture , and steepe it in 〈◊〉 water , not putting too much wat●● nor too little , but onely till it app● like durt , and then put into it 〈◊〉 cotten wieke , and there turning a● winding it till it hath sufficiently 〈◊〉 powder in euery place and 〈◊〉 cell , then draw it out , putting a 〈◊〉 dry dust vpon it , & hang it a dry● in the sunne or els-where , and 〈◊〉 being dry , you shall haue the 〈◊〉 excellent stoppel that may bee ma● for your vse at al times , leaving 〈◊〉 all such ingredients which ignora●● ●●●●eme so highly of , as aqua-vitae , 〈◊〉 wine , strong lee , quick-lime , ●ger , vrine , and diuers others , for ●ich i would not lose so much 〈◊〉 time as to repeat them , but 〈◊〉 goe forward , and shew how to 〈◊〉 all the parts of a rocket . chap. xii . the manner how to assemble and set together the parts of a rocket . when the rocket is finished and taken out of th● mould noted a , in the figure of the 3 chapter , an● the rocket is noted with the letter ● in the same figure , then must yo● ioyne to the end of the rocket , which is not choaked an empty cartoush 〈◊〉 coffin , much bigger then the rocke● is large , which is represented by 〈◊〉 in the same figure , in this cartous● you shall put your serpents , golde● rayne , starres , saucissons , or othe● things at your pleasure , but first of 〈◊〉 you must put in the bottome powder dust ; onelie enough to couer the bottome of the large cartoush ; and then put the serpents with the ends downeward which are to take fire ; and likewise the golden rayne in the same manner , but it is the custome to put a little powder dust amongst the stars ; this cartoush being thus filled , couer it with a single piece of paper , and afterward paste vpon that a picked cap made also of single paper , and to make perfect your rocket you must binde a rod of such length and waight , that being bound to the rocket , it must weigh down the rocket on your finger being neere to the rocket , and then stoupel your rocket , ●hat is to say , prime it with cotton-wieke , and it is thus finished either ●o fire or keepe . this method is fit for all sorts of rockets , great ones or little ones , except that little ones must haue the vpper cartoush no bigger then the rocket , onely to hold halfe a dozen of starres or serpents , or one saucisson for so much as many beeing fired together , great confusion would happen , if great rockets should bee put together , and not prepared otherwise . chap. xiii . how to represent diuers sorts of figures in the ayre with rockets . the first and most rarest is a tree or fountaine , and is made putting many little rockets vpon one great rocket , passing all the rodes of the little ones through the large cartoush of the great rocket , and if the little rockets take fire while the great one is mounting vp , they will represent a tree : but if they take fire when the great rocket is turning downe againe towards the ground , then they will bee like to a fountaine of fire , and if there bee two or three little rockets hauing no rods amongst others they will make divers motions contrarie to the rest most pleasing . the second figure is the golden rayne ; and that is made when manie quils filled ( as aforesaid ) are put vpon a great rocket : for certainelie all those quills taking fire will seeme like a great shower of fierie rayne to those who are vnder it , but to those who are a side of , like beautifull long haire . the third figure are starres , which are represented putting onelie manie starres vpon a great rocket . the fourth are serpents which are alreadie described , but to make all these prescribed figures varie , you may tye manie little ones together by the ends , which take not fire , the quils , or serpents may bee tyed in like manner ; but the thread wherewithall they are tyed , must be at least two or three inches long , betwixt each one , and you shall see diuers sorts of figures in the ayre , changing themselues into much varietie . chap. xiv . how to make fierie boxes . the fire-boxes are made of many rockets being put into a large cartoush the bottome whereof is couered with powder dust , and pierced in the middle to passe through a port fire or stoupell , to giue fire to the rockets within the cartoush or coffin , which flying out , leaue the cartoush most commonly whole and vncracked , those boxes are onely to be cou●red with a peece of paper , that the rockets taking fire may flie out without resistance ; and the reason why they are to bee couered , is because if manie be made one neere to another , they should not take fire all at once . chap. xv. how to make fierie lances . the vse of these lances is alwaies required in all great fireworkes , wherefore here shall be described the manner of their making . their cartoushes are to be made as other cartoushes for rockets ; onely these may be made of pastbord , and glued as they are a rowling , if it bee to make great ones , but if for little ones , then paper shall suffice , the cartoushes being made , let them be filled with the dry composition prescribed for starres in the 8. chapter of this treatise , and prime them with wet gun powder , & the lower end of the cartoush is commonly stopped with a peece of wood , to the end that they may bee nayled or stucke when they shall bee needfull , the wood being about two inches long out of the cartoush . chap. xvi . the manner how to make rockets for the water . take fire & water being two elements of contrary qualities , the one to the other cause the rockets which worke their effects in or vpon the water to appeare to the spectators more beautifull , and seem more rare and admirable , although that all sorts of rockets being fired , will worke their effects vpon or vnder the water , but this onelie is to be noted , that those which are made for the ayre , or for the ground , haue such strength and force , that beeing once kindled and cast into the water , they will consume themselues there , and not rise vp swimming as those which are made artificially for the water as followeth . to make good rockets for the water , the calliber of the mould ought to bee one inch of diameter , and in length eight inches , the breech to enter one inch , hauing no broach ; the rowler for the cartoush shall be three quarters of an inch of diameter , and the charger shal be somewhat lesser then the cartoush being ready to bee filled as the others . of two sorts of composition , you shall make one as followeth ( if you desire to make a great fierie tayle appeare vpon the water , then take one pound of salt-peter , halfe a pound of powder-dust , halfe a pound of brimstone-dust , and two ounces of charcoale-dust : but if you desire to haue it to burne cleere like a candle vpon the water , then take one pound of salt-peter , halfe a pound of brimstone-dust , and three ounces of powder-dust , all these must be well mingled together , as all other compositions ) and with either of these compositions , fill your cartoush , and ioyne to the vpper end a saucisson , and then couer it all with melted pitch , rosine , grease , or painting , to hinder the water from spoiling the paper : and to make it float and swim vpon the water , bind a rode about two foot long to it as to the others for the ayre . now if that you desire that this rocket charge his actions vpon the water , swimming now vpon the water , and now vnder the water , put here and there powder dust , powre to the quantity of halfe a spoonefull as you charge it ; also may you make it change colour , now red and then white fire , onely changing the composition in filling it , and so the industrious may adde many changes and diuersities as they shall thinke fit : but if you are to make a great number for a great fireworke , then the plainest are the best , onely filling therewith the first composition ; but they must be filled two or three fingers breadth with fine powder dust , to make them flye farre off , or else they must be made like rockets for the aire , and afterward charge them foure inches with composition made for water ; but to be the more certaine , it is best for those who haue great works , to make to trie one or two before they finish many , that the better they may attaine their designes , which with eie they may accomplish , if the rules prescribed be obserued ; for as i think there is not one rule neglected appertaining to the fabrication of these fireworkes prescribed ; and now i will set downe the manner how to make all sorts of ballouns and flying saucissons , which are absolutelie the beautifullest parts of fire-works for pleasure , and after them i will describe a braue fireworke for pleasure with the manner how to place , dispose and range euerie peece and part thereof , to make their play in order . chap. xvii . how to make girondells or fierie wheeles . a girondell ( or as some call it a fierie wheele ) is often required in great or little fireworks for pleasure , and therefore i haue thought fit and necessary to set downe their description , as well as of al other parts of fire-workes : for according to the application of the girondels in a fireworke , one may iudge of the enginiers industrie , for being well applied , they adorne very much a fireworke , and being ill applied they spoyle all . and to make them , you must make wheels of wood as bigge as you pretend to make girondells , and vnto those wheeles bind fast rockets of a meane bignesse , binding the mouth of one towards the tayle of the other , and so continuing vntill you haue filled your wheele quite round , which done , couer them with paper pasted very curiously about them , that the one taking fire , they take not fire altogether , but the mouth of one shall be left vncouered and ready primed , fit to take fire , the which ending shal giue fire backward to the next , and so one to the other , euery one his turne : there may bee bound fierie lances to these girondells either vpright , or neere overthwart , which will shew diuersitie of fire the wheele turning : also there may bee added to these wheeles boxes of fire , prouided that they be artificially applyed in such manner , that they ballance the wheele equally , although the proper vse of girondeles , is onely to garnish the angles of a great fire-worke , without much trouble , for that confusiō is too frequent in fire-workes ; and therfore it shall be expedient to auoide the multitude of fire-workes too neere compacted together ; but placing them as much distant as conueniently may be admitted , by which meanes you shall bee the better able to attaine your designes pretended . chap. xviii . the manner how to make ballouns . the ballouns being the perfectest part of all artificiall fire-workes for delight , i thought best to set their description heere apart from the others , to the end that the learners might the better and more easier attaine to the knowledge and perfection thereof ; and being that i haue already described the morter , which is represented by the figure a , following , i will onely referre the reader to the second chapter of the first treatise for warres , where hee he shall find sufficient instruction for the making of the instrument . but to make a balloune shall be required a woodden rowler , which is represented by the figure b following ▪ this rowler must be of such bignesse as you desire to make the inside of your balloune ; vpon which rowler , let there bee rowled as many pastbords as you shall think sufficient for strength being well glued together and choake this cartoush at the on● end , leauing a little hole for a portfire as shall follow , and glue it in . this portfire shall be made iust like vnto ● rocket for the ground , but only tha● the composition may be somewha● slower ; as for the ayre , and to know of what length this portfire ough● to be , it shall not bee amisse t● try a balloune filled with earth ; then your portfire being well fastned to the balloune ; place all your serpents within it , putting nothing else amongst them , but onely one or two saucissons , to breake the balloune on high , when the serpents be all on fire , these saucissons must be made of the length of your serpents , and your serpents may be of the bignes of your rockets for the ground before prescribed , but not so long , and they may bee filled with the composition either for the ground , or for the ayre : but it is to bee noted , that they must bee primed with the composition for the ayre , pressing verie stronglie the priming powder into the throat or gorge of the serpents , if it bee put in drie : but if that we●te , then onely with the end of a sticke , or else with ones finger put in a little ; as for other serpents and the two saucissons shall haue their primings somewhat longer then the serpents , to the end that all the serpents may be a fire before that the balloune breake . the serpents being not made too long , one may put two or three rankes in one balloune , as appears by the figure c , or one ranke of serpents , and over them many starres ; all these things being thus disposed within the cartoush , let it be choaked at the other end ; and then prime the ballouns with cotten wieke steeped in gunpowder as the stoupel before spoken of ; but this cotten must be well fastned to the end of the port-fire with strong packe-thread , which done , charge the balloune in your morter , as is taught in the 6. chap. of the first treatise ; and you may shoot it when you please . this balloun is represented perfect by the figure d , but if you will fill your ballouns with stars only , another manner of proceeding shall be required ; for as you put in your starres into the cartoush ; let there bee powder-dust mingled amongst them here and there to giue fire to the starres , and to breake the balloune being vp in the aire . there is also another sort of ballouns to be made , but the expence of making thē is so excessiue , that few or none will be at the cost , yet the description shall now follow . in stead of serpents made of paper , you may haue them iron about the bignes of your little finger , and one inch and a halfe of length , or two inches ; and neer to the bottome there must be a double bottome in the middle whereof there shall be a little hole , that one may fill the space between the two bottoms with corned powder , and the rest is to be filled with a composition somewhat slow , the diff●rence betweene those of iron , and the former of paper , is that many iron ones may bee laid in a lesser space ; but in stead of a pastbord cartoush , there must bee had a woodden box , made by a turner , and couered with canuas and glue ; the portfire must be made also of iron , like to a little hat , hauing in the bottom two or three little holes to giue fire to the serpents ; but for the expence of one of these , there may be made halfe a dozen of the others , nay neere a dozen , wherfore i would wish no man to trouble themselues with this sort , vnlesse it be for the pleasure of some great prince . chap. xix . how to make flying saucissons . the method which must be obserued in making flying saucissons , is most easie , prouided that one knoweth already the manner how to make the common sort before prescribed , for the cartoushes are to bee made all alike ; onely excepted that those which are for flyers , be somewhat longer then the others , they are to be charged in like maner as the others , but the corned powder being put in , there must also be a litle powder-dust put after it , and beaten with a mallet , as the rockets for the ground yet let not more then the thicknesse of a finger be of dust-powder , and then choake it almost quite together leauing onely a hole as big as a small goose-quill , to which you shall put a little wet powder-dust for priming . they may be made otherwise , as followeth , which will make a more beautifull shew ; first of all , you must charge the cartoushesas the common saucissons , and then choake them as the common leauing onely a little hole to take fire at , or if the hole chance to stop quite vp , open it with a bodkin , but the saucissons being charged and choaked , there must be part of the cartoush left ouer and aboue that which is charged , which part shal be filled either with powder dust , or els with composition of rockets for the aire beaten wit a mallet , as before mentioned , i thinke it shall be needles to tell you that they ought to be couered with chord , being that it is sufficiently demonstrated before , it is to be noted that the saucissons which haue the powder within the choaking , doth turne wonderfully in the aire , but the other sort which haue the composition after the choaking , flye vp like to a rocket , almost carrying a great tayle after them but the tayle of the others sheweth but very little , they are both sorts represented by the figure e , in the 18. chapter . chap. xx. how to make short gunnes for the saucissons . having already treated sufficintly and amply of the fabrication and making of the morter , in the imitation whereof most easily may bee made canons to shoote flying saucissons very high in the aire , making them of the one or the other matter or stuffe prescribed for the morter in the second chapter of the first treatise , but the powder sacke needs not , and the touch-hole ought to be in the middle of the bottome ; also it shall be necessary that euery canon haue a little breech to passe through a peece of wood , wherein they may be fastned , so that a port-fire may be layed from one to another , these are represented by the figure f , in the eighteenth chapter . chap. xxi . the manner how to dispose and build a great or little fire-worke . it is a custome and vsual thing among the braue and skilfull painters ; 1 to teach their apprentises how to draw limbs , or members , as the eye , the nose , the mouth , the eare , the hand , the foot , and afterward the whole bodie ; and in like manner , the most learned and famous philosophers , beginning their schooles , teach their disciples what is materia , forma , & primatio ; and afterward , totum compositum ; and to imitate them in this treatie , i haue taught the one after another , all the parties required are necessary for the composing & building of a beautifull fireworke for delight , hauing begun with the rockets for the ayre , afterward the rockets for the ground , the saucissons & rockets for the water , and following the ballouns and flying saucissons with all things belonging vnto them ; and to auoyd falling into the old prouerbe ( ex omnibus aliquid , & in toto nihil : to know somthing of euery thing , and nothing perfectly ) i haue here set downe after all these parts the description and manner how to assemble , build and dispose any manner of artificiall fireworke great or little : and to begin , you must first cause to be built a scaffold trianguler , square , round , or of such forme and bignes as you shall desire to haue your fire-worke , your scaffold being built , dispose thereupon your statues or figures which shall be prepared for it , let them be made of osiers , and couered with paper or canuas , and curiously painted as here is represented in this figure . mountains , buildings and many statues , all which are to be supposed , onely osiers and paper , or canuas painted , your figures or statues thus disposed vpon your scaffold , round about the flore therof , shal be layed your saucissons , being already fastned to peeces of timber , and to the pillers of your scaffold or raile , shall be fastned your firie lances one right vpward , and the other flat along , each distant , the one from the other about halfe a foot ; and vnder the firie lances , let there be nayled a ranke of boxes of fire , which shal be ranged vpon peeces of wood as the saucissons ; all your fireworkes being thus disposed , you may place in the side which is of least esteeme , your partments of rockets made like vnto square chests , or long boxes , of such bignes and length as shal be required to hold those rockets which you meane to place in each one : bu●1 these boxes must haue a false bottom full of holes for to passe euery rod of euery rocket apart , and hauing filled let the boxe ( which by proper name is called a partment ) be couered with a leafe or two of paper pasted close ; but to giue fire to the rockets , let there be made a hole thorow the partment , through it shall passe a little peece of stoupel , or cottē wieke and giuing fire to that , all the rockets within the partment , fly out , and in the same manner shall you giue fire to all your fierie lances with a stoupel going from the one to the other ; and as for your girondells , you shall giue fire to them with a match , as you desire that they should play , and by this meanes all your fire-workes shall begin to play at once , except those parts which shall bee reserued without priming to be fiered by the hand , as best shall seeme to the artist or enginier , and so the industrious shall not faile to accomplish his designes , obseruing all the rules prescribed ; which being at large laid down i will goe forward to the next chapter , and there shew how to make a most pretious vnguent for all maner of burnings , as well of common fire , as of artificiall fire , if by hazard anie mischance arise , chap. xxii . a most pretious vnguent for any burning . let no man wonder if ( hauing ended this treatise of fireworkes ) i take in hand to describe a little part of chirurgerie , whch i confesse to haue taken out of a treatise written by thybourel , a chirurgion of loraine , and hauing made experience of this vnguent diuerse times as well for burnings , as that for other accidents , i may say with boldnes & truth , that there was neuer the like secret of this kind left to posteritie , specially against hurts come by fire , and which leaues lesse scarres after the healing of the places wounded , and therefore i haue set downe the very words which thybourel hath written in the last chapter of his 4th . booke , intituled recueil de plusieurs machines militaires . take fresh hogges grease or lard , as much as you please , and boyle it , taking off the skim vntill there arise no more skim ; then set the lard three or foure nights in the ayre abroad , after which it must be washed in running water , to take away the saltish nature , and also to clense it white , then melt it , and keepe it for your vse . bacon may serue in stead of lard . otherwise . the white of an egge or fresh butter being mingled together and well beaten to an oyle are excellent . another sort most excellent . take a stone of vnslacked lime ( or otherwise called quicke lime ) and let it dissolue in cleere water , and when the water is setled , powre it gently out from the lime through a linnen cloth , then put as much sallet oyle as you take water together , and beating it all to an oyle , you shal haue a most excellent vnguent for all kind of burnings , neither of these vnguents haue any scarre , but are precious remedies for the afflicted we haue seene impostures ▪ couer sores with this water alone , but obseruing superstitious ceremonies , saying vaine prayers , but we assure the posteritie , that the water onely is sufficient to heale wounds and s●res , onely washing them with it , and couering them with a linnen cloath wet in the same water , without any superstition , it doth modifie and percute , by which it doth supply nature , and doth heale sores better then our ordinary vnguents . thus may you see how this braue chirurgion that set forth to the face of the world the perfection of this vnguent ( which cannot be sufficient-praised ) confirming by his own confession , that the chirurgions do not vse such good remedies in their shops and ordinarie operations ; wherfore i haue set downe his owne words , that no man may esteeme mee inuenter of calumnies , against the practitioners of chirurgery , nor any others , as many now adayes seemes to write with serpents tongues , stinging vertue on euery side , against whō viperous venoms patience is the only antedote , leauing them to sweat , vexe , and torment themselues in their insatiable rage , and to end my discourse touching the perfection of this vnguent , i will assure all these who shall haue neede and make vse thereof , that they shall find in operation what i haue here set downe in description . a treatise of practicall geometrie . to satisfie diuers of my friends and yeeld to their desires ( whose treaties haue bin such powerfull commands to me , that i haue beene constrained to lay aside and forsake my own proper will and follow theirs , i haue set forth this little treatise of practicall geometrie to the view and censure of the world , which i acknowledge to be vnworthy of so many singular and industrious wits , as yearly spring vp in this iland , and the adiacents thereunto , notwithstanding i haue giuen way to their requests for their priuat contentment , and to assure the world that i haue nothing , no not my owne will proper to my selfe , but that i will follow as neere as possible i may the precepts and documents of that ancient , wise , and diuine philosopher plato , who saith , non nobis nati sumus , sed patriae & amicis ; we are not borne for our selues , but for the seruice of our countrey and friends : then for the satisfaction of my friends and seruice of those who will accept these my labours , i haue cleerely and in few words set downe the manner how anie man ( who hath neuer so little studied geometrie ) may take any distance , or heighth , depth , or breadth with two little stickes , yea e●en strawes , being laied a crosse , also i haue set downe a method how to take any kind of heighth , distance or depth , with the sector without anie arithmetike or rule thereof : and also by the sines tangents and secants , the whole beeing very portable , to refresh the memorie , & to strengthen and augment the knowledge of those who ( for want of practise ) haue not the perfect vse of those instruments : then first of all i will set downe the manner how to accomodate and dispose the sticks , twiggs , or strawes for the measuring of any distance . the method how to make the crosse. hauing two stickes , the one long , and the other somewhat short as are represented in the figure following by cf , and de , then marke vpon the sticke cf , points the one distant from the other precisely , halfe the length of de , and let there be a hole made through the sticke de , so that it may slide vpon cf , from end to end , and you shall know the two parts of the crosse by these names , the longest part cf , shall be called the index , and the shortest de , the crosse . now if you haue any heighth to take , then fasten to one end of the crosse , as to d , a perpendicular or plummet , and for the more easie and iust operation , you should haue a foot to support the crosse ; the instrument being thus prepared , you may measure with great facility either heighth breadth , or depth , as followeth . proposition i. how to take a height accessible . let it be proposed to take the heighth of the tower ab , to the base or foot whereof one may easilie approach ▪ dispose the crosse of your instrument in such sort that dce be of equall distance there one from the other ; as thus , settle your crosse vpon the first point of the index ; then setting the instrument to your eye , goe either neerer , or retire far●her from the obiect you desire to measure vntill you see a the highest part thereof by the two extremities of the crosse cd , ( the inden being paralled to the earth ) which will happen in the point c , and not else-where : that being measured , will be alwayes the iust height of the tower required , onelie obserue that you must alwayes adde to the distance betweene you and the tower the length of the foot , which supporteth your instrument , and so you shall haue preciselie the heighth required : for scarce euer will it happen , that the instrument may be placed leuell with the base or foote o● the height required , but if that should chance to be , then the extremitie of the index c would ariue in the point g , and so nothing to be added , but onelie measure the distance betweene g and b , and that would be the iust height required ; but if it chance that you may not plant the instrument in the point c , by reason of some inconueniences which may happen retire further backe , and put forward the crosse to the second point of the index , and then accord your visuele lines to see the point a , ( the index alwaies being paralel to the ground ) which then will happen twice the height required , distant from the foot thereof : but if it happen that going backe you ascend anie little mountaine , or descend into any little valley , you are then to obserue some point in the wall of the tower , which the index shall direct you to by the line visuel , & adde onlie the height thereof vnto halfe the distance twixt you and the tower , and that shall be the height required most exactlie : and thus you shall neuer faile in your operations . proposition . ii. how to take a height inaccessible , or one height vpon another height . svppose the altitude bc , to be required , to the foot whereof one may come may come no neerer then to the point d , then at the point d , accord your visuell lines in b and c , the index being alwaies leuell with the ground and the crosse fixed vpon the first marks or point of the index , then set a marke there in d , and going backe towards f , as farre as e , and put forward the crosse to the second point of the index , and then direct your lines visuel againe in b and in c which will arriue in e , and not elsewhere , then measure the distance betweene de , which will be the altitude precisely required , but if you desire the heighth of the tower b , and mountaine leuell with the foote of your instrument , then you must adde the length of the staffe , which supporteth it as in former obseruations . and to haue the altitude a b vpon the top of bc , you must take two other obseruations in fg as before , setting your instrument in f , the crosse being fixed vpon the second point of the index , and direct your visuell lines in a and in c , and then set vp a mark in f , and goe backe , putting forward the crosse to the third point of the index , and direct your visuell lines againe in a and in c , which will happen in g , and not elsewhere , then measure the distance betweene fg , which shall bee equall to the altitude of the tower ac , and ha●●ing taken already the altitude bc , you may verie easilie substract the little altitude bc from the greater altitude ac , and then will rest the altitude ab , which is required . prop. iii. how to take any distance vpon a place accessible or inaccessible . if it were proposed to take the distance ab , and that the place were accessible onelie in the middle vpon the ●●ne cf , then dispose your instrument as before the crosse placed vpon the first point of the index , and going forward or backward vpon ●he line cf , direct your visuel lines 〈◊〉 a and in b by the two extreami●es of the crosse , the end of the index resting against your eie , then measure the distance betweene you and the point f , and that shall be iust half the distance required betweene ab , but if the place be inaccessible , so that you may not approch neerer then the point d , put forward the crosse to the second point of the index , & then direct your visuel lines to ab , and leaue a marke at d , and put forward the crosse one point more , and going backe vpon the line de , vntill you may direct your visuel lines by the extreamities of the crosse againe in a and b , then measure the distance between de , and that will be halfe the distance betweene ab , and so may you operate going backe , and putting forward the crosse . proposition iv. another manner how to take a distance inaccessible . svppose the distance ab to bee taken , and that b is the neerest place that may be required , then there must be set a marke , and withdrawing backward in a straight line towards c , and there againe plant another marke at c , then going right towards one side , as towards f , counting your places equall to the number which you haue alreadie found b and c , and there direct your visuel lines in bgc , as in this figure at d , leauing there a mark , goe straight along towards f , not moouing the crosse of your instrument , and going along make trial where your visuel lines may be directed again in a and in c , which will be in the point e , and not else-where , then leaue there a marke , and measure the distance betweene de , and that shall bee the distance which you require , which is ab , the demonstration of this proposition is grounded vpon the second and fourth propositions of 6 of euclide . prop. v. how to take a distance onely vpon a line parallell to it . let the distance ab bee required , the which may neither bee seene , nor come neere vnto , but onelie vpon the line or banke ck , then vpon that banke draw out a straight line with markes , as the line ck , paralell to the wall ab , and set a marke in k , then goe backe towards d , and direct your visuel lines in b and in k , by the extreamities of the crosse gh , then leauing the crosse in the same state and a marke at d , withdraw your selfe further back towards c , vntill you may direct your visuel lines to a and k , which will happen in c , and not elsewhere , and leaue there another marke , then measure the distance betweene cd , and the same shall bee the breach ab , equall to cd , and the demonstration of this proposition is grounded in the 29. and 33. propositions of the 1. of euclide . prop. viii . how to take the depth of a valley . to take the depth of a valley , there is somewhat more difficult then in the former operations , because there are more obseruations to bee made , and to begin you must from the point b obserue in some place opposite a ●a●ke leuell with the horison as a , the leuell whereof you may easilie take at this instrument , as is taught in the second proposition by the helpe of the plumbet : then from the point b , take the distance bc , as in the fift proposition , or else mecanikelie , which being done , direct your visuel lines from b to a , and to c , and leauing the instrument in same state , turning your selfe about , frame the same angle vpon the plaine , which will be fbh , then plan● markes vpon the lines bf and bh , and vpo● the line bh , count as many paces or fathoms as you shall haue found betweene b and c , and at the end of your paces ▪ 〈…〉 marke , which will bee at e , thi● being done , dispose your instrument to make a right angle , placing the crosse vpon the ●irst point of the index , for the crosse maketh alwaies a right angle when the crosse is vpon the fift point . the instrument being thus disposed , walke vpon the line bf , vntill you may direct your visuell lines ( by the extreamities of the crosse ) to b and e , or els to fe , which will happen in d , and no where else , then measure the line de , and it will be equall to the depth required g c , the demonstration of this proposition is grounded in the 26 , of the 1. of euclide , or vpon the equalite of the two triangles bg c , and bde , which are both equall and equall angles . although this operation be somewhat more obscure then the others , yet i thinke that it is sufficiently explained , and therfore i will goe forward to the vse of the sector . prop. ix . the manner how to take either distance or altitude with the sector . svppose the altitude ad were to be taken to the foot whereof you may approch open the sector 45 adding to it the sights then going forward or backward vpon the line di , vntill you may see the highest part of the altitude a , through the two vpper sights , the inferior branch of the sector , being paralell to the earth or horison , then measure the distance betweene the center of the sector and the tower , adding to that distance the length of the leg , which supporteth your sector , and that shal be the altitude required , as appeares in the figure following ab , and bc , are of equall distance , and adding the length of the foot of the sector , you will find , that it will be height of bd , which doth accomplish the altitude of the tower. but to take a distance in any plaine , as in the figure precedent , the same operation may be vsed , except onely the two branches of the sector shall be turned paralell to the horison or ground , hauing first made a right angle at the point g , or you may operate otherwise , first of all prolong a straight line as egh of what length you please , then open your sector to a right angle , and set it the point g , so that you may see through two sights the point e , and where the line visuel of the other two sights strikes along , set vp a merke as in i , then goe towards it , and at your pleasure in the same line , set your sector opening it , so that you may see the point e and g , and keeping your instrument at the same width , & in the same place place , only turne it to the other side , so that you may see the point g thorow the sights which before saw e , and where the other visuell line shall cut the first line egh , set a marke which will be in h precisely , and that shall be the distance required ge , the demonstration of this proposition is grounded vpon the 4. and 26. of the 1. of euclide . prop. x. how to take any distance or altitude inaccessible with the sector . to obtaine the altitude ab , you must first take the distance bc. as is taught by the 9. proposition precedent , and knowing the distance bc , which i suppose to be 100 fathom , set in the point c your sector , and direct your visuell line through the two vpper sights to the top of the altitude a , and let the branch of the sector be paralel with the ground , then leaving your instrument at the same width , let fall a perpendicular line vpon the line of the sector divided into equall parts , passing by the 100 number of the inferior branch noted d , and note what nūber the perpendicular doth cut vpon the vpper branch of the sector noted h , which i suppose here to be● the 150 part or number , and then set the two points of a paire of compasses vpon the two numbers , to wit , the one point vpon 100 , and the other point vpon 150. of the equall parties , then transport the points of the compasse all along one branch of the sector vpon the line of equall parties , and the two points shall denote as many parties vpon the line of the sector as the towre doth containe fathoms in altitude , adding the length of the foote which supporteth the sector , the demonstration of this proposition is grounded vpon the 4. proposition of the 6. of euclide . prop. xi . of sines , secants ▪ and tangents . because the most noble , most artificiall , and most certaine way of taking of altitudes , distances , or other dimentions , is by sines , secants , or tangents , i haue set downe their operations in such propositions as are vsuall in this subiect at the end of this treatise of practicall geometrie , and before i enter on the method of operation , it is necessary to define what the said sines , secants , & tangents are . 1. a righ● sine is halfe the subtence of of the double arke . a subtence , sometimes called a cord , is a right line drawne from any part of the circumference of a circle , vnto any other part of the same circumference , so the right line de is the subtence or cord of the ark dgh halfe of which is df , the sine of the arke dg ; and so is mn the subtence of the circumference or arke mgn , halfe of it is mi , which is the sine of the arke mg ; now the arke mg is halfe of the arke mgn , and mi is halfe of the subtence of that double arke , viz. mgn ; hence it is according to the definition aforesaid , that the sine of any arke is halfe the subtence of the double arke ; by the same reason ot is the sine of the arke bo and ms is the sine of the arke bom and so of others . note further that the totall sine , the sine of 90 , or the radius , is nothing else but the semidiameter of any circle , viz. cb , or cg . if a line be drawne tou●h a cir●l● , it is called a tangent , ( a tango ) as ●he line ab toucheth the circumference of the circle in b , and so ab is called a tangent line , and is s●●●uated on the terme of the radius cb , and perpendicular thereto , by the 18 proposition of the 3. of euclid . 2. the secant of an arke is a line contained betweene the center and the line tangent , so that it passe by the given arke , so if bo be a given arke , cq is the secant thereof , and if bm be a given arke , then is cr the secant thereof . 3. the tangent of an arke is a line contained betweene the tearme of the secant , and the touch point , so bq is the tangent of the arke bo , and br is the tangent of the arke bm , &c. proposition . xii . hovv to take any altitude or distance by the sines , tangents and secants . a of 51 , degrees will haue for his sines , 77715 , parts . b of 90. degrees will haue for his sines , 100,000 . parts . c of 39. degrees will haue for his sines , 62932. parts . then working by the rule of three , you say if the sines of a 77715. giue the side bc of 100 fathoms , how many fathoms will the sines of c , 6.932 for the side ab , and dispose your rule of three as followeth . if 77715 — 100 — 62932. and hauing multiplied the second number by the third or the third by the second , and diuided the product by the first number , and the quotient of the diuision will be for the side ab 80. fathoms , 70. inches , 4. lines and 11 / 12 parts of a line and ●o find out the side ac , you must operate in the same manner by the rule of three , & say if the sine a of 79715 giues the side bc of 100. fathoms , how many fathoms will the sine b giue , which is 100,000 . for the side ac , and hauing multipli●d the second number by the third , and diuided the product by the first , the quotient will be 128. fathoms , 48. inches , 7. lines , & ●4875 / 77715. part of a line , which is almost one line for the side ac , and thus may you know any kind of distance with great facilitie , onely knowing the angles and one side . prop. xiii . how to take any altitude or distance inaccessible by the sines . let the altitude ac bee proposed to be taken , and the neerest comming to it is b , then in that point b , take the angle abc , as in the chapter before , which is of 61. degrees , then assemble 61. with 90. the right angle opposite and the whole is 151 , which you must substract from 180 , and then will rest 29 for the angle a , and so the three angles of the ●●iangle are known , but neither side ; ●nd therefore to know one of the ●●des , that wee may operate by the ●●es , tangents and secants , retir● ●●rther backe or aside to d , and mea●●re your paces or fathoms from b to ● , which i suppose here to bee 300. ●aces , and in the point d , take the angle adb , which is 37. degrees , and then may know that the angle exterior abd , is of a hundred and nineteene degrees , for it is equall to the two interior angles abc and bac by the 32. proposition of the 1. of euclide , or otherwise it is the complement of the halfe circle , of which the angle interior abc of 61 degrees is taken out , now you haue the knowledge of two angles adb , and dab , the which being ioyned , substract them from 180. and then the third angle will remaine da b , then shal you know the three angles of the triangle a bd , and one of the sides by which you may come to the knowlege of the side a b of the first ●riangle a bc by the sine , and by the knowledge of the side a b , you may also know the side ac , by the sines , tangents and secants , as in the precedent chapter : and so in all manner of altitudes or distances , accessibles or inaccessibles , and it is to bee noted , that one is not boūd to wright backward , taking the second obseruation in d , but at the pleasure of the workeman to make choise of the fairest place in the field , so i thinke no difficulty shal be found in these works the manner how to take the plane of a towne , or any place out of musket-shot . svppose you were to take the plane abcde ; first , hauing considered that the scituation of the plane hath a crooked arke ba● ; those two lines must be supposed straight as eq and bp , making an obtuse angle at the point a , and being farre off from this plane in the point p , consider that the lines pb and qe , make but one angle in the point a , thē leauing a marke at p , withdraw from thence into some other place of field where your eye may rightly meete with the line ae , which will happen in q where you must set another mark now consider that if a line be drawne from q to p , it will forme a triangle apq , whereof you may know two angles , p qa and ap q which being done with your instrument , and you find the angle ap q to bee of 45. degrees , and pa q of 34. degrees , then adde 45. to 34. and commeth in the whole 79. which you must substract from 180 degrees , and there will rest 101 for the third angle paq by the 32. proposition , lib. 1. of euclide , and the angle eab is equall to the angle paq by the 15. proposition 1. then let vs conclude that we haue the angle bae of 101. degrees , which was vnknowne , then shall it be necessary in the place noted h , to know how the side cd is scituated in respect of the parts of the world , and with a declinatorie we shall find it to be seated north , west & southeast , which shall serue vs for the knowledge of all the rest : and in the former manner may be taken all the other angles of the plane proposed , and to haue the distance of each side of the plane , you must measure one onely as before taught , which i suppose it shall be b c , which shall bee found to bee 100 fathoms , and hauing found aside homologe to it or like to it , and diuided into an hundred parts equally , it shall serue for a scale to measure all the rest by . chap. i. a treaty of fortifications as well regularly as irregularly . it is not my intention to treate here of all manner of fortifications , but onely of those which by the generall and common opinions are held and approoued to bee the best for the defence and conseruation of deseruing places ; and to begin this treatise , i will set downe certaine rules which are now held for maximes of the best fortifications . let the flanked angle be open 90. degrees , or the neerest to 90. that may be it is the angle a in the next trianguler figure . let the flanking angle be not aboue 150. degrees open , but the lesser , shall alwayes be the best , this angle is blc in the same figure . let not the line of defence be longer then musket-shot , which is 100 , or 110 fathom , it is ck or bi in the same figure . the largest necke or gorge of a bastion or bulwarke is alwayes the best and the longest flanke lines , specially if eares be to be built vpon them , cn or mi are nose lines now shal follow al the denominations of fortifications for the better intelligence of the better treating of them . chap. ii. denominations of the parties of fortifications . a flanked angle is the point of a bulwarke in the figure following , it is the angle sbn. a flanking angle is blc , which is made by two lines of defence meeting in the point l. a line of defence is the distance from the flanke to the angle flanked , as here bi , or ck . the flanke is k or l. the line of the flanke is kn or im . the curtine is the strait line drawne from one flanke to the other , as here ki . the shoulder of a bulwarke is n or m. the pane of a bulwarke is bn . the eare is alwayes built vpon the line of the flanke , as in the second figure following . the capital or chief line is bi or fc bastion or bulwarke is a piece contained within two lines , two panes , and two flankes . the necke or gorge of a bastion is the distance betweene the two flanks for the entrie into the bastion . a rampard is the earth raised against the wall in the inside to strengthen it against canon shot . the parapet is the elevation aboue the string of the wall . the counter escarp is the exteriour brim of the towne ditch . a halfe moone is a peece loose from the towne raised of earth , and inuironed with a ditch to hinder the assault of the enemies , it is sometimes made in forme trianguler , but sometimes oblong as occasion is , now shall follow the treatise of the regular forts , and first of all the trianguler . chap. iii. how to build a trianguler fort. svppose a bc to be the triangle , where in a fort three square is to be built . from the point c , as the center , and from the distance cb , let the arke bta for 60. degrees be described , which shall be diuided into two equall parts at the point t. and againe , the arke bt into foure other equall parts , and o b shall bee an arke of 7½ degrees , by which draw the line co , and it shall forme the diminished angle ocb of 7½ degrees . and to find the point for the flanke diuide the angle qce in two equall parts by the straight lines ch , which teacheth vs the point i , for the flanke and then take the distance fi , and carry it to ek , and the point k shall be another flanke , then draw the lines of the flankes kn and im perpendicularly to the courtine ki , which is drawn from the flanke k to the flank i , and the same vpon the two other sides , and you shall haue the trianguler sort perfect . the flanked angle is of 45. degrees , and the flanking angle is 165. degrees open , which is somewhat farre from the best maximes of fortifications . chap. iv. how to build a square fort. let the square abcd bee in which you desire to build the fort , draw the two diagonales ad. cb , which cut e the center of the fort from the point d as center , and from the distance dc , let the arke cgf bee drawne , which shall bee diuided in three equall parts , and from the point g draw the straight line gd , which formeth the diminished angle gdc of 15. degrees , and the intersection of the line gd in h doth shew the line capitoll ch , which shall be transported into ikl , and then draw the straight lines ci. dh and their fellowes , and to find the point for the flanke , diuide the angle fdg in two equall parts by the line dm , which cutting the line ci doth shew vs the point n for the flanke , then take the distance in , and beare it to ho , and the point o shall be another flanke , then draw the courtine on , and from the points o and n draw the two straight lines op and n q perpendicularly to the courtine on . doe the same vpon each other side , and you will haue perfected the square fortres the flanked angle is of 60. and the flanking angle is open 150. degrees . chap. v. how to build the pantagone fort. the five sides and five lines being drawne from the point a as center , and from the distance ab . ●et the ●rke bd of 60. degrees be described , which shall bee diuided into ●oure equal parts , of which be is one ●nd from the point e ▪ draw the right ●ine ae , which cutting the line bc●t ●t the point f , doth giue the part bf●or ●or the capitall line ; which distance must be transported to the other lines ag , &c. then from the point b , draw the straight line bg , and so the others which shall bee lines of defence . and to find the flanke , diuide th● angle eac in two equal parts by the right line ha and the intersection which it maketh vpon the line bg at the point i shall be the flanke , then take the distance gi , and transport it into fk , and so to ig , and the point k shall be a flanke and the point i , then draw the line ki , which shall be a courtine , and draw the lines kl . and im , which shal be the flank lines being drawne perpendicularly to the courtine , and doing the same to euery other side , you shall haue the desired fort. chap. vi. how to build the fort hexagone . hauing diuided your circle into sixe equall parts , and drawne the sixe straight diagonall lines and the sixe sides . from the point b as center , & from the distance ab , let the arke adc of 60. degrees be described , and it shall be diuided into foure equall parts , whereof ad is one . from the point d , draw the straight line db , which cutting the line ac at the pont e , doth giue the distance ae for the capitall line , then transport that distance to bf . and to find the point for the flank diuide the angle d bc in two equall parts by the straight line g b , which cutting the line af at the point h doth shew that point for the flanke , then take that distance hf , and transport it to ei , and to all the rest . from the point i , draw the straight lines ik perpendicularly to the curtin ih , and draw the other line hl perpendicularly also , and doe the same vpon each other side , and you shall haue the hexagone perfect , but if you will make eares , they must bee built vpon the two third parts of the lines of the flanke ik hl as appeares at . chap. vii . how to build the heptagone . let bklmno be the heptagone giuen , and the center therof a from whence shall be drawn the seuen lines an. ak . ap , &c. then from the point k as center , and from the space kb , let the arke bca of 60. degrees be described , which shall be diuided into foure equall parts , whereof bc shall be one of 15 degrees , from the point c draw the right line ck , the which cutting the line an , at the point d , giueth that part for the capitall line . then take the distance nd , and carrie it to ki , and to al the rest likewise , then from the point n draw the right line ni , which shall be the line of defence , and all the others like vnto it . and to find the point for the flank , diuide the angle akc in two equall parts by the right line gk , which cutting the right line ni at the point f sheweth that intersection f , for the point of the flanke take the distance and cary it to d and e , and the point e shall be another flanke , then draw from e to f the line ( which makes the courtine ) then the two perpendicular lines for the flanke lines : whereupon shall be built the eares , and doing the same vpon each side your fort shal be perfect , as required . chap. viii . how to build the octogone . first let the square ab cd be made , & then the square efgh . and to finde the place for the flanke , diuide the angle adc by the strait line di , and the intersection k sheweth the point for the flanke , as in the forts precedent , and so transport to euery side as in the other , and you shall haue the fort finished . chap. ix . the description of the heigth , depth , and thicknes of euery part of a compleat fortification . ab the largiour or breadth of the rampard 66. foot . ac height of the rampard , 14. foot . ga the interiour heele of the rampard 14. foot . ef the breadth of the parapet 20. foot . eh height of the parapet 6. foot . bi . the exterior heele of the parapet 7. foot . ik . the couered walke vnder the false bray 20 foot . kl the parapet of the false bray 20 foot . mn the breadth of the ditch 120 foot , & the depth therof ought to be 10 foot . no the heele of the ditch 10 foot . op the couered walk of the counterescarpe . pq the counter escarpe 6. foot of height . chap. x. the manner how to fortifie places irregularly . vpon a line of 100. fathoms is to be made a tenayle ; vpon a line of 150. fathoms two half bastions . vpon a line of 200. fathoms a double tenayle . vpon a line of 250. fathoms or therabout is to be made one bastion , and two halfe bastions . chap. xi . a fortification irregular . svppose the place qrstv to bee fortified without diminishing the place , and having taken it vpon a faire sheet of paper and well considered , all the measures thereof then without this plane conduct the line ab of 250. fathom , and vpon that line ( according to the rules precedent ) build one bastion , and two halfe bastions taken from the octogon , and then shall you bee at the point a , and from the point a , draw the line ap of 150. fathom , or thereabout , vpon which you may build two halfe bastions ; then draw the line po , vpon which you shall as before build one bastion and two halfe bastions , and so vpon the line ox , and vpon all the others according to the length that they shall be found . but if it should be required , that the towne-walls should serue for the courtines , the figure following shall be an example either for a part or for all about a towne . chap. xii . another manner of fortifying irregularly . svppose that one would fortifie the plane baplmno , but in such hast , and with so little cost that the towne walls should serue round for the courtines , the plane then being taken vpon a faire sheet of paper , and hauing drawne the line cdef of 400. fathom , it shall be found necessary to build vpon the same one bastion two half bastions and a tenaile , viz. the bastion e , the two halfe bastions d and f , and the tenaile dc , & hauing drawn the lines round about the town , leauing sufficient space be●wene them and the walls to build bulwarkes or bastions , you may take for the length of euery line of defence , that is to say from the flanke of one bastion to the point of another , 100. or 110 fa●hom and so euery bastion shall bee scowred with musket-shot , as the forts built regularly . this may serue for an example to those who by chance , may haue occasiō to repair or strengthen any part of a towne , wall , or the whole , and for the fortifying of the wall , the earth must be raised in the inside as a rampard . a treatise of arithmetike . chap. i. addition since that arithmetike is absolutely necessary , and required in diuers and many geometricall operations , i haue added the examples following onely to renew and refresh the memorie of those who haue alreadie studied it ; and not those who are quite ignorant therin , ( commending them to large and ample treatises together with masters of the scien●e ) but for such as by a weake memory haue let slip the habitude which by practise they had in times past obtaind , who may easily recouer by this short treatie sufficient knowledge to performe any ordinary operation beginning with addition , which is a collection of many numbers in one , as hee who would adde together the numbers abc , following to haue the summe d , must begin with the first colon : and say 2 and 5 , or 7 and 1 is 8 , and set 8 vnder the line , as appeares by the example aboue , then in the second colon , say 3 and 4 or 7 , and pose them as before ; afterward say for the 3. colon 6. are sixe , & posing or setting the numbers collected directly vnder the figures not collected as 8 vnder 2 , and 7 vnder 3 , and sixe vnder sixe , but if any should bee aboue the number of 9 , then to set 0 in the place , and set forward all the tens . the proofe . may be made in casting all the 9 away , though many times fals but by substraction is the way most certaine , as thus , begin with the last collon and say 6 , cut of 6 , rest nothing , and giue the 6 vnder the line a flash , then 4 and 3 , or 7 and 7 , out of 7 rest nothing , and as before giue it a flash , then 1 , 5 and 2 , or 8 , which as before shall be made nothing , the 8 vnderneath . chap. ii. substraction . svbstraction is to take away a little number from , or out of a greater , as if one would from 8 6 4 2 take away 4 3 2 1 , then must the numbers bee disposed as followeth , the greater number vppermost , and the lesser vndermost , then draw a line : great number   8642. a lesser number   4321. b   rest 4321. c and say he that of 2 in the rank paieth one , rests 1 , the which set vnder the line , then of 4 pay 2 , rests 2 , which must also bee set vnder the line , and who payes 3 out of 6. rests 3. setting them as before , then 4. out of 8 rests 4. which shall bee also set as the others in the example aboue . the proofe . is made in adding the lesser number b with the rest c as followeth . little nummer .   4321   rest 4321 great number .   8642 and the sum shall be the first number a , if the substraction haue beene well made . chap. iii. multiplication . mvltiplication is the assumption of one number , as many times as the other , containeth in it selfe vnities . as if one would multiply 6. by 3 , that is , to take as oft 6 as 3 containes vnities , as in the example aboue , where 2 taken 4 times makes 8 , and 5 taken 4 times makes 20. so that the number a multiplied by the nūber b multiplicator 4 times comprehended , make the product 2608. the proofe . is made onely diuiding the product 2608 by the multiplication 4 and the quotient will be 652. if the multiplication were well made , as appeares in the example following . chap. iv. diuision . division is the separation of a number into aliquot partes thereof , as to diuide 5689 by 25. the figures must be disposed , as followeth , viz. the diuisor vnder the first figures of the number , which is to be diuided , as for example . and after the last figure of the number , shall bee drawne a halfe circle to separate the quotient . the numbers being thus disposed , then say 2 in 5 how many times , and it shall be found twice ; then set 2 behind the halfe circle as in the first example following ; and then say twice 2. are 4 of 5 rests 1 , dashing out the 2 and the 5. and set the 1 ouer 5 , and say againe twice 5 are 10. and strike out the 5 diuisor vnder the 6. and also the 1. ouer the 5 , then set forward your divisor one figure more as in the second example , and say 2 in 6. how how many times , and it shal be found 2 , and say twice 2 are 4 , and 4 out of 6. rests 2. which shall be set ouer the 6 , then say twi●e 5 are 10. and 10. out of 18. rests 8 and 1 out of 2. rests 1. then dash out the 2. and set 1. ouer it ; and also dash out the 5 and 2. diuisors , and set more forward the divisors , as in the third example , and say 2 how many times 18. and it shall be found 7. times , and having set the 7 , say 7 times 2 is 14. and 14 out of 18 rests 4 , and set the 4 ouer the 8 ; and to conclude , say 7 times 5 are 35 , and 35 out of 39 rests 4 , and 3 out of 4 rests 1 , and so your diuision is ended , as appeares here following by three examples one of each operation . the proofe . multiplie the quotient 227. by the diuisor 25 , and to the product partiall , adde the numbers which rest , viz. 14. if any rest , and then adde the whole together , and the product shall be the first number if the diuision hath beene well made as in the example following . chap. v. rules of fractions . a fraction is a number noting the partes aliquot of an entire or whole number , whereof it is said to be a fraction as a penny , the twelfth part of a shilling , one inch the foure and fortieth part of an ell , &c. chap. vi. how to reduce intiers and fractions all into fractions . to reduce 8¾ and 5⅔ all infractions you must multiplie 8 by 4 , saying 4. times 8 is 32 , and the 3 being added , makes 35 , which shall be set aboue a line iust vnder the first figures , and vnder that line set 4 , as in the example following , to shew that the 45 are al fourth parts , and doe in the like manner by the 5⅔ , and say 3 times 5 are 15 , and 2 makes 17. and so you shall haue 17. thirds , as in the example following . to reduce 8¾ and 5⅔ all into fractions . chap. vi. to reduce all fractions into one denomination . to bring these two fractions to one deno . the 35 quarters numerators must bee multiplied by the other numerators 17. thirds , and set the product ouer a line as here following , then multiply the 4 denominator by the other 3. denominator , and set the product of those vnder the line , and then will there be , addition of fractions . to adde ⅔ to ¼ the figures , dispose the figures as followeth , and say 3 times 1 is 3 , and set the 3. ouer a line aboue the head of the others , and then say 4 times 2 are 8. and set them ouer a line aboue the head of the others also , then say 3 and 8 are 11 , and set them ouer a line betweene the first numbers and the 11 , shall be numerators , and say 4 times 3 are 12 , & set them vnder the middle line , and those shall bee denominators , and so you shall haue eleuen twelfth parts as followeth . but if the numerator bee greater then the denominator , then it shall bee diuided by the denominator , and the product shall be an entire or entires , and what resteth ( if any rest ) shall bee fraction , which ought to be abridged , as appeareth here following . where the numerator 38 is greater then the denominator 24. then being diuided by the denominator 24. doth yeeld 1 intire , and 14 / 14 the which being abridged come to 7 / 12 , which is almost two thirds , and so of all others . chap. vii . additions of intiers and fractions . being proposed to 243⅔ vnto 462¼ , the intiers must be added as in the first chapter of addition and the fractions must be added as in the precedent chapter , and set product as appeares following . chap. viii . substraction of fractions . whosoeuer would substract ⅔ from ¾ must dispose the figures , as in the example following ; and first multiply the numerators by the denominators a crosse , as 3-times 3 are 9. and 4 times 2 are 8 , and set 9 and 8 ouer the lines aboue the heads of the others , and then say take 8 out of 9 , and there rests 1 , which must bee set ouer a line betweene both , and afterward say 3-times 4 is 12 , multiplying denominators by denominators , and set them vnder the middle line , which shall bee the denominators for the rest , as appeares cleerely in the example following . out of 9 pay 8 rest 1 chap. ix . substractions of intiers and fractions . to substract 1831 from 267 2 / ● the fractions must first be multiplyed as in the example following ; and say twice 2 are 4 , and set the 4 ouer a line , then 3 times 1 are 3 , and set them ouer a line , and then who payes 3 out of 4. rests 1 , which must be set ouer the middle line , which done , multiply the one denominator by the other , and set the product vnder that which doth rest , as followeth . but if the fraction of the receiued should be lesse then the fraction of the summe paid , then must there be one borrowed from the whole or intire number , and count it according to the denomination of the fraction ; for if the denominator bee 4 , then shall the intier be 4 / 4 , if 5 , then 5 / 5 , if 6 then 6 / 6 , &c. chap. x. multiplication of fractions . let there bee proposed a superficies in the forme of a paralellogram , vulgarly cald square , the sides whereof the one is in length 7 / 8 of a fathom , and the other in breadth ¾ , and these two fractions are to bee multiplied together to find out how much the whole superficies doth containe the figures must be disposed as followeth . and multiplie one numerator by the other numerator , and then one denominator by the other denominator , saying 3 times seuen is 21 , and set them ouer head , then foure times 8 is 32 , and set them vnderneath , and the whole will bee 21 / 32 parts of a fathom , which certainely containeth the required superficies . chap. xi . multiplication of entiers and fractions . to multiply ¼ by 2½ , you must first of al reduce the whole into fractions , and then as here aboue multiply numerator by numerator , and denominator by denominator , and the product will bee 45 / ●8 , as plainely appeares by the example following . but if it were proposed to multiply greater numbers , as 20 by 15 26 / 29 , then multiply the 15. intiers by the deno . 29. of the fraction , & then adde the numerator 26 of the same fraction ; which done will mount to 461 / 29 , then set the 461 ouer a line , and the 29. vnder it , and afterward multiply the 20 intiers by the 461. which done , diuide the product of the whole by the denominator 29. and the numqer required shall bee 317 27 / 19 , as appeares : chap. xii . the diuision of fractions . to diuide ¾ by ⅓ , each numerator is to bee multiplied by each denominator opposite , and set the product ouer a line aboue them , and then diuide the greatest product by the least as followeth . chap. xiii . to diuide intiers and fractions by intiers and fractions . to diuide 12⅔ by 3⅙ , they must first be reduced all into fractions as before , and then you must multiply the numerators by the denominators acrosse as followeth , and then diuide the greatest product by the least , as this example doth cleerely demonstrate . chap. xiv . evaluation of fractions which may not be abridged . svppose you were to abridge 7 / 9 parts of a fathom , first you must consider what are the parts of the intier or whole , as 6. foot , or 72. inches : then you must multiply the numerator 7 , by the denominator 72 parts , and let the product bee diuided by the denominator 9 , and then you will finde 56 inches for the eualuation of 7 / 9 parts of a fathom . by this meanes any fraction may be abridged as well in geometrie as as commerce , although they seeme not to be abridged . chap. xv. for the eualuation of measuring lands . you must consider that the fathom of 6 foot in length , doth containe in superficies 36. and that the 72 inches in length doth contain in superficies 5184 inches , and of other measures then to valuate a fraction of 19 / 4● parts of a fathom , square in superficies you must multiply 5184 by 19. and diuide the product by 47 , and there will be 2095 inches for the square of 29 / 47 of a fathom square and so of other like measures . chap. xvi . of the rule of three without fractions . mvltiply the second number 400 by the third 12. and product 4800 by the first number 4 , and the quotient shall be the number required , and dispose your rule as followeth . months — pounds — months . if in 4 — 400 — 12 the probation of this rule . is to multtplie the first number 4 by the fourth number 1200 , and to multiplie the second by the third , and the two products will bee equall if the rule bee well made . chap. xvii . of the rule of three with intiers and fractions . first all the intiers must bee reduced into fractions as followeth . yards pounds yards . if 2¼ 12½ 7½ 9 / 4 25 / 2 15 / 2 which done , you must multiply the second number of fractions as by the third number of fractions 15 , & then againe multiply the product by 4 the denominator of the first number , and then say 2 times 2 , or 4 , and 4 times 9 is 36 , which must bee set vnder the line , by which you shal diuide the first product 1500 , and the quotient shall be the number required , as appeares , heere followeth two examples , differing the one from the other ; whereof the manner of multiplying the one , is more easier then the other the first is multiplyed as the precedent , but the last is multiplied first by all the intirres , viz. by 3 , by 8 and by three , leauing the fraction ● by it selfe , and after all take the thir● of the intier , viz. of 50000 , saying th● third part of 5 is one rest 2 , for the 10 which is valuated at 20 , then say the third part of 20 is 6 , and so rests 2 for the second 0 , and so to the end , and what shall rest at last , shall be set ouer a line , and your 3 4th or 5 vnder the line , then all being added together , you shal diuide the product cutting off the figures to the quantitie of the first number , saying , by ten , by a hundred , by a thousand , by ten thousand , by a hundred thousand , & the remainder is the number required , as appeareth , 191⅔ . the first example . the second number being mul●●plied by the third , doth mount to 57500000 , and being diuided by the first multiplyed by 3 , as before is taught , the quotient will be 191 2 / ●0 . the second example . chap. xviii . extraction of the square roote . first dispose your numbers as followeth out of which you meane to draw the roote separating your figures by two and two beginning at the latter end ; but first strike the halfe circle 73 / 21 / 01 ( and then say the root of 73 is 8 , and set 8 before the half circle , & rests 9 , then double the quotient 8 , and say 2 times 8 are 16 , and set the 6 vnder the last figure of the second part of figures , and 1 vnder the first figure of the first part a● in this first example . then say how many times is 1 in 9 , and it shall be 5. which you shall also set vnder the 1 of the second separation , as apppeares in this second example . and then say 5 times 1 are 5 , which taken out of 9 rests 4 , and 5 times 6 are 30 , and 30 out of 32 rests 2 , and 3 out of 4 rest 1 , and then againe say 5 times 5 are 25 , which out of 3● rest 6. and 3. out of 12. rest 9. and then double the quotient , and say twice 5 are 10 set 0 vnder 0 of the last separation , and keepe ● in memorie , and say twice 8 are 16 , and 1 that i keepe in mind makes 17 , then set downe 7 vnder the 5 , and the 1 vnder the 6 of the middle separation , as appeares in this example following . and then say how many times is 1 in 9 and it shall be 5 times , which shall be set downe for quo●ient , and also vnder the last figure 1 , and then say 5 times 1 are 5 , out of 9 re●ts 4 , and 5. times 7 are 35 , which out of 36 rests 1 , and 3 out of 4 rests 1 , and 5 times 0 is 0 , and 5. times 5 are 25. out of 31 rests 6 , & 3 out of 10 rests 7 , and 1 out of 1 rests 0 , and so the rule is ended as appeares following . chap. xix . another example of the square root . after you haue separated your figures by two and two , and drawne 251 the square roote , there doth yet rest 268 , which must bee reduced into fractions , and to begin set that rest 268 ouer a line at the end of your root , and that rest shall be numerator of the fraction ; and to finde the denominator only , double the root 251 if it be bigger then the rest , but if less as here , adde one to the doubling of the first figure , saying twice 1 is 2 , and 1 that i adde makes 3 , adde only double the rest , and set it vnder the line , and that shall be the denominator of the fraction ; and to haue the root of this fraction here aboue , first take the root of the numerator , and set that root ouer a line , and it shall be numerator as appeares following . then draw roote of the denominator , and set it vnder the line , and that shall be a denominator , and so you shall finde 16 / 22 , and what rests is vnsensible . but because that this fraction 16 / 22 is not precisely perfect , and that there is a rest in each extraction , you may operate as followeth to haue it mooue exactly , adde as well to the numerator as to the denominator two 00 , or foure , or sixe , &c. and from each product or quotiēt out of one figure for euery two 00 which you shall haue added , and the more that you adde 00 , the more precisely you shall haue the roote as appeares following . but if it were proposed to extract the square roote of 16 / 25 , there would nothing rest , nor would it bee needfull to adde any 00 , for the root of 16 is 4 and the root of 25 is 5 , and so wee should haue 4 / 5 , and the like in all such other accidents ; and thus much for arithmetike . vale. finis . the contents . a treatise of fire-works for warre , page 1. the manner how to make the morter-peece . pag. 5. the manner how to make granades or mettle for the morter or hand , pag. 10. the manner how to make granades of canuas for the morter . page 16 how to make fierie arrowes . pag. 20 how the granads are to be charged into the morter . page 24 thn manner how to shoote the granads , page 28 a most violent method to set a towne on fire . page 33 how to make granads to cast with mens hands . pag. 39 how to make fierie wheeles to bee cast vvith mens hands . pag 45 how to make a ship of wild fire . pag. 48 how to make a petard . pag 55 a treatise of artificiall fireworkes for pleasure . page 61 a method to make moulds for rockets for the ayre . page 64 how to make flying rockets for the ayre . page 69 how to make moulds for rockets for the ground . pa. 74 how to make the composition for rockets vpon the ground page 76 the manner how to make serpents . pa 78 how to make golden rayne . pag. 81 how to make starres , pag. 83 how to make starres giuing great reports . page 86 the manner how to make saucissons , page 88 how to make stoupell or preparing of your cotton-wieke . pag. 91 thu manner hovv to assemble and set together the parts of a rocket . pag ▪ 94 hovv to represent diuers sorts of figures in the ayre with rockets . page 97 hovv to make fierie boxes . pa. 101 how to make fierie lances . pag. 103 the manner hovv to make rockets for the vvater . page 105 hovv to make girondels or fiery wheeles pag. 110 the manner hovv to make ballons . pag. 113 hovv to make flying saucissons . pa. 120 hovv to make short guns for the saucissons . page 123 the manner hovv to dispose and build a great or little fireworke . pag. 125 a most pretious vnguent for any burning . pag. 131 a treatise of practicall geometrie . page 136 the method hovv to make the crosse. pag. 139 hovv to take a height accessible . pag. 141 how to take a height inaccessible , or one height vpon another height . pag. 145 hovv to take any distance vpon a place accessible or inaccessible . page 149 another manner how to take a distance inaccessible . pa. 151 how to take a distance onely vpon a line paralell to it . pag. 165 hovv to take the depth of a vally . p. 157 the manner how to take either distance or altitude vvith the sector . pag. 161 how to take any distance or altitude inaccessible with the sector . pag. 165 definitions of sines , tangents , and secants . pag. 168 hovv to take any altitude or distance by the sines , tangents , & secants . pag. 171 hovv to take any altitude or distance inaccessible by the sines . pag. 176 the manner hovv to take the plane of a towne or any place out of musket-shot . page 180 a treatise of fortification , as vvell regularly as irregularly . pag. 184 denominations of the parties of fortification . pag. 186 hovv to build a trianguler fort. p. 189 hovv to build a square fort. pa 192 hovv to build the pan●agone fort ▪ p. 195 hovv to build the fort hexagone . p. 198 hovv to build the heptagone . pa. 201 hovv to build the octogone . p. 204 the description of the height , de●th , and thicknes of euery part of a compleat fortication . p. 206 the manner how to fortifie places irregularly . p. 209 a fortification irregular . p. 210 another manner of fortifying irregularly . p. 213 a treatise of arithmetike . addition . p. 216 of substraction . pag. 219 of multiplication . p. 222 of diuision . p. 224 hovv to reduce intiers and fractions into fractions . p. 229 to reduce all fractions into one denomination . pag. 230 ad●itions of intiers and fractions . p. 234 substraction of fractions . p. 235 addition of fractions . p. 231 substractions of intiers and fractions . p. 237 multiplication of fractions . p. 239 multiplication of entiers , and fractions . p 241 the diuision of fractions . p. 243 to diuide intiers and fractions by in●iers and fractions . p. 44 eualuation of fractions which may not be ●bridged . p 245 for the eualuation of measuring lands . p 246 of the rule of three without fractions . p ●48 the probation of this rule . p. 249 of the rule of three with intiers and fractions . p. 250 the first example . p. 253 the second example . p. 25● extraction of the square roote . p. 255 another example of the square roote . p. 258 military books printed for t. and i. egerton , military library , whitehall . 1. muller's works of fortification , attack and defence , engineering , artillery , &c. 2. simes's military guide for young officers , containing parade and field duty , regulations , orders , returns , warrants , &c. 8vo . 10s . 6d . 3. — military course for the government and conduct of a battalion , 20 copper-plates , coloured , 8vo . 10s . 6d . 4. — treatise on the military science . comprehending the grand operations of war , and general rules for conducting an army in the field , 4to . 15s . 5. — regulator , to form the officer , and complete the soldier , 8vo . 6s . 6. — instructor for non-commission officers and private men , 12mo . 2s . 6d . 7. rudiments of war ; comprising the principles of military duty , 8vo . 6s . 8. discipline for the norfolk militia , by lord townshend , &c. 52 copper-plates , 4to . 12s . 9. regimental book for the use of the major or adjutant , beautifully engraved , with proper heads , folio . 10. returns for horse , dragoons , and foot mus●er-rolls , attestations , furloughs , discharges , &c. 11. miller 's ( capt. ) art of self-defence , on copper-plates , folio , 10s 6d . 12. orders relative to the sale of commissions on full and half-pay . 13. new exercise by his majesty's order , 1s . 14. recruiting book for the army , 2s . 6d . 15. new art of war , by captain anderson , 8vo . 7s . 6d . 16. jones's artificial fireworks . 17. drummer's instructor , with english and scotch duty , with beatings , marchings , calls , &c. 18. cadet , a military treatise , 8vo . 5s . 19. phipps's military discipline , with copper-pl . 12mo . 4s . 20. general essay on tactics , 2 vol. 8vo . with 28 copper-plates , translated from the admired essai générale de tactique de guibert , 2 vols . bound , 14s . 21. lochee's military mathematics , 2 vols . 8vo . many copper-plates , 12s . 22. lochee's elements of fortification , many copper-plates , 8vo . 6s . 23. — on military education , 8vo . 2s . 6d . 24. — essay on castrametration ; or , instructions for forming camps , with copper-plates , 8vo . 4s . 25. soldern's ( gen. ) tactics , translated by landmann , 7s . 6d . 26. lochee's field fortification , with copper-plates , 8vo . 5s . 27. obrien's naval evolutions , with copper-plates , 4to . 10s . 6d . 28. military instructions for officers detached in the field , copper-plates , 12mo . 4s . 6d . 29. king of prussia's military instructions to his generals , cuts , 8vo . 5s . 30. — campaigns , 12mo . 3s . 31. dalrymple's military essay , cuts , 8vo . 5s . 32. bell's essay on military first principles , 8vo . 5s . 33. donkin's military collections and remarks , 8vo . 4s . 34. cambridge's account of the war in india , many large plates , 8vo . 6s . 35. general review , manoeuvres , and exercise , cuts coloured , 8vo . 3s . 6d . 36. wolfe's instructions to young officers , 12mo . 2s . 6d . 37. elementary principles of tactics , many copper-plates , 8vo . 6s . 38. antoni on gunpowder , fire-arms , and the service of artillery , by captain thompson , 10s . 6d . 39. elements of military arrangement , 2 vol. new edit . 7s . 40. lloyd's ( general ) history of the war in germany , vol. 2. 1l . 1s . 41. — political and military rhapsody . 42. treatise on military finance , 2s . 6d . 43. complete collection of marine treaties , subsisting between great-britain and the different powers of europe , &c. from 1546 to 1763 inclusive , 8vo . 6s . 44. tandon's french grammar , to learn without a master , 8vo . 2s . 45. beckford's descriptive account of the island of jamaica , 2 vols . 12s . 46. theatrical remembrancer , boards , 4s . 47. ireland's picturesque scenery of the river thames , 2 vol. 2l . 12s . 6d . 48. — picturesque scenery of the medway , 1l . 11s . 6d 49. english anthology , 6s . 50. pieces of ancient popular poetry , 4s . the mysteryes of nature, and art conteined in foure severall tretises, the first of water workes the second of fyer workes, the third of drawing, colouring, painting, and engrauing, the fourth of divers experiments, as wel serviceable as delightful: partly collected, and partly of the authors peculiar practice, and invention by i.b. bate, john. 1634 approx. 208 kb of xml-encoded text transcribed from 105 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2008-09 (eebo-tcp phase 1). a05657 stc 1577.5 estc s122341 99857492 99857492 23237 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a05657) transcribed from: (early english books online ; image set 23237) images scanned from microfilm: (early english books, 1475-1640 ; 575:15) the mysteryes of nature, and art conteined in foure severall tretises, the first of water workes the second of fyer workes, the third of drawing, colouring, painting, and engrauing, the fourth of divers experiments, as wel serviceable as delightful: partly collected, and partly of the authors peculiar practice, and invention by i.b. bate, john. [10], 14, [2], 15-112, [16], 121-192, [2] p. : ill. (woodcuts) [by thomas harper] for ralph mab and are to be sold by iohn iackson and francis church at the kings armes in cheapeside, imprinted at london : 1634. the title page is engraved. "the second booke, teaching most plainly, and withall most exactly, the composing of all manner of fire-works for triumph and recreation", "the third booke of drawing, limming, colouring, painting, and graving", and "the booke of extravagants" each has separate title page with imprint "london, printed by thomas harper for ralph mab. 1634" (with punctuation variations); pagination and register are continuous. the last leaf is blank. the leaf after p. 14 is printed as t4. an imprint variant of stc 1577. identified as stc 1577a on umi microfilm. reproduction of the original in the folger shakespeare library. binder's waste filmed at beginning. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng hydraulic machinery -early works to 1800. fireworks -early works to 1800. art -technique -early works to 1800. medicine -formulae, receipts, prescriptions -early works to 1800. 2006-04 tcp assigned for keying and markup 2006-04 aptara keyed and coded from proquest page images 2007-04 ali jakobson sampled and proofread 2007-04 ali jakobson text and markup reviewed and edited 2008-02 pfs batch review (qc) and xml conversion the mysteryes of natvre and art : conteined in foure severall tretises , the first of water workes the second of fyer workes , the third of drawing , colouring , painting , and engrauing , the fourth of divers experiments , as wel serviceable as delightful : partly collected , and partly of the authors peculiar practice , and invention by j. b ●●●nted at london for ralph mab and are to be sold by iohn iackson 〈◊〉 francis church at the kings armes in cheapeside 1634. to the reader . courteous reader , this ensuing treatise hath lien by mee a long time , penned , but in a confused and undigested manner , as i gathered it , practised , or found it out by industry and experience . it was not in my minde to have as yet exposed it to the publique view : but being sollicited by the intreaties of some , and those not a few , to impart to each particular person what his genius most affected ; i was enforced as well for the satisfying of their requests , as for the avoydance of many inconveniences , to dispose in some order such experiments as for the present i was content to impart . expect no elegancy of phrase , for my time would not afford that , ( nor indeed my selfe to be the transcriber . ) i endeavored as much as i could , to write in plaine termes , that in regard of the easinesse thereof it might suit with the meanest capacity . the whole book consisteth of foure parts : the first whereof treateth of vvater-workes . the second of fire-workes . the third of drawing , painting , graving , and etching . the fourth and last part treateth of severall experiments , as well serviceable as delightfull : which because they are confusedly intermixed , i have entituled them extravagants . now my chiefest ayme and end being the generall good , i could wish a generall acceptance , but that is too uncertaine to expect : i will content my selfe that i am already certaine that these my first and weak endeavours will finde acceptance with some , and i hope also with all honest and indifferent readers ; as for others , hap as hap may me , it is not to be doubted , but that i shall scape as well as many my betters have done before me . farewell . your wellwiller , j. b. to my friend the authour , upon his mysteries of nature and art. vvhen i scan over with a busy eye the timely fruits of thy vast industry , observing how thou searchest out the heart of knowledge , through th' untrodden pathes of art , how easily thy active minde discries natures obscure and hidden rarities , no greater wonder than thy selfe i finde , the chiefest rarity's thy active minde , which so fore-runs thy age . thy forward spring buds forth betimes , and thou art publishing ev'n in the morning of thy day , so soone , what others are to learne till th' afternoone . now since thy first attempts expos'd thou hast to publick censure , and the dy is cast , doubt not of good successe : the early rose ( thou knowst ) is snatcht at , ev'n before it blowes . climbe higher yet ; let thy quick-sighted eyes venture againe for new discoveries : nor be thou mizer-like , so envious , as to detaine what ere thou find'st , from us ; no , make the world thy debtor ; be thou still as open-handed to impart thy skill , as now thou art ; and may thy teeming braine bring often forth such lusty births againe . r. o. of water-works . it hath been an old saying amongst philosophers , and experience doth prove it to be true , non datur vacuum , that is to say , nature will not admit of any vacuity , or emptinesse . for some one or other of the elements , but especially ayre , and water doe insert themselves into all manner of concavities , or hollownesses , in , or upon the earth , whether they are such as are formed either by art or nature . for the one it is so obvious , and manifest , as that it needs not any proofe at all . as for the other , i shall make it manifest unto you by easie demonstration . let there be gotten a large vessell of glasse , or other , having besides the mouth another hole ( though but a little one ) at the top : poure water into the vessell by a tunnell thrust into the mouth of it , and you shall finde that as the water runneth into the vessell , a winde will come forth of the little hole , sufficient to blow out a candle being held over it . this proveth , that before the water was poured into the vessell ( though to our sight it appeared to bee empty ) it was full of ayre , which forced out of the vessell as the water ran in ; and the reason hereof is , because the water is by nature of a massie , subtill , substance ; and the ayre of a windy , light , evaporative nature : the knowledge of this , with the rarifaction of inclosed ayre , is the ground and foundation of divers excellent experiments not unworthy the knowledge of any ingenious artist whatsoever . the order of the things contayned in the first booke . experiments of drawing water by the crane . experiments of drawing water by engins . experiments of forcing water by ayre compressed . experiments of forcing water by engins . experiments of producing sounds by ayre and water . experiments of producing sounds by evaporation of water by fire . experiments of producing sounds by engins . experiments of motions by evaporating water . experiments of motions by rarifying ayre . of vvater-workes . to draw water by a crane . take any vessell , of what bignes you please , fill it with water , then take a crane ( that is a crooked hollow cane ) one end wherof , let be somewhat longer then the other ; put the shorter end of it into the vessell of water , and let the longer end hang out of the vessell , unto which longer end , put your mouth , and draw in your breath , and the water will follow ; then withdraw your mouth , and you shall see the water runne so long , till it come equall to that end of the cane which is within the vessell . another . take a deepe vessell , having two loopes on one of the sides , fill it nigh full with water : then take a hollow cane , like unto the aforesayd , but let there bee fastned unto the shorter end a wooden dish ; put the longer end heereof through the loopes on the side , and that end that hath the dish fastned unto it into the vessell of water , with your mouth as you did in the former , draw out the ayre , and you shall see that as the water runneth out , the crane will sinke lower and lower , and so will continue running untill the vessell bee drawen empty . how to make a conceited pot , which being filled with water , will of it selfe run all out ; but not being filled will not run out . make , or cause a pot to bee made of what fashion best liketh your mind , and make a large hollow cane to stand up in the midst thereof ; having at the bottome 2 or 3 small holes ; let the top of this cane be close : then make a hole in the bottome of the vessell , and put up a little cane hollow at both ends , into the other cane , so that the one end therof may almost touch the top of the great cane , and it is done . note , that if you put into this vessel so much liquor , that it swimme above the top of the cane , it will of its owne accord , run and never cease so long as there is any liquor in the vessell ; but if you fill it below the cane , it will not run at all of it selfe : the reason whereof is this ; the ayre being the lighter element , doth ascend into the higher place , but being drawne as in the two first demonstrations out of the crane , or forced , as in this , by the weight of the water in the vessell , the water then tendeth downewards unto its proper place . how to dispose 2 vessels upon one foot , that 〈…〉 wine may runne out of the one , as you shall put water into the other . let a , b , c , d , be the foot , at each end whereof , place a vessell equall in bignesse , the one to the other ; as d , e ; also let there passe a hollow cane from the one to the other , as a , r , a , the ends wherof must almost touch the tops of the sayde vessels ; in the vessell d , there must bee a hollow pipe , as f , whereby you may by help of a tunnel powr water into the vessell : also in the vessell e , there must be a crane , as g ; now if you fill the vessel e with wine almost unto the top of the crane , and afterwards stoppe the mouth of the vessell , that the ayre may not breath foorth , it will not run of it selfe : but if you put water into the vessell d , the ayre contayned in it , will passe through the hollow pipe , a , r , a , into the vessel e , where striving for a greater quantity of roome , it presseth the wine out of the vessell e , ( by the crane ) answerable in quantity unto the water powred into the vessell d. how to dispose 2 vessels upon one foot , the one being empty , and the other almost full of wine , and yet shall not runne out of the vessell , unlesse you fill the empty vessell with water , and then the one shall run pure wine , the other fayre water . let there bee 2 vessels placed upon one foot , having a hollow cane passing from one to the other ( as i taught in the precedent probleme ) but let there bee 2 cranes as f , g , one in each vessell ; then fill one of the vessels with wine , but not above the crane , so it will not runne of it selfe : but if you powre water into the other vessell , untill it bee full , it will cause that wine shall runne out of the one , and cleare water out of the other . to make that the water conteined in one vessell , shal ascend into another vessell placed above it . let a , b , c , d , bee a vessell having a partition in the middle , as e , f , let there be placed upon this vessell , a cylinder of glasse cleare , and very transparant , that will contayne the same quantity of water , that one of the partitions will , as i , g , h ; in the lowermost partition towards the bottome , let there bee a cocke , and out of the same vessell let two pipes be made to passe , the one wherof reacheth almost unto the top of the cylinder , the other must come out by the side of the cylinder : also out of the upper partition there must come another pipe . moreover there must be a hole , through the top of the uppermost partition as y. fill the lower partition at the pipe , also the upper partition by the hole y : note then that if you turn the cocke as the water runneth out of the lower partition , the water contained in the upper partitiō wil ascend throgh the pipe into the glasse cylinder . when all the water in the lower partition is runne out at the cocke , then the water which before did ascend into the cylinder , will fall backe againe into the upper partition : after this manner may you compose an artificiall water clocke , if you note the howres upon the cylinder , and make the cocke after such manner , as that the water may issue out but by droppes . to make a cup or vessell that so oft as you take the liquor out of it , so oft it shall fill it selfe , but never runne over . svppose a to bee a vessell full of water , having a pipe comming from the bottome , and rising up into a cup of the just height that the vessell is of ; over the vessell fild with water , let there be placed another vessel , as e. from this vessell must come a pipe , and reach with in the other vessell . now ouer this vessell there hangeth , as it were , the beame of a scale ; at the one ende whereof , is fastened a peece of boord , hauing a leather nayled upon the top ; at the other end of this beame must hang a weight , but not full so heauie as the peece of boord lethered is . fill both these vessells with water , and the cup also ; note then , that if you sucke out the water in the cup by the pipe on the side of it , the water in the vessell will come into it , untill it is in both of equall height : now as the water falleth downe in a , the peece of boord that is hanged unto one end of the beame falleth after it ( because it is heauier then the weight ) and so giueth way unto the water in e , which runneth into it ; and when the vessell is filled againe with water , it beareth up the sayd peece of boord against the pipe of the vessell e , so that the water can run out thereat no longer , except the water bee againe drawne out of the cup ▪ of drawing water by engines . before i begin with these , take a word or two by the way . let it bee a generall notion that no engine for water workes of what sort soeuer , whether for seruice , or meere pleasure , can be made without the help of succurs , forcers , or clackes ; euery of which , i haue orderly explayned both by words and demonstratiue figures . a succur is a box , which is made of brasse ( hauing no bottome ) in the middest of which , there is a small bar goeth crosse , the same hauing a hole in the middle of it ; this box hath a lid so exactly fitted unto it , that being put into it , no ayre nor water can passe betweene the creuise : this couer hath a little button on the top , and a seame that goeth into the box , and so through the hole of the aforesayd crosse barre , and afterwards it hath a little button riueted on it , so that it may with ease slip up and downe , but not be taken , or slip quite out . a forcer is a plug of wood exactly turned and leathered about ; the end that goeth into the barrell , is semicircularly concaue . a clacke is a peece of leather nayled ouer any hole , hauing a peece of lead to make it lie close , so that the ayre or water in any vessell may thereby bee kept from going out . how to harden leather , so as the same shall last much longer in succurs of pumps , then it doth unprepared . lay such leather as is well tanned to soake in water , wherein there hath beene store of iron filings a long time , or else in the water that hath lien a long time under a grinstone , into the which such yron as hath beene from time to time ground away , hath fallen and there setled . the making of a pumpe to draw water . svppose a b c were a deepe wel , wherein you would make a pumpe to draw water to the surface or superficies of the earth . first therefore you must prouide a pipe of lead , or a peece of timber bored through , so long as will reach unto the bottome of the well : that part that standeth in the water must bee cut with two or three arches , as it were , if it be wood ; if leade , it must haue somewhat to beare it a little from the bottome , that the water may thereby bee let into the pipe . towards the bottome of the pipe in the water there must bee fastned a succur ; also another of these succurs must be fastned about two foot aboue the top of the ground ; then haue a bucket fitted unto the hole of the wood or leaden pipe ; let it bee well leathered about , and haue a clacke at the bottome of it , and let it bee hanged with a sweepe as the figure sheweth : note that after you haue filled the distance betweene the lower succur , and the bucket with water , that if you lift up the sweepe , it will thrust downe the bucket upon the water , and presse it , the water being pressed upon by the bucket , beareth up the clacke , and comes into the bucket ; then if you pull downe the sweepe , the clacke shutteth , and so the water remaynes in the bucket , which being drawen upward , there being nothing to follow but water , both the succurs open , and there commeth into the pump so much water as the buckets drew out . the making of an engin , whereby you may draw water out of a deepe well , or mount any river water , to be conveyed to any place within three or foure miles of the same . also it is used in great ships which i have seene . svppose a b c d to be a deepe well , and e f to be a strong peece of timber fastned athwart the same , a good way in the water . in this planke let there bee fastened a peece of timber with a strong wheele in it , as g h , hauing strong yron spikes droue athwart the wheele within the creuise , and strongly riueted on each side : let them be three or foure inches distant from each other . let there bee likewise made in the sayde planke two holes , in which set two hollow posts , that may reach to the top of the well , or so much higher as you desire to mount the water ; let them bee made fast that they stirre not . in the bottom of one of these posts , there must be fastned a barrell of brasse , as g h , made very smooth within , and betwixt those two posts at the top ; let there bee fastned unto them both another peece of strong timber to hold them fast , lest they start asunder ; and in the midst of that make a mortice , and in it fasten a strong peece of timber with a wheele like to the former mentioned ; the pin whereof ought to bee made fast unto the wheele , and haue a crooked handle to turne about , that by turning of it , you may turne the wheele also . then prouide a strong yron chayne of length sufficient , hauing on euery third or fourth linke a peece of horne , that will easily goe through the brasse barrell , and a leather of each side of it , but somewhat broader then the horne ; put this chayne under the lower wheele in the well upon both the hollow posts , draw it ouer the upper wheele , and linke it fast and straight . turn then the handle round , and it will turne the chayne round , whose leathers comming up the brasse barrell , will beare the water before them ; this goeth very strongly , and therefore had neede bee made with wheeles and wrought upon by horses , for so the water is wrought up at broken wharfe in london . to make an engin , which being placed in water will cast the same with violence on high . let there be prepared a strong table , with a sweepe fastened at the one end thereof , to lift up and downe ; unto the end of the sweepe , let there be linked a peece of yron hauing two rods of length sufficient ; let there bee made a hole quite through the midst of this table , whose diameter let be about fiue or six inches ; then prouide two peeces of brasse in forme of hattes , but let the brim of the uppermost be but about one inch broad , and haue diuers little holes round about it ; also in the crown of this must bee placed a large succur , and ouer it a half globe , frō the top of which , must proceed a hollow trunke aboute a yard long , and of a good wide bore ; then take good liquored leather , 2 or 3 times double , & put betweene the board and the brims of this , and with diuers little screws put through the holes of the brimme , screw it fast unto the top of the table . note that the table must bee leathered also underneath the compasse of the brimme of the lower brasse . now the lowermost brasse must be of equal diameter ( in hollownesse ) unto the other , but it must be more spirall towards the bottome , and must haue eyther a large clacke or succur fastned in it ; also the brim of this must be larger then that of the uppermost , and haue two holes made about the midst on each side one ; bore then 2 holes in the table , on each side of the brasse one , answerable unto the holes of the brim of the lower brasse , throgh which holes put the two rods , of the yron hanged unto the sweepe through them , and riuet them strongly into the holes of the lower brasse . place this in water , and by mouing the sweepe up and downe , it will with greater violence cast the water on high . experiments of forcing water by ayer compressed . let there bee a large pot or vessell , hauing at the side a peece of wood made hollow , hauing a clacke of leather with a peece of lead upon it , within the vessell also let there be a pipe through the top of the vessell , reaching almost to the botom of it : at the top of which let there be a round hollow ball , and on it a small cocke of brasse . note that if you fill the said vessell halfe-full of water , and blow into the hole of the pipe , at the side , your breath will lift up the clack , and enter the vessell , but when it is in , it will presse down the clack : blow into it oftentimes , so shall there bee a great deale of ayre in the vessell , which will presse so hard upon the water , that if you turne the cock at the top , the water in the vessell will spin out a good while . another . let a , b , c , d , be a great vessell , having a partition in the middle : let there bee a large tunnell at the top of it , e , f , whose neck must go into the bottom almost of the lower vessell : let there be a hollow pipe also coming out of the partition , and almost touch the top of the upper vessell . in the top of the upper vessell let there bee another pipe , reaching from the bottom of the upper vessell , and extending it selfe out of the vessell a good way : let the top of it hang ouer the tunnell . in the top of the upper vessell let there be a hole besides , to be stopped with cork , or otherwise : when you will use it , open the cork-hole , and fill the upper vessel with water : then stop it close againe , and poure water into the tunnell , and you shall see that the water in the upper vessell will run out of the pipe into the tunnell againe . and so will continue running untill all the water in the upper vessell be run out . the reason thereof is this ; the water in the tunnell pressing the ayre in the lower vessell , maketh it ascend the pipe in the partition , and presse the water in the upper vessell , which having no other way but the pipe , it runneth out thereat . the forcing of water by pressure , that is the naturall course of water in regard of its heavinesse and thinnesse , artificially contrived to break out of what image you please . let a , b , c , d , bee a cestern placed upon a curious frame for the purpose , let the bottom of this frame be made likewise in the form of a cestern : through the pillers of this frame let there passe hollow pipes from the bottom of the upper cestern , and descend to the bottom of the lower cestern , and then run all to the middle thereof , and joyne in one , and turne up into the hollow body of a beast , bird , fish , or what your fancy most affecteth : let the hole of the image whereat the water must break out , be very small , for so it will run the longer . fill the upper cestern with water , and by reason of the weight thereof it will passe through the pipes , and spin out of the hole of the image . experiments of forcing water by engins . let there bee an even streight barrell of brasse of what length and bignesse you please : let the bottom of it be open , and let the top be closed , but so that it be hollow on the outside like a basin : in the midst whereof let there bee a straight pipe erected , open at both ends , also let there be another short pipe at the side of it , which let bee even with the top of the basin on the outside , but stand a little from it on the side having thus prepared the barrell , fit a good thick board unto it , so that it may slip easily up and down from the top of the barrell unto the bottom , nayle a lether about the edges of it , and another upon the top of it : on the underside of it let there be fastned a good stiffe , but flexible spring of steele , which may thrust the board from the bottom to the top of the barrell : let the foot of this spring rest upon a barre fastned acros the bottom of the barrell ; let this board also have tied at the middle a little rope of length sufficient . when you use it , bore a little hole in the table that you set it on , to put the rope thorow , and pull the rope down , which will contract the spring , and with it draw down the board : then poure in water at the basin untill the vessell be full : note then , as you let slack the rope , the water will spirt out of the pipe , in the middle , and as you pull it straight , the water will run into the vessell againe . you may make birds , or divers images at the top of the pipe , out of which the water may break . another manner of forcing water , whereby the water of any spring may be forced unto the top of a hill . let there be two hollow posts , with a succur at the bottom of each , also a succur nigh the top of each : let there be fastned unto both these posts a strong peece of timber , having , as it were , a beame or scale pinned in it , and having two handles , at each end one . in the tops of both these hollow posts fasten two brasse barrels , made very even and smooth within , unto these two barrels let there be fitted two forcers , lethered according to art , at the tops of these forcers must be fastned two yrons , which must bee linked unto the aforesaid beam ; from each post below towards the end of the barrels , let there bee two leaden pipes , which afterward meet in one , to conduct the water up to the place desired , which if it bee very high , there will be need of some succurs to catch the water as it cometh . the description of an engin to force water up to a high place : very usefull for to quench fire amongst buildings . let there be a brasse barrell provided , having two succurs in the bottom of it ▪ let it also have a good large pipe going up one side of it with a succur nigh unto the top of it , and above the succur a hollow round ball , having a pipe at the top of it made to screw another pipe upon it , to direct the water to any place . then fit a forcer unto the barrell with a handle fastned unto the top ; at the upper end of this forcer drive a strong screw , and at the lower end a screw nut , at the bottom of the barrell fasten a screw , and at the barre that goeth crosse the top of the barrell , let there be another screw nut : put them all in order , and fasten the whole to a good strong frame , that it may stand steddy , and it is done . when you use it , either place it in the water , or over a kennell , and drive the water up to it , and by moving the handle to and fro , it will cast the water with mighty force up to any place you direct it . experiments of producing sounds by ayer and water . let there bee had in a readinesse a pot made after the forme of the figure following , having a little hole at the top , in the which fasten a reed or pipe , also another little hole at the bottom : presse this pot into a bucket of water , and it will make a loud noyse . another let there be a cestern of lead or such like , having a tunnell on the top : let it bee placed under the fall of a conduit , and at the one end of the top , let there come out of the vessell a small pipe , which let bee bent into a cup of water , and there will be heard a strange voice . over this pipe you may make an artificiall tree with diuers birds made to sit therein . how to make that a bird sitting on a basis , shall make a noise , and drink , out of a cup of water , being held to the mouth of it . provide a cestern , having a tunnell at the one end of the top , and a little cane coming out of the other end of the vessell ; on the top of which let there be a bird made to sit , also at the bottom of the cestern , let there bee a crane to carry away the water as it runneth into the vessell . place this vessell with its tunnell under the fall of a conduit of water , and the bird will sing ; and if you hold a cup of water under his bill , hee will drink and make a noise . a device whereby severall voyces of birds cherping may be heard . prepare a cestern having divers partitions , one above another ; let them all have cranes in the bottoms to carry the water from one to another ; also let each cestern have his severall pipe , all of them coming out at the top of the cestern , on whose tops let birds bee artificially made , with reeds in them : also in the top of the upper cestern let there bee a tunnell . place it under the fall of a conduit of water , and you shall heare so many severall voyces as there are birds . a device whereby the figure of a man standing on a basis shall be made to sound a trumpet . prepare a cestern having within on the lid fastned a concave hemisphere , in whose bottom let there bee made one or two holes : let there also be a hole in the top of the sayd cestern , whereby it may bee filled with water as occasion serveth . also let there bee made to stand on the top of this cestern the image of a man holding unto his mouth a trumpet : this image must likewise have a slender pipe coming out of the cestern unto the trumpet , in this pipe or cane there must be a cock , nigh unto the cestern . also there must come out of the concave hemisphere at the side of the cestern , a little short pipe , having a clack on it within the vessell . fill the cestern about two thirds full of water , and then cork it up fast , blow then into the vessell at the pipe on the side divers times , and the ayer will force the water out of the hemisphere , and make it rise up on the sides of it ; turne then the cock , and the weight of the water will force the ayer out of the pipe , and so cause the trumpet to sound . hercules shooting at a dragon , who as soone as he hath shot , hisseth at him . let there be a cestern having a partition in the midst , in the partition let there bee a deep succur , having a small rope fastned unto the top of it : let the one end of the rope come out of the upper lid of the cestern , and bee fastned unto a ball , the other part thereof let it be put under a pulley ( fastned in the partition ) and let it be carried also out of the upper cestern , and be fastned unto the arme of the image , which must bee made to slip to and againe , and to take hold of the string of a steele bow that is held in the other hand . at the other end of the cestern let there bee made an artificiall image of a dragon , through whose body must come a small pipe with a reed artificially fastned in the upper part thereof . note then , that when you put up the ball , the image will draw his bow , and when you let it fall , the dragon will hisse . experiments of producing sounds by evaporation of water by ayer . prepare a round vessell of brasse , or latin , having a crooked pipe or neck , whereto fasten a pipe : put this vessell upon a trevet over the fire , and it will make a shrill whistling noyse . to make two images sacrificing , and a dragon hissing . prepare a cestern having an altar of brasse or tin upon it , let therebe in the cestern a hollow pipe turning up out of the cestern at each end ; also in the middle within the altar , also on the side of the altar into the body of a dragon artificially made , with a reed in the mouth of it . let there bee two boxes at the tops of the pipes , on the ends of the cestern , having two crooked pipes or cranes comming out of them . fill the boxes with water when you occupy it , also put fire upon the altar , and the dragon will hisse , and the water in the two boxes being wrought upon by the heat of the fire comming thorow the pipes , will drop into the fire . these two boxes ought to be inclosed in the bodies of two images , and the two short cranes comming out of them in her armes and hands . experiments of producing sounds by engins . prepare a vessell after the forme of the figure marked with the letters a , b , c , d , place it upon a frame , as f , g , h ; this vessell must have a hole in the bottom , with a pipe fastned in it , as q , to convay the water conteyned in it into a vessell or tub set under it , marked with the letters r , s , t , also a frame must bee fastned at the top of it , as g , h , l , having so many bels with little beaters or hammers to them ( artificially hanged ) as are requisit to expresse your de-desired tune . lastly provide a sollid peece of timber , whose lower part must bee fitted unto the aforesayd vessell , so that it may easily slip up and down , and so high as that its foot resting upon the bottom of the vessell , the upper part thereof may stand somewhat above all the bels . note likewise that that part of this wood aboue its bottom or foot must be cut away about three quarters of an inch . vpon this wood thus fitted must bee fastned severall pins equall unto each bell , from the top unto the foot thereof , so disposed that they may orderly presse down the inward ends of the hammers of each bell , according as the tune goeth : when you use it , fill the cestern almost with water , and put the fitted peece of timber into it , and as the water runneth out at the bottom , it it will play upon the bels : note that it were very requisit to haue a cock fastned to the pipe on the bottom of the vessell , that therewith you might at your pleasure stay the water . the like engines might be made to play upon wyer strings disposed upon a concavous water , to make the musick resound , but because this description giueth light enough for the framing of diuers other , i thought good here to omit them . experiments of motions by rarifying water with fire . let there be an altar having a pipe comming out of it , and entring the body of a hollow ball , let there come out of the same ball a crane , whose lower end make to hang ouer a bucket fastned to a rope , and hanging ouer a pulley , of which rope the other end must bee wound about two spindles , hauing two doores fastned unto them , and at the and of the same rope let there bee a waight fastned . so the fire on the altar will cause the water to distill out of the ball into the bucket , which when by reason of the water it is become heuier then the weight , it will draw it up , and so open the said gates or little doores . experiments of motions by rarifying ayre by fire . let there be a round vessell of glasse , or horn , and on the top of it a vessell of brasse , and in the midst a hollow pipe spreading it selfe into foure seuerall branches at the bottom : the ends of two of the branches must turn up , the ends also of two must turn down ; upon these foure branches fasten a light cord , with seuerall images set upon it . rarifie the ayre thē by laying a red-hot iron upon the top of the brasse or tin vessell , and it will turn the wheele about , so that you would think the images to bee living creatures . another way . first prepare a round peece of wood , hauing a brasse box in the midst , such as they make to hang the mariners compasse with , but a good deale bigger , round about this peece of wood fasten divers shreds of thin lattin , standing obliquely or ascew , as the figure doth represent ; round about these fasten a coffin of thin pastbord , cut into seuerall formes of fishes , birds , beasts , or what you please . prepare a lantern with oyled parchment , sufficient to conteine it , in the midst of whose bottom must bee erected a spindle with a narrow point , to hang the pastbord cut into formes upon : upon each side let there be a socket for to set a candle in , also let there bee made a doore in the bottom to put the candles in at , and after to be shut , and it is done . if you set two candles in the sockets , the heat of them will turne the whole pastbord of formes round . amongst all the experiments pneumaticall , there is none more excellent than this of the weather-glasse : wherefore i haue laboured to describe the making thereof as plainly as it possibly might be . what the weather-glasse is . a weather-glasse is a structure of , at the least , two glasses , sometimes of three , foure , or more , as occasion serueth , inclosing a quantity of water , and a portion of ayre proportionable , by whose condensation or rarifaction the included water is subject unto a continuall motion , either upward or downward ; by which motion of the water is commonly foreshewn the state , change , and alteration of the weather . for i speak no more than what mine experience hath made me bold to affirme ; you may ( the time of the yeere , and the following obseruations understandingly considered ) bee able certainly to foretell the alteration or uncertainty of the weather a good many houres before it come to passe . of the severall sorts and fashions of weather-glasses . there are diuers seuerall fashions of weather-glasses , but principally two . 1 the circular glasse . 2 the perpendicular glasse : the perpendiculars are either single , double , or treble . the single perpendiculars are of two sorts , either fixt or moueable . the fixt are of contrary qualities ; either such whose included water doth moue upward with cold , and downward with heat , or else upward with heat , and downward with cold . in the double and treble perpendiculars , as the water ascendeth in one , it descendeth as much or more in the other . in the moueable perpendicular the glasse being artificially hanged , moueth up and down with the water . how to make the water . i must confesse , that any water that is not subiect unto putrifaction , or freezing , would serue the turne , but art hath taught to make such a water as may bee both an ornament to the work , and also delectable to the eye . take two ounces of vardigrease in powder , and infuse it so long in a pint of white wine vineger , untill it hath a very green colour , then poure out the vineger gently from the vardigrease : take also a pint and a halfe of purifide may-dew , and put therein 6 ounces of roman vitreoll in grosse powder , let it stand till the vitreoll bee throughly dissolved ; then mix this with the former water , and strain them through a cap paper , and put it into a cleane glasse well stopped , and ' its ready for use . another . take a gallon of rayn water that hath setled , infuse therein a day and a night 4 pound of quick lyme ; stir it about with a cleane stick oftentimes in the day ; in the morning poure the cleere water off from the lyme , into a brasse pan , and adde thereto 3 pound of sal armoniack ; let it stand fiue or six houres , afterwards stir it about untill it be of a perfect blew colour , then straine it through a browne paper rowled within a tunnell , and reserue it for your use . this water is not so good for use as the former . how to make the circular glasse . first you must prepare two glasses , the fashion whereof let be like unto the figures marked with the letters a , b , and c , d. the glasse c , d , is open at both the ends , also in the middle there is a neck comming up of sufficient widenesse to receiue the shank end of the glasse marked with the letters a , b. then fill the glasse c , d , a third part , with either of the waters , and diuide the glasse into so many equall parts as you would haue degrees ; rarifie the ayre in the head of the glasse a , b , by holding it to the fire , which being yet warme , reuerse the shank of it into the neck of the glasse c , d. note that if the water do not ascend high enough , you must take the glasse a , b , out againe , and heat it hotter ; if it ascend too high , heat it not so hot . if it be in the dog-dayes , and extreme heat of summer , 1 and 2 are good degrees ; if the weather be most temperate , then 3 and 4 are best ; if a frost , 9 or 10. when you haue hit an indifferent degree , lute the joynts very close , and fasten a ribben unto the top of the glasse to hang it by . in this glasse the water will with cold ascend the glasse a , b , with heat it will descend the glasse a , b , and ascend the hornes of the glasse c , d. how to make the single perpendicular glasse , whose water ascendeth with cold , and descendeth with heat . prepare two glasses after the fashion of these figures underset , f , g , i , i. alwayes chuse those upper glasses that haue the least heads , else they will draw the water too fast , and presse it too low : also let not the shank of the glasse bee too wide : it is no matter to bee curious in chusing the lower glasse . hauing prouided both these glasses , make a frame for them about one inch longer than the shank of the glasse f , g , hauing a hole at the top to put the same thorow . there ought to be a great deale of care had in making the frame so , that the foot thereof may bee of a greater compasse than the top , to the end that it may stand firm , and not be subject to be turned down , which will distemper the whole work . after you have provided the frame , proceed to the making of it after this manner . put both the glasses into the frame , and then divide the shank of the glasse f , g , into so many equall parts as you would haue it haue degrees ; write figures upon paper , and paste them on ( with gum tragagant dissolued in faire water ; ) then fill the bottom glasse 2 thirds with the water , and rarifie the ayre in the glasse f , g , so often untill you haue hit such a degree as is most fitting for the temper of the weather , put in a little crooked hollow cane for the ayre to passe in and out at , but let it not touch the water : then stop it about the joynts of the glasse with good cement , that nothing may come out . make an artificiall rock about it , with peeces of cork dipt in glew , and rowled in this following powder , and it is done . the powder for the rock . take mother of pearle 2 pound , small red corall di ▪ pound , antimony crude 4 ounces , and make a grosse powder of them . to make the single perpendicular glasse , ascending with heat , and descending with cold . prepare two glasses after the fashion of the figure a , b , and c , d : let the glasse a , b , haue a small pinhole at or about the top of all , and let the glasse c , d , haue besides the hole at the top , another hole at the bottom with a short pipe . prouide such a frame for this as you did before for the other ; then put the glasses into it , fasten the bottom glasse to the bottom of the frame , hauing a hole at the bottom , thorow which the pipe of the glasse c , d , may passe , fit a cork unto it : then lute the two glasses together , so that no ayre may passe between the joyning ; divide then the shank into so many degrees as you please , and figure it as before i taught you , then with the heat of a candle , rarifie the ayre in the glasse c , d , and fill it a third part full of water , and then put the cork fast in . note that if the first heating of the glasse rayse not the water unto your content , you must repeat it over and over , untill it doe : when it is sufficient , then stop the cork in very firm , that no water may come out , and it is made . how to make the double perpendicular glasse . prepare two glasses like unto the figure marked with the letters a , b , the one of them must have a small hole in or about the head thereof . prepare likewise for the bottom a vessell of the fashion of the figure g , h , having two mouthes , at each end one , also a cocke in the middle , as k : divide then the shank of the glasse without the hole in the top , into equall parts , and set figures upon it ▪ next lute them both fast into the necks of the bottom vessell . ( but first remember to put them in a frame : ) when the cement is dry turn the cock of the bottom vessell , and rarify the ayre in the glasse that hath no hole at the top ; then set the bottom vessell a little way into a vessell filled with water , and it will suck up the the water as it cooleth , when the bottom vessell is full , also the water mounted in that top glasse without a vent , up to a fitting degree ; ( the temper of the weather regarded ) then depresse ( but gently ) the glasses into the vessell of water , untill the water be come up into the glasse with the vent at the top sufficiently , that is , so that in both the glasses may bee contained so much water as will fill the shank of one , and about 2 or 3 degrees of the other ; then turne the cock , and take away the vessell of water from under them , let them down , and fasten the bottom vessell unto the bottom of the frame , and make a rock about it , or else what other works you please , that the art may not be discerned . lastly , set figures upon both , but first upon that without the vent , beginning from the bottom , and proceeding upwards , then lay your hand upon the head of it , which will depresse the water , which when it commeth equall to the degrees , paste the same degree on the place of the water in the other glasse with the vent , and it is done . after the same manner is the treble glasse made : but whereas in the double glasse there was but one glasse that had a vent at the top , there is two in this , both whose shanks must contain the iust quantity of water that the glasse without the vent will containe . if you do well obserue the form of the subsequent figure , you cannot goe amisse . how to make the moveable perpendicular glasse . first prepare the glasse a , b , fill it almost top-full of water , provide also the glasse k , l , having a loop at the top of it : divide it into so many equall parts as you would haue degrees , and on the mouth thereof fasten a thin board , that will easily slip in and out of the bottom glasse , make then a waight of lead or brasse somewhat heavier than both the glasse and board fastned thereto ; and then tie a little rope to the loop of the glasse a , b , and the waight at the other end thereof . rarify the ayre contained in the glasse l , and reverse it into the glasse a , b , filled with water , and hang the plummet over two little pulleys fastned in a frame made for the purpose , and as the glasse k , l , cooleth , the water will ascend the same , and so by the change of the outward both the glasse and water will move accordingly . of the use of all the severall sorts of weather-glasses . albeit the formes of weather-glasses are divers , according to the fancy of the artist , yet the use of all is one and the same : to wit , to demonstrate the state , and temper of the season , whether hot or cold ; as also to foreshew the change and alteration thereof . 1 note therefore , that the nature and property of the water in all the glasses that have no vent holes at the top , is , to ascend with cold , and descend with heat . but in them that have vents , it descendeth as much as it ascendeth in these . 2 the sudden falling of the water is an evident token of rayne . 3 the continuance of the water at any one degree , is a certaine token that the weather will continue at that stay it is then at , whether it be fayre , or foule , frost or snow . but when the water either riseth or falleth , the weather will then presently change . 4 the uncertaine motion of the water is a signe of fickle weather . the single perpendicular with a vent , moveth upwards with cold , and downwards with heat , and is quite contrary in quality to the former , only that it moveth uncertainly in fickle and uncertaine weather , and keepeth a constant place in stayed weather . these rules are all certaine and true : now you may according to your owne observation frame other rules , whereby you may foretell the change of the weather the water being at any one degree whatsoeuer . a water-clock , or a glasse shewing the houre of the day . let there be provided a deepe vessell of earth , or any thing else , that will hold water , as a , b , c , d , provide also a glasse made after the fashion of the figure marked with the letters e , f , g. it must bee open at the bottom , and haue also a small hole at the top , thorow which if you can but put the point of a needle , it is sufficient . this glasse must not bee so long as the vessell is deepe , by about two inches . then take a iust measure of the length of the glasse k , ● , g , and set it on the inside of the vessell a , b , c , d , from the bottom towards the top , and then make a rase round about the vessell ; there must bee fitted unto this earthen vessell , a pipe reaching from the top of the outside thereof , ( where there must bee a cock unto it ) and going to the bottom , where it entreth the same , and againe extendeth it selfe almost unto the circle or mark rased on the vessell a , b , c , d. fill then the vessell with fayre water up to the rase , or circle , and turne the cock , and put the glasse into the water , and you shall see that the glasse by reason of its heavinesse , will tend toward the bottom of the vessell , but very slowly , by reason that the ayre contained therein hath so small a vent : turne an houre-glasse , and at the end of each houre make a mark upon the glasse equall with the water , and it is done . when the glasse is quite sunke to the bottom of the water , turn the cock , and with one blast of your mouth at the pipe , it will ascend againe . another fashioned one . prepare a vessell , as a , b , c , d , having a very small cock unto it , whose passage ought to bee so small , as that the water might issue out but by drops . prepare likewise a vessell , as e , f , g , h , having at one end of it a piller of a foot and a halfe , or two foot high : let there be fitted unto this vessell a board , so that it may freely without stay , slip up and down : towards one side of this board , there must be a good big hole , which must bee placed under the cock of the other vessell . then fasten unto the top of this board , the image of time or death , and pointing with a dart upon the piller aforesaid : turn then an houre glasse , and at the end of every houre , make a figure on the place of the piller that the image with his dart pointeth at , and it is made . for note , the dropping of the water out of the cock thorow the hole of the board whereon the image standeth , causeth the same to ascend by little and little . mark the figures . another artificiall water-clock , which may bee set conveniently in a double weather-glasse . first prepare a cestern , as a , b , c , d , partition in the middle , let there bee made two pipes , the one whereof must reach out of the upper cestern , and descend almost to the bottom of the lowest cestern , as i , k ; the other must be a short one , and haue a very small hole , that the water may thereby issue out of the upper cestern but by drops ; also at the side nigh the bottom of the upper cestern , let a small pipe enter . to the upper cestern fit a board , ( with a peece of lead nayled upon it to make it somewhat heavy ) so that it may easily slip up and downe in it ; this board must haue a loop to fasten a rope unto , and you must so poyse the said board , that it being hung up by a line , may hang even , and levell . then prepare a box to put ouer the cestern , which ought to stand about six inches aboue the cestern . in the top of this box let there be fastned a long pulley with a creuice to put a small rope ouer , in this creuice it were fitting to fasten small pins , to the end that the rope might turn the sayd wheele as the water faleth from under the board : let the spindle of this pulley come out at one side of the box whereon there is a dyall drawn , contayning so many houres as you would haue it go for ; unto this end of the spindle let there bee fitted a needle , or director , to shew the houre , then put a small cord ouer the pulley in the box , fasten one end thereof to the loop of the board , and at the other end let there bee tied a waight not quite so heauy as the board , then fill the upper cestern with water , and the board will presse it out into the lower vessell , at the pipe o , drop by drop , and as the board sinketh lower , it will by meanes of the rope upon the pulley , turne the index fastned unto the spindle of the pulley about the dyall ; you may set it by an houre-glasse or watch : when it is quite downe , if you doe with your mouth blow into the pipe at the side of the cestern , the water will all mount up againe into the upper cestern . a wheele which being turned about , it casteth water out at the spindle . let a , b , be a tub hauing in the bottom a brasse barrell , with a hole open quite through one side of it : let d , e , f , be a wheele , whose spindle must bee also hollow , and haue a hole through one side of it , so that being put into the hollow barrell , both the holes may be equall together . note then , that so long as these holes are equall together , the water will run out at the spindle of the tub , but if you turne the wheele to another side , it will not run . a water-presser , or the mounting of water by compression . let there bee prouided a barrell of brasse , of what length and widenesse you please , let it bee exactly smooth within , and very tight at bottom ; unto this barrell fit a plug of wood leathered about , and let there bee made diuers small holes quite through it , wherein fasten diuers formes and shapes of birds , beasts , or fishes , hauing very small pin-holes through them , for the water to spin out at : you shall do well to make this plug very heavy , either by pouring molten lead into certaine holes made for the purpose , or else by fastning some waight unto the top : fill the barrell with water , and put the plug into it , which lying so heavy upon the water , it will make it spin out at the pin-holes of the images placed thereupon . how to compose a great or little peece of water-worke . first prepare a table , whereupon erect a strong frame , and round about the frame make a moat with a leaden cestern to be filled with water ; let the leaden moat somewhat undermine as it were the frame , which ought to be built in three stories , one aboue another , and euery one lesser than another . within the middle story fasten a very strong iack that goeth with a waight , or a strong spring , the ending of whose spindles ought to be crooked , thus z , whereby diuers sweeps for pumps may bee moued to and againe , whose pumps must go down into the moat , and haue small succurs unto them , and convayances towards their tops , whereat the water may be mounted into diuers cesterns , out of some wherof there may be made convayances in their bottoms , by small pipes running down into the riuer or moat again , and there breaking out in the fashions and formes of dragons , swans , whales , flowers , and such like pretty conceits : out of others the water may fall upon wheeles , out of whose spindles , the water turning round , may bee made to run . in the uppermost story of all , let there bee made the forcer by ayre , as i taught before , or else a presser , hauing at the top , neptune riding on a whale , out of whose nostrils , as also out of neptunes trident , the water may be made to spin through small pin-holes ; you may also make diuers motions about this work , but for that the multitude of figures would rather confound than instruct the reader , i haue of purpose omitted them . the second booke , teaching most plainly , and withall most exactly , the composing of all manner of fire-works for triumph and recreation . by i. b. london , printed by thomas harper for ralph mab. 1634. to the reader . courteous reader , there hath a desistance been occasioned since the inception of this work , by reason of the occurrence of certaine authours , that contrary unto my knowledge had laboured so fully herein ; but after consideration had ( that for the most part they were but translations ) i thought it might bee no lesse lawfull and commendable for mee than for others , to communicate unto such as are yet desirous of further information , that wherein i have bestowed both cost and paines . notwithstanding , i haue so used the matter , as that i might not derogate from the estimation had of others to increase mine owne . read it throughly , iudge indifferently , and if thou likest it , practise considerately . if thou art ignorant herein , i am sure it will instruct thee , and though well experienced ( which perhaps thou art ) i make no question , but that thou mayst finde somewhat which thou hast not heard of before ; so farewell . your wellwiller i. b. of fire-workes . i haue euer found ( in conference with diuers desirous of instruction in any art or science whatsoeuer ) that the summe and chiefest end of all hath been , to know the reasons and causes of those things they were desirous to be informed in . wherefore i thought good , before i came to the matter it selfe , to set down some few praecognita or principles ( as i may so call them ) whereby such as are ingenious , upon occasion , may informe themselues , if they stand in doubt of the cause of any thing that is heereafter taught . certayne praecognita or principles , wherein are contayned the causes and reasons of that which is taught in this booke . 1 the foure elements , fire , ayre , earth , and water , are the prima principia ( i meane the materialls ) whereof euery sublunary body is composed , and into the which it is at last dissolued . 2 euery thing finding a dissolution of those naturae catenae , that is , meanes whereby their principia are connected , and ioyned together , their lighter parts ascend upward , and these that are more grosse and heauy , doe the contrary . 3 it is impossible for one and the selfe same body to possesse at one time two places ; it followeth therefore , that a dense body rarified , and made thin , eyther by actuall or potentiall fire , requireth a greater quantity of room to be conteyned in , then it did before . hence it is , that if you lay your hand upon a glasse , hauing a straight mouth reuerst into a dish of water , it rarifieth the ayre contayned therein , and makes it breake out thorough the water in bubbles . also , that gunpowder inclosed in the barrell of a gun , being rarified by fire , applied unto the touch-hole , it seeketh a greater quantity of roome , and therefore forceth , the bullet out of the barrell . this is called violent motion . 4 according unto the strength and quantity of a dense body rarified , and according unto the forme and length of its inclosure , it forceth its compresser further or neerer at hand . thus much shall suffice to haue spoken concerning the praecognita : now i will passe ad majora , & ad magis necessaria : to wit , those necessary instruments , and seuerall sorts of ingredients , that ought to be had in readines . as for the instruments they are these ; morters and pestles , serces , also seuerall sorts of formers , paper , parchment , canuas , whipcord , strong binding thread , glew , rosin , pitch , with diuers vessells meet to contayne and mingle your compositions in . the ingredients likewise are chiefly these , saltpeter , rochpeter , sulpher , charcoale , good gunpowder , filings of steele , oyle of peter , and spirit of wine . instructions for chusing your ingredients . saltpeter is very good , if that being layd upon a board , and fire put to , it rise with a flamed ventosous exhalation , raysing no scum , nor leauing no pearle , but onely a blacke specke burnt into the boord . the best brimstone , is quick brimstone , or li●e sulphur , and that sort is best that breaketh whitest ; if this cannot be gotten , take of the whitest yellow brimstone . the best coales for use are the sallow , willow , hazel and beech ; onely see they be well burnt . euery of these ingredients must be powdred finely and searsed . all kindes of gunpowder are made of these ingredients imposed , or incorporated with vineger , or aquauitae , and afterward grayned by art : the saltpeter is the soul , the sulphur the life , and the coales the body of it . the best sort of powder may be distinguished from others , by these signes : 1 if it be bright and incline to a blewish colour . 2 if in the handling it proue not moyst but auoydeth quickely . 3 if being fired , it flash quickly , and leaue no dregs nor setlings behinde it . a device to try the strength of divers sorts of gunpowder . 1 such as operate in the ayre , as rockets , serpents , raining fire , stars , petards , dragons , fire-drakes , feinds , gyronels , or fire-wheeles , balloons . 2 such as operate upon the earth , as crackers , trunks , lanterns , lights , tumbling bals , saucissons , towers , castles , pyramids , clubs , lances , targets . 3 such as burn in or on the water , as rockets , dolphins , ships , tumbling bals . part of either of the three kindes are simple , and part are compounded ; part also are fixed , and part moueable , first i will treat of the diuers compositions , and then of the formers , coffins , and manner of composing euery of them . of the divers compositions of fire workes . first of the compositions of fire workes , for the ayre ; and therein first i will speake of the compositions for rockets , because that all moueable fireworkes haue their motion from the force of them accordingly applied . compositions for rockets of all sizes , according unto the prescription of the noted professors , as mr malthus , mr norton , and the french authour , des recreationes mathematiques . a composition for rockets of one ounce . take of gunpowder , saltpeter and charcoale , of each one ounce and a halfe , mingle them together , and it is done . note heere , as i told you before , that all your ingredients ought to be first powdred by themselues , and afterwards mixed very well together . a composition for rockets of two and three ounces . take of gunpowder fowre ounces and a halfe , saltpeter one ounce , mixe them together . a composition for rockets of foure ounces . take of gunpowder fowre pounds , saltpeter one pound , charcoale fowre ounces , mingle them together . a composition for rockets of fowre ounces . take of gunpowder fowre poundes , saltpeter one pound , charcoale fowre ounces , brimstone halfe an ounce , mingle them together . a composition for all middle sized rockets . take of gunpowder one pound , two ounces of charcoales ; mingle them . a composition for rockets of five or six ounces . take of gunpowder two pound fiue ounces , of saltpeter halfe a pound , of charcoale six ounces , of brimstone and yron scales , of each two ounces , mingle them . a composition for rockets of ten or twelve ounces . take of gunpowder one pound and one ounce , saltpeter fowre ounces , brimstone three ounces and a halfe , charcoale one ounce , mingle them . a composition for rockets of one pound , or two . take of saltpeter twelue ounces , gunpowder twenty ounces , and charcoale three ounces , quicke brimstone and scales of yron , of each one ounce , mingle them . a composition for rockets of eight , nine and tenne pounds . take saltpeter eight pounds , charcoale two pounds twelue ounces , brimstone one pound fowre ounces . note that no practitioner ( how exact soeuer ) ought to relie upon a receipt , but first to trie one rocket , and if that be too weake adde more gunpowder , if it be too strong let him adde more charcoale untill hee finde them flie according unto his desire . note that the charcoale is only to mitigate the violence of the powder , and to make the tayle of the rocket appeare more beautifull . note also that the smaller the rockets be , they need the quicker receipts , and that in great rockets , there needeth not any gunpowder at all . the composition for middle sized rockets may serve for serpents , and for rayning fire , or else the receipt for rockets on the ground , which followeth heereafter . compositions for starres . take saltpeter one pound , brimstone halfe a pound , gunpowder fowre ounces , this must be bound up in paper or little ragges , and afterwards primed . another receipt for starres . take of saltpeter one pound , gunpowder and brimston of each halfe a pound ; these must be mixed together , and of them make a paste , with a sufficient quantity of oile of peter , or else of fayre water ; of this paste you shall make little balles , and roll them in drie gunpowder dust ; then drie them , and keepe them for your occasions . another . take a quarter of a pinte of aqua vitae , and dissolue therein one ounce , and a halfe of camphire ▪ and dip therin cotten bumbast , and afterwards roule it up into little balles ; afterwards rowle them in powder of quick brimstone , and reserue them for use . another receipt for starres , whereof you may make fiends and divers apparitions according unto your fancie . take gum dragant , put it into an yron pan , and rost it in the embers ; then powder it , and dissolve it afterwards in aqua vitae , and it will become a jellie , then straine it ; dissolve also camphire in other aqua vitae . mixe both these dissolutions together , and sprinkle therein this following powder . take saltpeter one pound , brimstone halfe a pound , gunpowder three pound , charcoale halfe a pound ; when you have mingled and stirred them well together , mixe them well with the aforesayd jelly , and then make it into little balles , or into what fashion else you please , then cool them in gunpowder dust , and keepe them for use . compositions for receipts of fireworkes , that operate upon the earth . for rockets there needeth onely gunpowder finely beaten and searced . likewise for all the other sorts , searced gunpowder will serue , which may be abated , or alayed with charcoal dust at your pleasure . compositions for fireworkes that burne upon , or in the water . a receipt for rockets that burne upon the water . take of saltpeter one pound , brimstone halfe a pound , gunpowder halfe a pound , charcoales two ounces . this composition will make the rockets appeare with a great fiery tayle . if you desire to have it burne cleare , then take of saltpeter one pound , three ounces of gunnepowder , brimstone halfe a pound . a receipt of a composition that will burne , and feed upon the water . take masticke halfe a pound , white frankincense , gum sandrake , quickelime , brimstone , bitumen , camphire , and gunpowder , of each one pound and a halfe , rosin one pound , saltpeter fowre pounds and a halfe , mixe them all together . a receipt of a composition that will burne under water . take brimstone one pound , gunpowder nine ounces , refined saltpeter one pound and a halfe , camphire beaten with sulphur , and quicksilver ; mixe them well together with oyle of peter , or linseed oyle boyled , untill it will scald a feather . fill a canvas ball with this composition , arme it , and ballast it with lead at the bottome , make the vent at the top , fire it well and cast it into the water , and it will fume and boyle up slowly . a receipt of a composition that will kindle with the water . take of oyle of tile one pound , linseed oyle three pounds , oyle of the yelks of egges one pound , new quick lime eight pounds , brimstone two pounds , camphire fowr ounces , bitumen two ounces ; mingle all together . another . take of roch peter one pound , flowre of brimstone nine ounces , coales of rotten wood six ounces , camphire one ounce and a halfe , oyle of egges , and oyle of tile enough to make the mixture into a paste . if you make a little hole in the top of an egge , and let out all the meat , and fill the shell with the following powder , and stop the hole with wax , and cast it into a running water , it will break out into a fire . take of salt-niter , brimstone , and quick-lyme , of each a like quantity , mix them . how to make stouple , or prepare cotten-week to prime your fire-works with . take cotten-week , such as the chandlers use for candles , double it six or seuen times double , and wet it throughly in saltpeter water , or aqua vitae , wherein some camphire hath been dissolued , or , for want of either , in faire water ; cut it into diuers peeces , rowle it in mealed gunpowder , or powder and suphur ; then dry them in the sun , and reserue them in a box where they may lie straight , to prime starres , rockets , or any other fire-works . how to know the true time , that any quantity of fired gun-match that shall doe an exployt at a time desired . take common gun-match , rub , or beat the same a little against a post to soften it ; then either dip the same in salt peter water , and drie it againe in the sunne , or e●se rub it in a little powder and brimstone beaten very small , and made liquid with a little aqua vitae , and dried afterwards ; trie first how long one yard of match thus prepared will burne , which suppose to be a quarter of an howr , then fowre yards will be a iust howre . take therefore as much of this match as will burne so long as you will haue it to be ere your worke should fire , binde the one end unto your worke , lay loose powder under , and about it lay the rest of the match in hollow , or turning so that one part of it touch not another , and then fire it . a water called aqua ardens . take old red wine , put it into a glased vessell , and put into it of orpment one pound , quicke sulphur halfe a pound , quicke lime a quarter of a pound ; mingle them very well , and afterwards distill them in a rosewater still : a cloth being wet in this water will burne like a candle , and will not be quenched with water . take one of these coffins , put it into the former , and take the composition for middle-sized rockets ( mentioned before ) and put thereof spoonfull after spoonfull , untill you haue filled the coffin unto the top of the former , after the putting of euery second spoonfull into the coffin , with a mallet giue two or three blowes upon the head of the rammer , that the composition may bee well rammed into the coffin : euery third or fourth driuing m. norton wisheth ( if the rockets are to be fired in three or foure dayes ) to dip the rammer in gum-dragant , and camphir dissolued in spirit of wine , or good aqua vitae : but if it will bee a month before they will bee fired , then dip the rammer in oyle of peter , or liquid varnish , and linseed oyle mixed together : if you would haue the rocket to giue a report or blow , then within one diameter of the top , driue a bottom of leather , or six or eight double of paper , pierce and prime either of them through in three or foure places , and fill the rest of the coffin with whole gunpowder ; afterwards driue another bottom of leather , and then with strong packthred choak the coffin close un●o it : then take the rocket out of the former , and prime it at the broach-hole with a peece of prepared stouple , and binde unto it a straight rod 6 or 7 times the length of the rocket , and so heavy , that being put on your finger , it may ballast the rocket within two or three diameters of the same : mark the following figure , which represents a rocket ready made and finished , a , b , the rocket , c , the stouple that primeth it , d , e , f , the rod bound unto the rocket with two strings , g , h , i , the hand that poyseth it . how to make serpents . the coffins for serpents are made of paper rowled nine or ten times upon a rowler not much thicker than a goose quill , and about foure inches long . the coffins must bee choaked almost in the midst , but so that there may bee a little hole , through which one may see : the longest part of the coffins for serpents must be filled with the composition specified before : if you would haue it wamble in the ayre , then choak it not after the composition , but if you would haue it wamble , then halfe-choak it , as is demonstrated by the following figure , the shorter end of the coffin must bee filled with whole gunpowder , and choaked quite up , as appeareth at b , in the figure m , n , o , which is the figure of a serpent ready made . how to make rayning fire . take diuers goose quils , and cut off the hollow ends of them , and fill them with the composition before mentioned , stopping them afterwards with a little wet gunpowder , that the dry composition may not fall out . how to make starres . i haue sufficiently taught the making of these in describing their compositions , wherefore i will now onely present the figures of them unto your view ; a , a , signifieth two that are bound up in paper or cloth , and peirced , and primed with stouple : the other two , e , e , signifie those that are made up without paper , and need no priming more than the powder or sulphur dust that they are rowled in . how to make petards . you must make the coffins for them either of white yron , or else of paper , or parchment rowled upon a former for the purpose , and afterwards fitted with a couer , which must be glewed on : these coffins must be filled with whole gunpowder , and peirced in the midst of the broad end , and primed thereat with prepared stouple ; the paper ones must be couered all ouer with glew , and the peirced . the figure of a petard ready made , and primed , is signified by the figure e. how to make compounded rockets . first you must make the rocket i taught you before ; you must not choake the end of it , but eyther double downe halfe the coffin , and with the rammer and a mallet , give it one or two good blowes : then with a bodkin pierce the paper unto the composition , or else drive a bottome of leather fitted unto the bore of the rocket , and pierce it through in two or three places ; then pare or cut off the coffin equall thereunto ; to this end of the rocket you must binde a coffin wider a great deale then the rocket is ; strew into it a little gunpowder dust , that it may cover the bottome of this coffin , and put therein with their mouthes downeward eyther golden rayne , or serpents , or both ; also starres , or petards ; you must put some gunpowder dust among these ; when you have filled the coffin with these or such like , cover the top of it with a peece of paper , and paste upon that a picked crowned paper , balast it with a rod , and it is finished ; the figure followeth . how to make fiends , or fearefull apparitions . these must bee made of the compositions for starres , wrought upon cotton weeke dipped in aqua vitae , wherein camphire hath beene dissolved , and after what fashions your fancy doth most affect . how to make fire boxes . you must make the coffins for fire boxes of paste-board , rowled upon a former , of what bignesse you list ; then binde them about with packthread , and glew over the cords ; also glew bottoms unto them , which must be pierced with a bodkin to prime them at . in these boxes you may put golden rayne , starres , serpents , petrars , fiends , devils . the tops of these fire boxes must bee covered with paper as the compound rockets . note that you must strew gunpowder dust a pretty thicknesse on the bottome of the fire-boxes , and prime the hole at the bottome with prepared stouple . how to make swevels . swevels are nothing else but rockets , having in stead of a rod ( to ballast them ) a little cane bound fast unto them , where through the rope passeth . note that you must be carefull to have your line strong , even & smooth , and it must be rubd over with sope that it may not burn . if you would have your rockets to returne againe , then binde two rockets together , with the breech of one towards the mouth of the other , and let the stouple that primeth the one , enter the breech of the other ; both kinds are expressed by the figures , the uppermost whereof representeth the single one ; a b signifieth the rocket ; d e , the cane bound unto it , through which a rope passeth . the lowermost representeth the double rocket ; a b signifieth one rocket , and c d another ; e the stouple that primeth the one , and entreth the breech of the other ; the cane that the rope passeth thorough is supposed to be behinde the two rockets . how to make gironells , or fire wheeles . the making of fire wheeles consisteth onely in the placing of rockets , with the mouth of one towards the tayle of another , round about certaine moveable wheels ; wherefore i thinke it sufficient only to describe the diversity of their fashions which follow . how to make flying dragons . the flying dragon is somewhat troublesome to compose ; it must be made eyther of dry and light wood , or crooked-lane plates , or of thin whalebones covered with muscovie glasse , and painted over . in the body thereof , there must bee a voyde cane to passe the rope through ; unto the bottome of this cane must bee bound one or two large rockets , according as the bignesse and weight of the dragon shall require ; the body must bee filled with divers petrars , that may consume it , and a sparkling receipt must be so disposed upon it , that being fired , it may burne both at the mouth and at the tayle thereof ; then hang the wings on in such wise , that they may shake as the dragon runnes along the line ; you may dispose divers small serpents in the wings ; marke the figure . how to make fire drakes . you must take a peece of linnen cloth of a yard or more in length ; it must bee cut after the forme of a pane of glasse ; fasten two light stickes crosse the same , to make it stand at breadth ; then smeare it over with linseed oyle , and liquid varnish tempered together , or else wet it with oyle of peter , and unto the longest corner fasten a match prepared with saltpeter water ( as i have taught before ) upon which you may fasten divers crackers , or saucissons ; betwixt every of which , binde a knot of paper shavings , which will make it flie the better ; within a quarter of a yard of the cloth , let there be bound a peece of prepared stoupell , the one end whereof , let touch the cloth , and the other enter into the end of a saucisson : then tie a small rope of length sufficient to rayse it unto what height you shall desire , and to guide it withall : then fire the match , and rayse it against the winde in an open field ; and as the match burneth , it will fire the crackers , and saucissons , which will give divers blowes in the ayre ; and when the fire is once come unto the stoupell , that will fire the cloth , which will shew very strangely and fearefully . how to make balloones , also the morter peece to discharge them . the diameter of the hollownesse of the morter peece must be one foot , the longer it is the further it will carry . let the diameter of the hollownesse of the sacke be the third part of a foot , and halfe a foot deepe ▪ it must have a square foot , and a portfire to strew into the bottome of the sacke on the side of it ; this portfire is to be made like a cane about three inches long , and have a bottome sodered unto the inside of the screw , which bottome must be pierced with a small touch-hole . this morter peece may be made of yron , red copper , or for a neede with pastbord , armed with cord , and glewed ouer , but the sack , and foot of it must bee made of wood , and the pastbord morter must bee nayled fast upon it . a balloone must be made of canuasse rowled eight or nine times upon a former , it must bee made so , that it will easily go into the morter peece ; into this balloone you may put rockets , serpents , starres , fiends , petards , and one or two saucissons to breake the balloone ; then choak it up with cord , and prime it with a little cane rammed full of a slow composition ; fill the stock of the morter peece full of whole gunpowder , then screw on the portfire , o , then put the balloone done to the bottom of the morter with the cane that primeth it , downward into the stock ; then with tallow or grease stop the chinks between the balloone and the morter , and it is ready to bee discharged , which you may do by putting fire to the portfire , and while that burneth , retreat out of harmes way . a , the figure of the morterpeece with its portfire . o , b , c , a balloone ready made . d , an empty coffin for a balloone . of fire-works for the earth . how to make rockets for the earth the moulds for these rockets for the earth are not made like those for the ayre , because that it is required that these should last longer , and haue a more gentle motion : obserue therefore the following directions for the making of them , which may serue for all occasions , without any alteration for bigger or lesser . let the diameter of their hollownesse bee halfe an inch , let their hollownesse be five or six inches long , let the rowler for to rowle the coffins on , bee the third part of an inch thick , and let the rammer to charge it bee a thought lesse , let the breech bee three quarters of an inch long , and let the breech enter halfe an inch into the mould , then fill it with the composition proper for it , obseruing those rules in the ramming it , as you did in ramming rockets for the ayre ; when you haue filled it within an inch of the top of the mould , double down a quarter of the coffin , beating it with three or foure strokes of the mallet ; then with a bodkin peirce it in two or three places , and then put in the quantity of a pistoll charge of whole gunpowder , then double down the halfe of the coffin , giuing it a gentle blow or two with the mallet , and with a strong packthred choak the rest of the coffin , and what remaineth after the coffin is choaked , cut it of , and it is made . how to make crackers . it is well known , that euery boy can make these , therefore i think it will be but labour lost , to bestow time to describe their making : only thus much , if you would make a cracker to giue forty , fifty , a hundred , or two hundred blowes , one after another , then binde so many crackers upon a stick , so that the end of the one may ioyne to the mouth of the other . how to make trunkes . these you may make of paste-board , paper , or wood , and of what bignesse and length you please , and ram them full of the composition of rockets for the earth ; if you would have them to change colour , then alter the composition that is , put in two or three spoonfulls of the composition of rockets for the water , and ramme that in , then put in two or three spoonfulls of the composition of rockets for the ayre , and ramme that in , then put in two or three spoonfulls of gunpowder dust , and ramme that in , doe so till you have quite filled it then tie a bottome of leather upon it , and pierce it and prime it with stoupell ; after the same manner may you make lanternes and lights . how to make tumbling balls . make a ball of canvas , and fasten in it a double rocket for the earth ; you may stuffe the rest of the ball with a slow composition of two parts charcoale dust , and one part of gunpowder dust , mingled together , and put divers petrards amongst it . how to make saucissons . saucissons are of two sorts , eyther to be placed upon a frame , or such like , and so to bee discharged with a trayne of gunpowder , or else to bee discharged out of the morter-peece . the standing saucisson is thus made ; you must roll paper or canvas , nine or ten times upon a roller as a , b , and choake the one end of it : fill it then with whole gunpowder , and then choake the other end also , then cover all the saucisson with cord , and glew it over ; then pierce one end of it , and prime it with a quill filled with gunpowder dust ; place it upon a forme having a a hole for the quill to passe thorough ; then fire it by a traine of gunpowder layd under the frame , it will give a report like a canon : marke the figure f f. how to make the flying saucisson to be delivered out of the morter peece . make a coffin for this , as you did for the former ; first , fill it almost with whole gunpowder , then put upon that gunpowder dust , which you must ramme hard into the coffin , so that it may bee one finger thicke ; then choake it close , and arme , and prime it as you did the former . it is represented by the figure , k m. how to make a fire sword . you must make a sword of woode , having a deepe channell in the backe of it , wherein place first a rocket for the ground ; then two or three serpents upright ; ( with their mouthes inward ) let the stoupell that primeth the rocket come under the mouth of the serpents , so that being kindled , it may set them on fire , and enter the breech of the next rocket , so fill the channell quite full with rockets and serpents , binde the rockets fast into the channell , but the serpents must be placed so , that being once fired , they may fly out of the channell , and it is made : mark the figure g , p. the description and making of three sorts of fire-lances . to make the first fire-lance , whose figure is noted a , you must make a hollow trunk of what length or bignesse you please , either of wood , paper , or pastbord rowled on a rowler , and armed with some cord and glew : first put into the bottom of whole gunpowder about one or two fingers thick ; then ram upon it a pastebord peirced with a little hole in the middle , hauing a quill fastned in it , which quill must be filled with a slow composition , or else with gunpowder dust : this quill must stand up in the lance two or three inches ; then fill the coffin up to the top of the said quill with starres , and strew among the starres some gunpowder dust , then put pastebord ouer them , having a hole for the quill fastned in the former bottom of pastebord to passe ; then upon this pastebord ram gunpowder dust one or two fingers thick , then put a row of serpents in , and in the midst of the serpents put a cane open at both ends , and filled with gunpowder dust ; this cane must be somewhat longer than the serpents , and it must passe through a pastebord , which must bee put ouer : then put some more gunpowder dust , and ram it in upon it , and upon that put another row of serpents , with a cane in the midst of them filled with a slow composition , and upon them put gunpowder dust , or else a slow composition , ramming it in till the lance bee full ; then put a pastebord upon it , and in the midst of the pastebord put a little cane filled with a slow composition , then fasten it upon a staffe of what length you will , and it is made . to make the second fire-lance , you must prepare a trunk like unto the former , first ram in the bottom of it some of the composition of rockets for the earth about two fingers thick , then put a pastebord upon it , having a petard fastned in the middest ; this pastebord must bee pierced in three or foure places , round about the petard , that thereby the powder that is rammed ouer the pastebord may take fire : then ram in some more composition upon the petard , about two or three fingers thick , then another petard , then more composition , so doing untill you have filled the trunk : then fasten it upon a staffe , and and prime it as you did the former , it is represented by the figure noted b. the description and making of two sorts of fire-clubs . to make the first you must make an ovall ball of pastebord , canvasse , or parchment glewed together , which you must first fill with a slow composition , ram it in , and then bore divers holes round about it , and put therein serpents , fire bals , or what you will : fasten it upon a staffe , and prime it in the top with a cane filled with a slow composition : this is represented by the figure a , a. to make the second you must fill divers canes open at both ends ( and of a foot long , or more , or lesse , as you think fit ) with a slow composition , and binde them upon a staffe of foure or five foot long ; prime them so that one being ended , another may begin : you may prime them with a stouple or match ( prepared as before ) make an osier basket about it with a hole in the very top to fire it by , and it is done . the figure f , f , representeth the staffe , with the canes bound upon it . the figure marked g , representeth the staffe having a basket wrought over it . how to make a fire-target . make a target of osier twigs , or else of light wood , & binde upon it divers canes filled with a very slow composition : the canes must bee open at both ends , and primed with stouple , that one may give fire unto another : in the midst of all you may set up a large cane also , if you please , which you may fill with the same composition as you did the others . mark the figure l , m , n , o : of fire-works for the water . how to make rockets for the water . the diameter of hollownesse of the mould for rockets that swim on the water , must be one inch , and eight inches long : let the breech enter into the body of the rocket one inch , and it must have no broach at all in it . let the diameter of the thicknesse of the rowler bee three quarters of an inch , the rammer must be a thought lesser ; then ram it full of the composition of rockets for the water ; joyne to the upper end of it a saucisson : then couer it all over with melted pitch , rosin , wax , or tallow , to the end that the water may not spoyle the coffins ; and to make it float along the water , binde a rod about two foot long , as you did unto the rockets for the ayre : now if you would have the rocket to change his actions , ( that is , to swim one while above the the water , and one while under the water ) then put into it in the filling , one spoonfull of composition , and ram that in ; then one spoonfull of whole powder , and ram that in ; and then another of composition , and after that another of whole gunpowder , so do untill you have filled it quite . if you would have it change colour , then shift the composition divers times , ( that is , put in one spoonfull of the composition of rockets for the water , then another spoonfull of the composition of rockets for the ayre , or rochpeter and gunpowder mixed ) untill you have filled it . how to make a rocket that shall burne a good while in the water , and then mount up into the ayre . first you shall make a rocket for the water , and binde unto the lower end a stick about two foot and a halfe long , having a large hole in the end thereof : then tie unto it ( but loosly , so that it may easily slip out ) a rocket for the ayre , and let the stouple that primeth for the rocket for the ayre , enter into the breech of the water rocket , then let the end of the rod of the rocket for the ayre enter into the hole of the rod of the rocket for the water : besmeare then both the rockets with tallow , grease , or wax , or any oyle colour that the water may not spoyle the coffins of the rockets ; then hang a stone at the bottom of the stick that hath the hole in it , to make it sink down into the water ; then fire the water rocket , and cast them into the water ; the fired rocket will burne in the water , and being consumed , will giue fire unto the other rocket , which being loosly tyed , will slip the bond , and mount up into the ayre . this is represented by the figure g , g. the floating rocket mentioned before , is expressed by the figure noted i , k. the description and making of two sorts of fire bals for the water . for to make the first , you must make a ball of canvas , about the bignesse of a foot-ball , or bigger if you please , and fasten in it a double rocket for the water : if you will , also you may stuffe the rest of the ball with the composition that will burne under the water , and cut holes in the sides , and therein fasten other bals , and petrards in them : then cover the ball over with tallow , pitch , or painting , except the place where the rocket is primed , and it is done . it is represented by the figure noted with a , and it will tumble up and downe in the water . to make the second fire-ball , you must first make a ball of canvas , pasteboard , or such like , and cut a wide hole in the top of it , and place in it a channell of tinne pierced in divers places : fill the channell with the compositions of rockets for the water ; against every hole therof , place a petrard : cover it with a cover , pitch it over , and prime it , then ballast it with leade , or a stone , that the vent may burne upwards , and it is done . it is represented by the figure b. how to make a dolphin . you must make the body of it of pasteboard glued together , fill the body with the composition of rockets for the water , pierce it in the back with divers little holes , wherein put serpents , besmeare the body all ouer with the following pap : take gunpowder dust , foure ounces , camphire , and sulphur , or brimstone in powder , of each one ounce , make them into a soft pap with oyle of tiles , then binde unto it a large rocket for the water , which rocket must be armed ( as afore ) that the water may not hurt it : then ballast it with a wyre , hauing at each end a piece of lead of weight sufficient , and it is done . marke the figure . i might haue beene infinite in the describing of such like with ships , towres , castles , piramides . but considering that it would but increase the price of the booke , and not better your understanding : since all consist of the former workes , which are so plainely described , as that the most ignorant may easily conceiue thereof , and ( if any whit ingenious ) thence contriue others , of what fashion they list . finis . the third booke of drawing , limming , colouring , painting , and graving . by i. b. london . printed by thomas harper , for ralph mab , 1634. the third booke of drawing , painting , limming , graving . the art of drawing is in it selfe most excellent , and most worthy commendations in whosoever it is : yea it is an art so necessarie unto all ingenious artists , as that in no wise they can be without it , and my selfe haue found it to bee true , that the sight of a good draught is more unto an ingenious person , then a whole chapter of information ; wherefore i have , according unto my knowledge and practise therein , faithfully penned the same ; for the use of all such as beare affection unto the art , and are desirous to be instructed therein : and for that divers persons cannot attaine unto it , or perhaps are loath to bestow any time to practise it : whereby they might come to a requisite perfection : for such i have set downe certaine directions , and those so facile , and easie ; that persons altogether unskilfull , may ( having a patterne ) worke very well ; but before i begin , it behooveth that i prescribe what things are to be had in readinesse to worke withall : first therefore provide good smooth and cleare paper , divers plummets made of blacke leade , oker , or blacke chalke , or else charcoals made of ash , sallow , or beech , split in sunder , and pointed ; also a wing : having provided these your implements , you shall thus begin to worke . first , let the thing , whose pourtrature you intend to take , stand before you , so that the light be not hindred from falling upon it , and with a pointed peece of charcoale draw it rustically ; which when you have done , consider a while whether all the parts thereof are proportionable , and whether it carry the semblance of the thing that you drew it from , which if it do not , wipe it out with your wing , and begin anew : but if it be faulty on one part onely , wipe onely that part out , and draw it againe ; whensoever it liketh you , or that you have so drawne it , that you can finde no great fault in it : wipe it over gently with your wing , so that you may perceive the former strokes : then with your blacke chalke , or blacke lead plummets , draw it as perfectly , and as curiously as you can , and shadow it according as the light falleth upon it ; this way is workeman like , and the most difficult of all , yet by a little practice may easily be attained unto : so that the persons stand well affected unto the art. instead of white paper , you may take light coloured blew paper , and draw upon it with charcoale , and white chalke pointed , which will shew very wel : but note , that after you have made your draught , you must wet it in faire water , and let it dry of it selfe ; this will make the drawing to hold fast on , which would otherwise easily be wiped off . this may serve for such as are contented to take some paines to attaine so noble a science . but for others there are divers other helps , which follow in order . how to take the perfect draught of any printed , or painted picture . take a sheete of venice ( or in stead thereof ) of the finest white paper that you can get : wet it all ouer with cleane sallet oyle : then wipe the oyle off from the paper , as cleane as you can , so that the paper may be dry , otherwise it will spoyle a printed picture by the soaking through of the oyle : hauing thus prepared your paper , lay it upon any painted or printed picture , and you shall see the picture through the same more perfectly appearing , then through glasse , and so with a blacke lead pen , you may draw it ouer with ease , and better first with a soft char-cole , and then with a pen. after that you haue thus drawne the picture upon the oyled paper , put it upon a sheete of cleane white paper , and with a little sticke pointed , or ( which is better ) with a feather taken out of a swallowes wing : draw ouer the picture againe , and so you shall haue the same very prettily and neatly drawne upon the white paper , which you may set out with colours , as shall be taught hereafter . another way . having drawne the picture , first open the oyled paper , put it upon a sheete of cleane white paper , and pricke ouer the same drawing , with a good big pin , then from the cleane sheete , that is pricked , pounce it upon another : that is , take some small coale , powder it fine , and wrap it in a piece of tiffanie or such like , and binde it up therein loosely , and clap it lightly ouer all the pricked lines by little and little , and afterwards draw it ouer again with a pen or pencill , or otherwise as you please . another way very pretty and easie to be performed . take some lake , and grinde it fine , and temper it with linseed oyle , and afterwards with a pen , draw with this mixture ( in stead of inke ) all the out stroaks of any printed picture , also the muscles : then wet the contrary side of the picture , and presse it hard upon a sheete of cleane white paper , and it will leaue behinde it all the stroake of the said picture that you draw ouer . another way much like the former . take printers blacking , grinde it fine , and temper it with faire water , and with a pen dipt therein , draw ouer the master stroakes and out lines of the muscles : wet then a faire paper with a spunge , and clap the picture upon it , pressing it very hard thereupon , and you shall finde the stroakes you drew , left upon the faire paper . an easie way to lessen any picture : that is , to draw a picture from another , in a lesser compasse . first , with a ruler , and a blacke lead plummet , draw a line at the very top : also another at the bottome paralell , or equally distant from the other : from the upper line , let fall two perpendicular or plum-lines euen unto the lowermost line , so those foure lines will make a square : now you must diuide this square into diuers equall parts , with a paire of compasses , and draw lines with a ruler and blacke lead plummet , quite over the picture : so the lesse lines will divide the picture into equall parts or squares : then take a faire paper , and make as many squares upon it , as there is in the picture : you may make them as little as you will , but be sure that they are equall , and of just number with those in the picture . having thus crossed your picture , and drawne over your faire paper into squares , take a blacke lead pen , and draw the picture by little and little , passing from square unto square , untill you have finished the whole : still observing the order of the squares as they stand in either : then draw it ouer with a pen , in which second drawing of it over , you may easily mend any fault : when it is dry , rub it over with the crum of white bread , and it will take off all the blacke lead strokes , and your draught onely will remaine faire upon the paper or parchment . here i might have entred into discourse of drawing paralels , perpendiculars , making of squares , and such like : but to deale truely , i was as loth to trouble my selfe , as to wearie you : you shall neede onely to provide a ruler of thin brasse or copper , having a crosse thwart one end of it : the charge will not be much , nor the use tedious : the figure followeth , noted a , b. let a , b , c , d , be a line given , whereon to erect a perpendicular or plumb line : lay the ruler so , that the crosse over the end of it , may lye full upon the line , then draw a line by the side of the rule , and it is done . a verie easie way , to describe a towne , or castle : being within the full sight thereof . for the effecting of this , you must have a frame made , and crossed into equall squares with lute strings , and figured at the end of each string : this frame must have a foot , wherein it must be made to be lifted higher or lower as occasion serveth ; also you must divide your paper that you are to draw upon into so many equal squares as your frame containeth : having the like figures at the ends of each line that there is on the frame ; before this frame must be placed a style or bodkin having a little glasse on the top of it for to direct the sight . note now that the nearer any thing commeth unto the center , the lesser it appeareth : hence it is that a towne of a mile , or more long , or a huge great castle , at a distance may be comprehended , and that easily within the limits of so small a frame ; by the stile direct your sight from one part to another , beginning at one square , and proceeding through the rest in order as they lie ; marke well the following figure . how to make a deske : by meanes whereof you may draw , and that most exactly with great facilitie any printed picture , or sollid image . first let there be a frame made , and with hinges let be joynted unto a board of equall breadth unto it : let this frame also have two stayes at the top , at each end one , by meanes whereof the deske may be raised higher , or lower , as need shall require ; then fasten to the frame a peece of pure cleare glasse fitted thereunto , and it is finished . the figure followeth . the deske . the manner of using this deske is thus , if the picture that you intend to draw be a printed one , then first fasten it next unto the deske with waxe , paste , or such like : upon it fasten a sheet of faire paper : if it be in the day-time place the backe of it towards the sunne ; if it be in the night that you worke , place a lampe behinde it , and so you shall see perfectly every ( even the least ) stroake of the picture , which with your penne you may draw as acurately as any limmer whatsoever . if it be a solid peece , then place it behinde the deske , betweene the light and the deske : then fasten a sheet of cleane white paper upon the deske ; raise then the deske higher , or lower untill you see the perfect shadow of the image through your deske , and paper , and then draw the posture of the image , and shadow it afterwards ( without the deske ) as light falleth upon it . an easie way to take the naturall , and lively shape of the leafe of any hearbe or tree , which thing passeth the art of man to imitate with pen or pensill . first take the leafe that you would have , and gently bruise the ribs and veines on the backe-side of it , afterwards wet that side with linseed-oyle , and then presse it hard upon a peece of cleane white paper , and so you shall have the perfect figure of the said leafe , with every veine thereof , so exactly exprest as being lively coloured , it would seeme to bee truly naturall , by this we learne , that nature being but a little adjuvated or seconded with art , can worke wonders . now for the farther information of such as are desirous of exemplarie instruction , i have set downe in order following the delineation of the proportion of such things as in my iudgement seemed most necessarie for young beginners , and those in such easie demonstrations as for the most part they consist of equall squares , and require no more for their right understanding , then diligent observation , i might have filled a whole booke of such like : but having considered that what i had done , was a sufficient ground for a farther procession , i thought fitting to leave each person to the exercise and practise of his best invention . i thought fitting to give you a word or two , wherefore i have not made the crosse pricked lines to passe through the figures . the reason is , 1 because the figure would have beene thereby somwhat defaced ; 2 because some chuse rather to draw without such rules ; 3 for others with a ruler and black lead plummet they may crosse the figures through , and with white bread crums take out the same againe at pleasure . of painting . the principall end and subject of this art , is to set out things both in proportion of parts , and livelinesse of colour . for the former , the proportion of parts , i have given sufficient information for the meanest capacitie in the precedent part of this tractat : now therefore i will speake of the other , the colouring or setting out in colours . but first provide a frame or easel called by artists , which is very necessary to worke upon , especially in greater pieces of worke : the forme whereof followeth . also you must provide divers little shels to put your colours in , also pensils of all sorts , both for priming and other : a light ruler of one foot and a halfe , or two foot long : and colours of all sorts ground very fine upon a porphire or marble . having provided these , you shall set to worke , observing the subsequent directions . painting may be performed either with water colours , or with oyle colours . first i will speake of water colours , wherein i shall observe two things . first , the diversitie of colours , and preparations . secondly , their mixture , and manner of laying them on the ground . first of the first , the diversitie of colours and their preparation . colours are either simple or compounded , meerely tinctures of vegetables , or substances of minerals , or both : the simple colours are such as of themselves , being tempered with the water or oyle , doe give a colour . the compounded are such , whose ingredients do exceed the number of one . vegetables are rootes , juces , berries , and such like things as grow out of the earth . minerals are such as are dig'd out of the earth , as earth , and stones , &c. all which follow in order , as well their preparations , as description . first note that every colour to be ground , ought first to be ground with the gall of a neat : then let them dry of themselves in a cold place , afterwards grinde them with gumme water for your use . now i am come to the second thing observable ( to wit ) the mixture and laying the colours on the grounds , which is thus : your colours prepared for use , ought to be tempered according unto direction , still observing a meane : and to that end , mixe them by little and little , till the colour please you ; first you must lay on the ground colour , and let it dry throughly : then with a small pensill , pricke on the second colour , else it will be apt to run abroad , nor can you worke it so well , to make it seeme liuely , as you may by pricking it on , especially in small peeces . if you are to paint ouer maps , or printed pictures that haue writing in them , they use to lay on the thinnest colours , and alwaies before you lay any colours upon paper , wet the backe side of it with faire water , wherein store of allum hath beene dissolued , and let it dry of it selfe : after wet it againe , and let it dry : doe it the third time , for this will strengthen the paper , that the colour shall not sinke through it , and moreouer it will make the colour shew the brighter , and last , the better . to make gum water to temper your colours with . take cleane water , and put into it of gum arabicke a little , and let it stand untill the gumme be dissolued . now you must haue a care that it be neither too thicke , by reason of the gumme , nor yet too thin : for with the one you cannot worke well , and the other will not binde the colour fast . a purple colour . take two pound of heidleber , two ounces of allum , halfe an ounce of ashes of copper , halfe a pound of water ; put them into a skillet , and let them boyle till a third be consumed : when it is cold , straine it into a cleane vessell , and let it stand a while , then straine it into another , and then let it stand till it be thicke enough . a crane colour . you must onely grinde blacke lead with gum water . browne colour . take good browne , and grinde it with gumme water : his false colour is made with two parts browne , and a third part white lead , sad it with the same browne . hayre colour . take vmber or spanish browne , grinde it , temper it with gumme water . a blew . boyle mulberries with allum . an emerauld colour . take verdigreese , and grinde it first dry , and put unto it a little of the gall of a neat : also of saffron , and the juyce of rew , of each a little : grinde them together , and put them into a shell , and let it dry there : when you would use it , grinde it againe with vineger or verjuce , and a little neats gall dissolved in either of them . his false colour is two parts greene , and a third ceruse : it must bee sadded with a good greene . a motlie greene . this colour is compounded of red and greene . a blacke colour . first you must lay on a light blacke , mingled with white lead , and afterwards when it is dry , sad it with good blacke ; for sad blacke , mixe indie baudias with gumme water . a marble or ashe colour . this is compounded of blacke and white . a russet or sad browne . this colour is made by compounding a little white , with a good quantity of red . a browne blew . take two parts of indie baudias , and a third of ceruse and temper them with gumme water . a brasse colour . this is compounded of masticot and vmber . a gold yellow for armes . take orpment , and masticot , grinde each by themselves : but in grinding of the masticot , adde a little saffron , and worke with them . note you may alay your orpment with chalke , and sadde it with browne of spain or o ker de luke . azure . take of white lead foure ounces , of indicum two ounces , put them into a leaden pot with vinegar : boyle them well , and that which swimmes on the top is the colour . a purple or violet colour . this is a compounded colour , and it is made either by mixing a quantitie of azure , and a portion of turnsole : or else by mixing a quantitie of russet , and a quantitie of azure : sanguine or blood-colour . this is likewise a compounded colour , and it is made by mixing a good quantitie of cinaper with a little blacke . orange-tawny . this colour is compounded of a bright red , and a bright yellow . a lyon-tawny . this colour is made by mixing red lead and masticot together . a carnation , or flesh-colour . first you must lay on a white colour tempered with gumme-water , and when it is drie you must go it over againe with vermillion or lake , or else you must temper ceruse and vermilleon together , and being dry , go over it againe with lake or vermillion . a peach colour . this is compounded of ceruse and vermillion . a skie colour . this colour is compounded of vermilleon and azure . a blood red . this colour is made of cinaper , and afterwards sadded with vermilleon at the sides , or else with a browne colour . a bloudy colour , grinde cinaper , lake , and cinaper tops , put them into good water , and if they be too light , put to them a little turnsole . a lincoln-greene . this colour is compounded of a good greene and saffron . a poppin-jay greene . this colour is compounded of azure , and masticot . a good yellow . take saffron , or cambugium , and temper it with gum-water , sad it with vermilleon . a sable or blacke . take a torch , hold it under a lattyn bason , temper that blacke with gumme-water . a velvet-blacke . bvrne harts-horne on a colliers hearth ; then grinde it with the gaul of a neat , put it into a shell , and let it dry in the shade : when you would use it , grinde it againe with gumme-water . to write gold with pen or pensil . take a shell of gold , and put a little gum-water unto it , and temper it together , and then you may write with it as with other colours . to make azure , or bise sadder . take blew turnsole , wet it in gum-water , and then wring it out , and mixe it either with bise , or else overshadow the bise with it . red colour . take vermillion , and temper it with gumme water : his false colour is two parts vermillion , and a third part ceruse . another red. take russet , and temper it with gumme-water , clay it with ceruse , and sad it with it selfe . another red. take brassill in grosse powder , allum in powder : steep them in gum water a night and a day : then straine it , and keepe it for use . a greene colour . take copper plates , put them in a copper pot , & put distilled vineger to them : set them in a warme place till the vinegar become blew , then put it out into another leaded pot , and poure more vinegar into it again ; let it stand so till it become blew ; this do so many times till you thinke you have enough : then let it stand till it be thicke . to make good inke . take two handfuls of gauls , cut each gaul into three or foure peeces , poure into them a pint of beere or wine , then let it stand eight houres ; straine it from the gauls , and put vitreoll therein , and to the vitreoll a third part of gumme , set it on the fire to warme ; but let it not seethe , and it will be good inke , and of these gauls you may make inke foure or five times more . to seethe brasill . take an ounce of brasill , twelve ounces of beere , wine , or vinegar , put it in a new pot , let it stand a night ; and in the morning set it on the fire , and let it seethe till halfe be consumed : then put into it two peny worth of allum beaten together , and as much beaten gum-arabicke : stirre them well together , and let them seethe againe ; if you desire to have it somewhat darke , then scrape a little chalke into it when it seetheth : let it not seethe over the pot : when it is cold straine it through a cloth , and put it into a glasse well stopt . aurum musicum . take one ounce of salarmoniack , one ounce of quick-silver of counterfein , halfe an ounce of brimstone , bruise the brimstone , and set it on the fire , but let it not be over hot ( lest it burne ) then take the salarmoniacke , and the quicksilver being in powder : mixe them well together , then mingle with them the brimstone : stirre them well , and quickly with a sticke till the brimstone become hard , then let it coole , grinde it on a stone , and put it in a glasse well stopt with waxe , and set it in a pan with ashes ; make a fire under it , and let it stand halfe a day in that manner ( but not over hot ) till a yellow smoke riseth on it , and when the yellow smoke is gone it is prepared . argentum musicum . take an ounce of tynne , melt it , and put thereto one ounce of tartar , and one ounce of quicksilver , stirre them well till they be cold : then beat all in a morter , and grinde it on a stone ; temper it with gumme-water , and write therewith , and afterward polish it . to write a gold colour . take a new hennes egge , make a hole at one end , and let the substance out , then take the yolke without the white , and foure times as much in quantitie of quicksilver ; grinde them well together , and put them into the shell ; stop the hole thereof with chalke , and the white of an egge , then lay it under an henne that sitteth with sixe more , let her sit on it three weeks , then breake it up , and write with it . to write with gold out of a pensil . take honey , and salt a like quantitie , grinde them well , and put to them a leafe of gold , with a little white of an egge ; put it into a mussell shell , and let it purifie ; then temper it with gumme-water , and write with it , pollish it . or else grinde a leafe of silver , or gold , very small with gumme-water , and wash it in a mussell shell as aforesaid . to temper azure of bise . take azure or bise , and grinde it on a stone with cleane water ; then put it in a broad glasse , or shell , and when it hath stood a while all the dregs will fleet above , and the cleane colour will fall to the bottome ; then poure out the water with the dregs , and poure the azure in cleane water againe ; then stirre the colour and water together , and let it stand , and fine , and after that poure out the water , and dregs againe : do thus till it be well purged ; then grinde it againe on a stone with gumme-water , and put it into a horne , or shell ; when you paint or write , stirre it , and let the sticke drop into the pen , for it will sinke to the bottome as lead . to temper turnsole . take turnsole , and wet it once or twice in cleare water , and let it lye till it be well steeped ; then wring it into a dish till the colour be good , and sad ; with this you may flourish red letters , or vestures , and this colour shall be darked , sadded , or renewed with blacke inke . to make colouring , called vernix : to varnish gold , silver , or any other colour on vellem , paper , timber , stone , &c. take bengewine , and bray it well betwixt two papers , then put it into a viol , and poure on it aqua vitae , that it may stand aboue the bengewine three or foure fingers , and let it steepe so a day or two ; then put to it for halfe a violl of aqua vitae fiue or sixe chieues of saffron slenderly stamped ; this done , straine it , and with a pensil vernish therewith any thing gilded , which will become bright and shining , drying it selfe immediately , and will continue the brightnesse many yeares ; but if you will vernish on siluer , then take the white that is found in bengewine and dresse it with aqua vitae as afore , leauing out the saffron , and the said vernish made with these onely is very good to varnish all things as well painted , as not painted : for it maketh tables of walnut tree and hebene to glister if it bee laid on them , and all other things , as iron , copper , or tin gilded , or not : it maketh bright , preserveth and aideth the colour , and dryeth incontinent without taking dust . to make a double size to lay gold or silver on an embossed ground . take venice ceruse , white lead , plaister of an old image , or chalke , any of these made in fine powder , and ground with the white of an egge , and a little water : this will make a good bottome to lay silver on . but when you use any of these to lay under gold , put to it a little saffron , put not too much water ; mingle it after discretion , and looke the size be thicke standing : put the size thus tempered , in a horne or shell in some celler , or shadowed place , where it may stand moyst seven dayes , till it be perfect clammy and rotten , and once a day stirre it ; the elder the size is , it is the better . if there stand any bubbles on the size , put in eare waxe , for that is a remedy thereto , and before you lay it on your worke , lay the size on a scrow , and dry it , and when it is dry , bend it , and if it bend and breake not , then it is perfect , and if it breake , put to it a little water to make it weaker , and proue if it cleaueth fast to the booke , if not , put glayr thereto , and make it more stedfast : the like size may you make of gipsium , bolearmoniacke , red or yellow oker , orpment or masticot , with browne of spaine , or red lead : if euery of them be ground seuerally , and tempered as afore . of painting in oyle . here you must provide one thing more then you did before : that is , a pallet ( so called by artists ) whereupon you must put a small quantitie of euery such colour you are to use , the forme whereof followeth . the colours to be used , are altogether such dry substances as i mentioned formerly : as oker , vermilion red lead , vmber , spanish browne , lam-blacke , gambugice , masticot , orpment , ceruse , or spanish white , blew and greene bise , verdigrease , and a multitude of such like , which may be had at the rose in cornehill , london . your colours must be ground all very finely , and tempered with linseed oyle ; and to preserve them , put them in little earthen pans , and put water upon them , and cover them , that the dust come not at them : thus they may be kept a great while , and from thence you may take them as your use doth require . there are divers colours which without the admixture of another colour , will not be dry a great while ; as lake , verdigrease , lam-blacke : with such you must temper a little vmber or red lead . divers painters there are , that having haste of worke , doe use to temper their colour with one part of fatte oyle , and two of common linseed oyle , and by this meanes they make the colours dry the sooner : this fat oyle is onely linseed oyle exposed to the weather , and so it becommeth thicker : yea sometimes you shall see it so thicke , that you may cut it almost like butter : it may bee made likewise by boyling of it a little while , but the former is the best . as for the tempering of your colours , i can prescribe no surer way then experience with diligent observation . of graving . it is possible for one to be a good painter , and yet not to be able to draw well with the pen , because there is not required in a painter such a curious and exact carriage of the hand : but it is impossible for one ever to grave or etch well , except he can draw well with the pen. first therefore presupposing you can doe the first before you attempt the second , you must provide divers graving tooles , both long and short : some for hard worke , some for sweet worke , some for smaller worke , and some for greater : also a peece of a beaver hat , and a good oyle stone , smoothed on one side , and free from pin holes , and plates of copper or brasse exactly polished . of gravers . there are two principall sorts of gravers , the long and the short : the long are straight , and for to engrave plates withall , especially the greater , and these are to be held as the figure following doth expresse : where you may note that the pummell of the graver resteth against the ball of the thumb , and the point is guided with the forefinger . and there ought to bee a little bagge of sand under your plate , to the end that you might turne your plate upon it as your worke doth require . the second sort is a short graver , and turneth up somewhat at the end , and that is to engrave letters and scutchions in plate seales , and smaller plates , being fastened in some convenient instrument : this must be held likewise according unto the expression of the figure following : where it is to be noted , that the pummell of the graver is stayed against the further part of the hand , and is guided by the inward side of the thumbe . it were needfull that there were a piece of leather like a taylors thimble , about the end of the thumbe , waxed or glued , whereby to guide the graver more steadily , and stay it upon occasion . how to make gravers . provide some good crosse-bow steele , and cause it to be beaten out into small rods , and softned : then with a good file you may shape them at your pleasure : when you have done , heat them red hot , and dip them straight downe into sope , and by so doing , they will bee hard indeed . note that if in the dipping of them into the sope , you turne your hand never so little awry , the graver will be crooked . these gravers made and hardened after this manner , doe farre exceed all the other gravers . if your gravers be too hard , heate them a little , and thrust them into tallow , and they will be tougher . the oyle stone is to whet your gravers on ; drop one or two drops of sallet oyle upon it , and whet your graver thereon , and it will have an edge presently . how to smooth and pollish copper plates . because that in the printing with copper plates , the least scratch , though it be scarce visible , receiveth its impression , and so many times disgraceth the worke : i have set downe a way to smooth plates for impression . first , take a piece of brasse , or copper , of what bignesse you intend , of an indifferent thicknesse , and see as neere as you can , that it bee free from fire flawes . first beat it as smooth as you can with a hammer , then rub it smooth with a pumice stone that is void of gravell , ( least it race it , & so cause you as much more labour to get thē out ) burnish it after with a burnishing iron , having first dropped a drop or two of sallet oyle on it : then rub it over with a cole , prepared as is after taught , and lastly with a peece of beaver hat dipt in sallet oyle , rub it very well for an houre : thus you may polish it exactly . how to prepare your coales . take beechen charcole , such as when they are broke , doe shine , such as are void of clifts , and such as breake off even : burne them againe , and as soone as they are all through on fire , quench them in chamber lye : after take them out , and put them in faire water , and reserue them for your use . having prepared all things in a readinesse , you must haue a draught of that you intend to cut or engrave . take the plate then , and waxe it lightly ouer , and then either pounce the picture upon it , or trace it , or by drawing ouer the lines of the picture with ungummed inke , reprint it upon the plate : then worke upon it , obseruing the shadow , so that being printed , it may stand right , for it will be backward upon your plate : when you haue cut one stroke , drop a little sallet oyle upon your peece of bever , and rub over the said stroke , for by this meanes you shall better see the stroke , and how to cut the next equall unto it , and so the rest proportionally distant one from another ; but to worke by a candle , you must place a glasse of faire water betweene the candle , and a paper betweene that and the plate , ( which casteth a true light ) or you will never be able to worke truely and aright . of etching . etching is an imitation of engrauing , but more speedily performed . things may be expressed to the life thereby , but not so sweetly as by the graver . it is thus performed ▪ the plate you are to etch upon , must first exactly be pollished , afterwards ouerlaid but very lightly with a ground made for the purpose , ( of which anon ) and thereupon must be pounced , drawne , or traced , the thing that you are to etch : then the said ground is to be pierced with diuers stiles of seuerall bignesse according as the shadowes of the picture doe require : afterwards the edges of the plate are to be raised with soft waxe and strong water , ( for so they terme it : ) ( it is to be had at the signe of the legge in foster lane a distiller ) is to be put upon it , which in those places were the strokes , are required to be lightly performed , is to be abated or alayed with faire water , which hauing dured a while upon the plate , will eate into it , as it were engraven , then put it into cold water , and wash it about , and it will leaue eating further , and then take off the ground and it is done . ared ground for etching . take red lead , grinde it very well , and temper it with varnish . a white ground . take one ounce of waxe , and two ounces of rosin , melt them together , and adde thereto a quarter of an ounce of venice ceruse ground fine , lay it on while it is hot . a blacke ground . take asphaltum two parts , bees waxe one part ; melt them together , and being warme , lay it on very thinly with a fine lawne ragge . if it seeme somewhat red in any one part , hold it over the smoake of a linke or waxe candle , and it will be amended . note that it is a principall thing in this art to lay the ground on aright . another way how to engrave with water . take verdigrease , mercury sublimated , vitreoll , and allum , a like quantity , beate all to powder , put them into a glasse , and let it stand so halfe a day , and stirre it often , then lay on the plate , waxe , mingled with linseed oyle , or red lead with linseed oyle , and write in it that you meane to grave , then put the water on it , and let it so remaine halfe a day , if you will have it very deepe , let it lye longer . if you will engrave images , &c. lay the waxe on the iron or steele , thin , and draw what you will theron , that it may touch the mettall , then put the water into the strokes , and it will be engraven . how to engrave on a flint stone . take a flint , and write on it what you will , with the fat or tallow of an oxe , afterward lay the flint in vineger , foure dayes . finis . place this betweene folio 14. and 15. the booke of extravagants : wherein amongst others , is principally contrived divers excellent and approved medicines for severall maladies . by i. b. london . printed by thomas harper , for ralph mab : 1634. to the reader . courteous reader , forasmuch as there were divers experiments that i could not conveniently , or rather my occasions would not permit me to dispose in such order as i would have done ; i thought it would not bee amisse to call them by the names of extravagants , and so to set them downe as i found them , eyther inserted amongst other my notes , as i put them in practise , or as they came into remembrance . how to make a light burne under the water , being a very pretty conceypt to take fish . let there be a glasse , as a , having a hole at the bottome , to put a candle in with a screwed socket . the socket must have a loope at the bottome , whereunto you must hang a weight of such heavinesse , that it may draw the body of the glasse under water . the necke of this glasse must bee open , and stand above the water ; also about the necke must bee fastened a good broad peece of wood ; round about which ( but on that side of it that is next unto the water ) must be placed divers peeces of looking glasses ; so the light of the candle in the glasse body will bee multiplied according unto the number of them . all the fishes neere unto it will resort about it , as amazed at so glorious a sight , and so you may take them with a cast net or other . how to make an image hang in the middle of a glasse . make the lower part of the image of hard wax , and the upper part of wood , and overlay it with oyle colours ; then put it into a globe glasse filled with fayre water , and which way soever you turne the glasse , the image will still hang in the middle , and stand as it were upright ; which , to my knowledge , hath been a thing causing no small admiration among divers that have not understood the cause of it . how to make five or six dice of the ordinary bignesse of dice , such as you may game withall , and such as would be taken by their lookes to bee ordinary dice , and yet all of them to weigh not above one grain . take a peece of elder , and pith it , lay the pith to dry , and then make thereof with a sharp knife five or six dice , and you shall finde it true that i haue sayd . to lay gold on any thing . take red lead ground first very fine , temper it with linseed oyle : write with it , and lay leafe gold on it , let it dry , and pollish it . to lay gold on glasse . grinde chalk , and red lead , of each a like quantity , together , temper them with linseed oyle , lay it on ; when it is almost dry , lay your leafe gold on it , when it is quite dry polish it . to make yron as soft as lead . take black flints , powder them very finely ; then put the powder in an iron pan , and make it red-hot , then cast it on a marble stone , till it be almost cold , then make it red-hot againe , and let it coole , and grinde it so long till it cleave to the stone , and grinde as it were clay ; then put that in a glasse , and set it under the eaves of a house , where the sunne commeth not nigh in the day , then the night after take out the water that you shall finde in the glasse above the powder , then take that powder and grinde it with the water , and put it in a stillatory , and let it still out the halfe ; afterward poure the water againe on the sayd powder , and still it againe with a soft fire ; then take and seethe that water till the halfe bee wasted , then take some iron blade that is new broke , and put it together , and hold it so a little while ; then take of the water which was sod to the half , and with a feather lay it first to the one side of the blade , and when the water is cold , lay it on the other side , and it will soder fast with this water ; and with this water you may make steele as soft as lead . it is likewise a soveraigne water to help the gout , being anoynted where the griefe is , for it giveth ease very speedily . to colour tin , or copper , &c. of a golden colour . take linseed oyle , set it on the fire , scum it cleane , then put therein of amber , and aloe hepaticum , a like quantity , then beat and stir all well together with the oyle till it wax thick ; then take it off , and cover it close , and set it in the earth three dayes : when you would use it , strike your metall all ouer therewith , and so let it dry , and it will be of a golden colour . to gild iron with a water . take running water 3 pound , rochallum 3 pound , and roman vitreoll one ounce , of vardigrease one penny waight , saltgem three ounces , orpment one ounce , boyle all these together , and when it begins to boyle , put in lees of tartar and bay salt , of each halfe an ounce ; make it seethe , and being sod a pretty while , take it from the fire , and strike the iron over therewith , then let it dry against the fire , and then burnish it . to soder on iron . set your joynt of iron as close as you can , then lay them so in a glowing fire ; then take of venice glasse in fine powder , and the iron being red-hot , cast the powder thereon , and it shall soder of it selfe . if you clap it in clay , it will be the surer way . to gild on iron or steele . take one ounce of argall , three drammes of vermileon , and two drams of bol armeniack , with as much aqua vitae , then work and grinde them all together on a stone , with linseed oyle ; having so done , put there to lapis calaminaris as big as a hazell nut , and grinde therewith in the end three or foure drops of varnish ; take it off the stone , and strain it through a linnen cloth into a stone pot , ( for it must bee as thick as hony ) then strike over your iron therewith , and let it dry , and then lay your gold or silver on , as you would do upon the varnish . a varnish like gold , for tin , silver , or copper . take small pots well leaded , then put therein six ounces of linseed oyle , one ounce of mastick , one ounce of aloes epaticum ; make them altogether in fine powder , and then put it into your sayd pot , and cover it with such another ; yet in the bottom of the uppermost pot make a small hole , wherein put a small stick with a broad end beneath to stir the other pot withall , and when the pots are set just together , close them all about with good clay , and couer them all over also , leaving the hole open above to stir the other pot with the stick : set it over the fire , and stir it as often as it seetheth , and when you will gild , pollish your metall over first , and then strike this over the metall , and let it dry in the sunne . to lay gold on iron , or other mettall . take liquid varnish l. 1. turpentine , & oyle of lynseed , of each an ounce : mixe them all together : with this ground you may gild on any mettall , first striking it upon the mettall , and afterward lay on the gold or silver . when it is dry , polish it . to make ice that will melt in fire , but not dissolve in water . take strong water made with saltpeter , allum , and oyle of tartar , of each , one pound . infuse them together , then put into them a little aqua ardens , and it will presently coagulate them , and turne them into ice . a cement as hard as stone . take powder of loadstone , and of flints , a like quantity of either , and with whites of egges , and gumme dragant , make paste , and in a few dayes it will grow as hard as a stone . to make paper waved like unto marble . take divers oyled colours , put them severally in drops upon water , and stirre the water lightly , and then wet the paper ( being of some thicknesse ) with it , and it will be waved like a marble : dry them in the sun. to make copper or brasse have the colour of silver . take sal armoniacke , allum , and salt , of each a like quantity , and with a little filings of silver , let all be mixt together , then put them into the fire , that they may be hot , and when they shall cease to smoke , then with the same powder moystned with spittle , rub your copper or brasse . how to make glew to hold things together as fast as stone . take of the powder of tile sheard , two pound , unslakt lyme , foure pound , oyle of lynseed , a sufficient quantity to temper the whole mixture ; this is marvellous strong . to make a thinne glew . take gluten piscis , beate the same strongly on an anvill , till it be thin ; after lay it to soke in water , untill it be come very soft and tender : then worke it like paste , to make small rowles thereof , which draw out very thinne , and when you will worke with it , put some of it into an earthen pot , with a little water , over the embers , and skim the same very cleane , and let it seeth a little while , then worke with the same : keeping it still over the fire . with this glew you may fasten peeces of glasse together . to make iron have the colour of brasse . first , polish it well , rub it after with aqua sortis , wherin the filings of brasse are dissolved : the like may bee done with roman vitrioll dissolved in vineger and faire water , of each a like quantity . to make wood or bone red for ever . take the powder of brazill , mingle it well with milke , but so , that it be very red , and put therein , either wood or bone , letting it lye in eight dayes , and it will looke red for ever . how with one candle to make as great a light , as otherwise of two or three of tbe same bignesse . cause a round and double glasse to be made , of a large size , and in fashion like a globe , but with a great round hole in the top , and in the concave part of the uppermost glasse , place a candle in a loose socket , and at the same hole or pipe which must be made at the side thereof , fill the same with spirit of wine , or some other cleere distilled water that will not putrifie , and this one candle will give a great and wonderfull light , somewhat resembling the sunne beames . a cement for broken glasses . beate the whitest fish glew with a hammer , till it begin to waxe cleere , then cut the same into very small pieces , suffering the same to dissolve on a gentle fire , in a leaded pan , with a few drops of aqua vitae , then let some other that standeth by , hold both the pieces that are to bee cemented , over a chafingdish of coles , till they be warme : and during their heat , lay on the dissolved glew with a fine pensill : then binde the glasse with wyre or threed , and let it rest till it be cold . an admirable secret of representing the very forme of plants , by their ashes , phi●osophically prepared , spoken of by quertitanus and angelus salae . take saith hee , the salt both the fixed and the volatill also . take the very spirit , and the phlegme of any herbe , but let them all be rightly prepared ; dissolve them , and coagulate them , upon which if you put the water stilled from may dew , or else the proper water of the herbe you would have appear , close them all very well in a glasse for the purpose , and by the heat of embers , or the naturall heat of ones body , at the bottome of the glasse , the very forme and idaea thereof will be represented : which will suddenly vanish away , the heat being withdrawne from the bottome of the glasse . as i will not argue the impossibility of this experiment , so i would be loth to employ mine endeavours , untill i were expert therein . a device to bend glasse canes , or make any small worke in glasse . let there be a vessell of copper about the bignesse of a common foot-ball , as , a , let it have a long pipe at the top as c. which must be made so that you may upon occasion screw on lesser , or bigger vents made for the purpose . fill this one third part with water , and set it over a fornace of coals , as f , g , h , i , and when the water beginneth to heat , there will come a strong breath out of the nose of the vessell , that will force the flame of a lampe placed at a convenient distance as k : if you hold your glasse in the extention of the flame it will melt suddenly ; so you may worke what you will thereof . there are that instead of this globe make use of a pipe , as a , fastned in a sticke as , f , of which i have made use , but hold it not so convenient for those that are not accustomed thereunto . an excelleut water for any morphue , or scurvinesse in the face . take of quicke sulphur 2. ounces , blacke sope , the rankest and illest favoured that can bee got : binde them up in a cloth , and hang them in a pint of the strongest wine vineger for the space of nine dayes ; herewith wash the morphue in the face or elsewhere , and let it dry in of it selfe . this water will for the present staine the face with a yelow collour , which will weare away in time . how to soften iron . take of allum , sal armoniacke , tartar , a like quantitie of either , put them into good vineger , and set them on the fire : heat your iron , and quench it therein . a good cement for broken glasses . take raw silke , and beat it with glasse , and mixe them together with the whites of egges . another . take of calcined flints , quicke lyme , and common salt , of each a like quantity : mingle them all together with the whites of egges ; then take a linnen cloth and spread it over with this mixture , and put it upon the fracture , and let it dry ; afterwards annoint it with linseed oyle . how to cause that the same quantitie both of powder and shot discharged out of the same peece shall carry closer , or more scattering . take the quantitie of a pease of opium , and charge it amongst the shot , and this will make the shot to flie closer together then otherwise it would . this i had of a sea-man , who had made triall hereof , as he said , and unto whom i sold some for the same purpose . a baite to catch fish with . take cocculus indiae ℥ ss , henbane-seeds , and wheaten flower , of each a quarter of an ounce , hive honey as much as will make them into paste . where you see most store of fish in the river , cast of this paste into it in divers little bits about the bignesse of barley cornes , and anon you shall see the fish swimme on the top of the water , some reeling to and fro as drunken , others with their bellies upwards as if they were nigh dead ; so that you may take them either with your hands , or a small net at the end of a sticke made for the same use . note here , that if you put the fish that you thus take , into a bucket of faire and fresh water , or if it raine after that you have cast this your bait into the water , they will revive and come to themselves to your admiration ; and this was told me by a gentleman of good credit , that hath often made use thereof . i have heard that the stinking oyle drawne out of the roots of polipody of the oake by a retort , mixed with turpentine , and hive-honey , and being anointed upon the bait will draw the fish mightily thereto , and make them bite the faster : and i my selfe have seene fishes , as roches , and taken in the dead time of winter with an angle , bayted onely with paste made of wheaten flowre , but it hath beene in the morning , and when the sunne hath shined . how to write without inke that it may not be seene , unlesse the paper be wet with water . take some vitriol , and powder it finely , and temper it with faire water in any thing that is cleane , when it is dissolved , you may write whatsoever you will with it , and it cannot be read , except you draw it through water wherein some powder of galls hath beene infused , and so it will shew as blacke as if it had beene written with inke . how to make white letters in a blacke feild . take the yelke of a new layd egge , and grinde it upon a marble with faire water , so as you may write with it : having ground it on this wise , then with a penne dipt into it , draw what letters you will upon paper , or parchment , and when they are through drie , blacke all the paper over with inke ; and when it is drie , you may with a knife scrape all the letters of that you wrote with the yelke of the egge , and they will shew faire and white . how to sodder upon silver , brasse , or iron . there are two kindes of sodder , to wit , hard sodder , and soft sodder . the soft sodder runneth sooner then the hard : wherefore if a thing be to be sodered in two places , which cannot at one time well be performed , then the first must be sodered with hard soder , and the second with soft : for if the first be done with soft , it will unsoder againe before the other be sodered . note , that if you would not have your soder to runne over any one part of the peece to be sodered , you must rub over that part with chalke that you would not have it runne upon . note likewise that your soder must be beaten thinne , and then laid over the place to be sodered , which must be first fitted together , and bound with wyer as occasion shall require . then take burras , powder it , and temper it with water like pap , and lay it upon the soder , and let it drie upon it by the fire : afterwards cover it with quicke coals , and blow them up , and you shall see your soder run immediately : then presently take it out of the fire , and it is done . hard soder is thus made . take a quarter of an ounce of silver , and a three penie weight of copper , melt them together , and it is done . soft soder is thus made . take a quarter of an ounce of silver , and a three penie weight of brasse , melt them together , and it is done . how to gild silver , or brasse , with water-gold . first take about ℥ . ii . of quicke silver , put it into a little melting pot , and set it over the fire , and when it beginneth to smoke , put into it an angel of fine gold : then take it off presently for the gold will presently be dissolved in the quicke silver , which if it be too thinne , you may through a peece of fustian straine a part of the quicke-silver from it . note likewise that your silver , or brasse , before you go about to gild it , must be boyled in argol , and beare , or water , and afterwards scratcht with a wyer brush : then rub the gold , and quicke-silver upon it , and it will cleave unto it , then put your siluer or brasse upon quicke coales untill it begin to smoke : then take it from the fire , and scratch it with your wyer brush : do this so often till you have rubd the quicke-silver as cleane off as you can , then shall you perceive the gold to appeare of a faint yellow colour , which you may make to shew faire with sal armoniacke , bole armoniacke , and vardigrece ground together , and tempered with water . how to take the smoake of tobacco through a glasse of water . first fill a pinte glasse with a wide mouth , almost full of faire water : fill also a pipe of tobacco , and put the pipe upright into the glasse of water , so that the end of the pipe may almost touch the bottome of the glasse : then take another crooked pipe , and put it into the glasse , but let the end thereof not touch the water : waxe then the mouth of the glasse , that no ayre may come in nor out , but at the pipes : then put fire unto the tobacco , and sucke with your mouth , at the end of the crooked pipe , and you shall see the smoake of the tobacco penetrate the water , and breake out of a bubble , and so come into your mouth . to colour ivory or any other bones , of an excellent greene colour . take aqua fortis , wherein dissolue as much copper , as the said water is able , then let the bones that you would have coloured , lye in the same all night , and they will be like a smaragdin colour : mizaldus . how to make birds drunke , so that you may take them with your hands . take such meate as they loue , as wheate , barley , and lay the same to steepe in the lees of wine , or else in the juyce of hemlockes , and sprinckle the same in places where birds use to haunt . a way to catch crowes . take the liuer of a beast , and cut it in diuers pieces , put then into each piece , some of the powder of nux vomica , and lay these pieces of liuer in places where crowes and rauens haunt . anon after they haue eaten them , you may take them with your h●nds , for they cannot flye away . how to take crowes or pigeons . take white pease , and steepe them eight or nine daies in the gall of an oxe : then cast the same where they use to haunt . you may make partridges , duckes , and other birds drunke , so that you may take them with your hand : if you set blacke wine for them to drinke in those places whereunto they resort . another . take tormentill , and boile it in good wine : put into it barley or other graine : sprinckle this in those places you haue appointed to take birds in , and the birds will eate the pieces amongst the graine , which will make them so drunke , that they cannot flye away . this should be done in the winter , and when it is a deepe snow . another way to take birds . make a paste of barley meale , onion blades , and henbane seeds : set the same upon seuerall little boards , or pieces of tiles , or such like , for the birds to eate of it . how to make brasse white for ever . take egge shels , and burne them in a melting pot : then powder them , and temper them with the whites of egges ; let it stand so three weekes : heate your brasse red hot , and put this upon it . how to make marble . take ℥ vj. of quicke lime , put it into a pot , and poure upon it , one pinte of good wine : let it stand fiue or sixe dayes , stirring it once or twice a day : then poure off the cleare , and therewith temper flint stones calcined , and made into fine powder , then colour it , and make of it what you please , and let them dry . how to whiten copper . take a thin plate of copper , heat it red-hot divers times , and extinguish it in common oyl of tartar , and it will be white . to make saltpeter . take quick lyme , and poure warm water upon it , and let it stand six dayes , stirring it once or twice a day : take the cleare of this , and set it in the sunne untill it bee wasted , and the saltpeter will remaine in the bottom . how to make corall . take of red lead ground , ℥ 1. vermilion finely ground , ℥ ss . unquenched lyme , and powder of calcined flints , of each ℥ vj. these powders must bee tempered with a lixivium that is made with quick lyme and wine : adde unto the whole a little salt ; then make thereof what you list ; then boyle them in linseed oyle . how to make pearles of chalk . take some chalk , and put it into the fire ; there let it lie untill it break : temper it then with the whites of egs . then make of it divers fashions of pearles , both great and small : wet them being dried , and cover them with leafe gold , and they are done . an approved and excellent plaster for ach in the raines of the back , or in any other part whatsoever . take one pound of black sope , and foure ounces of frankincense , and a pinte of white wine vineger : boyle all together upon a gentle fire , untill it be thick ; spread it then upon a lether , and apply it unto the grieved place . if the ach bee very great and fervent , then adde unto it a little aqua vitae , and it will be much better . an excellent oyntment for the shingles , morphew , tetters , and ringwormes . take a quarter of a pound of sope , and mingle with it two drams of the powder of black ellebor , litharge of silver in fine powder , two ounces , vardigrease halfe an ounce , and a quarter of an ounce of glasse in powder , and as much quicksilver , make them all into an oyntment by stirring them well together ; wherewith anyont the grieved parts . this is approved and true . an excellent balme , or water for grievous sore eyes , which commeth either of outward accident , or of any inward cause . take two spoonfuls of the juyce of fennell , and one spoonfull and a halfe of the juyce of celandine , and twice as much hony as them both ; then boyle them a little upon a chafingdish of coales , and scum away the dregs which will ascend , but first let it coole somwhat , and then let it run through a fayre cleane cloth : then put it into a violl of glasse , and stop it close . put a little quantity of this into the eye . this medicine is approved , and more precious than gold . a speedy way to asswage the paine of any scald , or burne , though never so great , and to take the fire out of it . take old lawn rags , dip them into runnet , for want of it dip them into verges , and apply them cold upon the grieved place , shifting them for halfe an houre together , as oft as they dry : this i have known to give ease in an instant , and quickly to take out the fire . an approved oyle for to heale any burne or scald . take of housleek one handfull , and of brooklime as much , boyle them in a quart of creame untill it turne unto an oyle ; boyle it very gently : with this oyle a little warmed , anoint the grieved place twice a day , and it will soone make it well . an oyntment , very excellent and often proued , for the same . take a good quantity of mosse scraped from off a stone wall , fry it in a fryingpan with a call of mutton suet a good while , then straine it , and it is done . dresse the grieved part therewith once or twice a day , as you shall see fitting . another oyntment for a burne . take one part of sallet-oyle , and two parts of the whites of egs , beat them together exceeding well , untill they come to be a white oyntment , wherein dip the feather of a black hen , and anoynt the grieved place divers times every day , untill such time as the scales fall off , using in the meane while neither clothes nor any outward binding . this , sayth minshet the authour , though it seeme to be a thing of no estimation , yet was there never found any more effectuall for a burn than it is . an excellent oyntment for a green wound . take foure handfuls of clownes , allheale , bruse it , and put it into a pan , and put to it foure ounces of barrowes grease , sallet-oyle halfe a pound , bees wax a quarter of a pound ; boyle them all untill the iuyce be wasted ; then straine it , and set it over the fire againe , and put unto it two ounces of turpentine , then boyle it a little while more , and it is done . put hereof a little in a saucer , and set it on the fire , dip a tent in it , and lay it on the wound , but first lay another plaister round about the wound , made of diapalma mollified a little with oyle of roses . this cureth very speedily all greene wounds , as saith m. gerard. a balsam of wonderfull efficacy . take burgundie pitch , brimstone , and white frankincense , of each one ounce : make them into an oyntment with the whites of egges : first draw the lips of the wound , or cut , as close as you can , then lay on some of this spread upon a cloth , and swathe it ouer afterwards . an excellent healing water , which will drie up any old sore , or heale any greene wound . take a quarter of a pound of bolearmoniacke , powder it by it selfe , then take an ounce of camphire , powder it also by it selfe : also take foure ounces of white coppras in powder : mixe the coppras and camphire together , and put them into a melting pot , and set them on the fire , untill they turne unto water : afterwards stirre it untill it come to be as hard as a stone : then powder it againe , and mixe it with the bole-armoniacke : keepe this powder close in a bladder , when you would use it , take one pinte and a halfe of faire water , set it on the fire , and when it is even ready to boyle , put into it three spoonfuls of the powder ; then take it off from the fire , and put it into a glasse , and let it stand untill it be cleare at the top , then take of the clearest , and wash the sore very warme therewith , and dip a cloth foure double in the same water , and binde it fast about the sore with a rowler , and keepe it warme : dresse it thus twice a day . a water for a fistula take one pint of white wine , 1 ounce of juyce of sage , three penie weight of borace in powder , camphire in powder the weight of foure pence : boyle them all a prettie while on a gentle fire , and it is done : wash the fistula with this water , for it is certainly good , and approved to be true . a water for the toothache . take ground ivie , salt , and spearemint , of each an handfull : beat them very well together , then boile them in a pint of vineger ; straine it , and put a spoonfull of it into that side that aketh , and hold downe your cheeke . another water approved for the same . take red rose leaves halfe a handfull , pomegranate-flowers as many , two gaules sliced thinne : boyle them all in three quarters of a pint of red wine , and halfe a pint of faire water untill the third part be wasted : then straine it , and hold a little of it in your mouth a good while : then spit it out , and take more . also if there be any swelling on your cheeke , apply the strainings betweene two clothes as hot as may be suffered . this i have knowne to do good unto divers in this citie , when as they have beene extreamely pained . to make a water for the eyes . take lapis calaminaris , and burne it in the fire nine times , and quench it in white wine , and beat it into powder , and when you use it , put it into rose-water , and drop the water into the eye . for deafenesse . take a good quantitie of camomill , and two handfuls of greene wormewood , and seethe them in a pot of running water till they be very well sodden , and put a funnell over it , and let the steame go up into the eare , and then go to bed warme , and stop your eare with a little blacke wooll , and a grain of civet : do this morning and evening , and with gods assistance you shall finde ease . an excellent electuary for the cough , cold , or against flegme . take of germander , hissope , horehound , white maidenhaire , agrimony , bettony , liverwort , lungwort , and harts-tongue , of each one handfull : put these to nine pints of water , and let them boyle to three pints ; then let it coole and straine it . to this juyce put of clarified honey halfe a pound , fine powder of liquorice fiue ounces , fine powder of enulacampana root three ounces , boyle them to the thicknesse of an electuary . take of this at any time , but specially in the morning fasting , as also at night when you go to bed , or two houres after supper , the quantitie of a wallnut or nutmeg . a very excellent salve to heale , well proved , for any old sore , or new wound . take of waxe , rosin , sheeps suet , turpentine , of each a like quantitie , sallet oyle also as much : mixe them all together , and take the juyce of smallach , of planten , of orpin , of buglosse , of comfery , of each a like quantitie : let them boyle untill the iuyce of the hearbes be consumed ; and in the seething put a quantitie of rose-water , and it will be a very good salue . a soveraigne water to heale a greene wound : and to stanch bloud . take a pottle of running water , and put thereto foure ounces of allum , and one ounce of copras , and let them seethe to a quart , and then straine it , and keepe it in a glasse , and wash the wound , and wet a cloth , and lay to the sore , and with gods helpe it will soone be healed . for the byting of a mad dogge . take brine , and bathe the wound : then burne claret wine , and put in a little mithridate , and so let the patient drinke it ; then take two live pigeons , cut them through the middle , and lay them hot to his hand if he be bitten in the armes . if in his legges , to the sole of his feet . an oyle for any ach. take a pound of unwashed butter , and a handfull of red mints , and a handfull of camomill , a handfull of rew , two ounces of oyle of exeter : stamp the herbs to a juyce , and boyle them with the butter ; straine them in a cloth , and rub them out very well : this so done , take the oyle of exeter , and put to them , and stir them well together , and put them into a gally pot , and where the ach is anoint the place against the fire , and lay a browne paper on it , and wrap a cloth about the place , and keepe it warme : proved to be excellent . to stanch the bleeding of a cut . take a peece of a felt hat , and burne it to a coale ; beat it to powder , and put it in the cut , and it will stanch the bleeding presently . or else apply linnen rags that in the spring of the yeere have beene often washed in the sperm of frogs , and afterward dried in the sunne . for an ague , to bee layd to the wrists . take a handfull of soot , a spoonfull of bay salt , halfe a spoonfull of pepper ; bruse them together , and temper them with two yelks of egs ; spread it on a cloth , and lay it to the wrists . almond milke for the cough of the lungs . take foure spoonfuls of french barly well washed , and boyle it in three wine pints of faire water , unto a pint and a halfe ; then take it from the fire , and let it coole , and settle ; then take the cleere liquor , and straine therewith a quarter of a pound of sweet almonds blanched , and beaten ; then set it on the fire , and let it boyle a while till it begin to grow thick ; then beat two yelks of egs , and put them to it ; stirre them well together , and put to it as much fine suger as will sweeten it , and a spoonfull of damask rose water , and so let it boyle a while longer , till it be as thick as good creame ; eat of it warm twice or thrice a day , but at breakfast especially . for a scald head . take a pinte of running water , and as much mercury as a good walnut , three or foure branches of rosemary ; boyle these all together till a third part be boyled away , or thereabout , and every morning and evening wash the infected place with some of this water cold , and a quarter of an houre after or lesse anoint the place with lamp oyle , and every morning after the first dressing try to pull up some of the hayre as easily as you can : have care where you set this water , for it is poyson . if you shave the head , and apply a plaster called emplastrum cephalicum cum euphorbio , it is also excellent . for to heale a red face that hath many pimples . proved . take foure ounces of barrowes grease and as much oyle of bayes , halfe an ounce of quicksilver killed with fasting spettle , then take two spoonfuls of wilde tansie water , or honisuckle water , and let all be ground in a morter three houres at the least , untill you see nothing of the quicksilver , and so keep it close in a glasse ; the older , the better ; and when you go to bed anoint the face , and look that you keep it from your eyes . to wash the face , if it be given to heat . take snailes , beat them shels and bodies together : steep them a night in new milke : then still them with the flowers of white lillies . to make vsquebach . take a gallon of the smallest aqua vitae you can make , put it into a close vessell of stone ; put thereto a quart of canary sacke , two pounds of raisons of the sunne stoned , but not washed , two ounces of dates stoned , and the white skinnes of them pulled out , two ounces of cinamon grossely bruised , foure good nutmegs bruised , foure good liquorish sticks sliced , and bruised , tye up all your spices in a fine linnen cloth , and put them into your aqua vitae , and tye up your pot very close , and let this infuse a weeke , stirring it three times a day , then let it runne through a jelly bagge close covered ; keepe it in glasse bottles . to make almond butter . take two pound of almonds , and blanch them , and let them lye all night in cold water : then grinde them in a mortar very small , and put in a blade of mace or two ; then straine it through a strong cloth as neare as you can , that the milke be not too thin , and let it seethe a prettle while : then put in a little rose-water , and a little salt when you take it off the fire , and stirre it still : then take a bigge cloth very cleane , and let two hold it ; then you must take the milke and cast it round about the sides of the cloth that the whay may come from it ; then with a saucer put it downe from the sides : then knit the cloth , and hang it up untill it have left dropping ; then take it forth , and season it with fine sugar and rose-water . to make ielly for one that is in a consumption , or troubled with a loosenesse . take the feet of a calfe , and when the haire is cleane scalded off , slit them in the middle , and cut away all the blacke veines , and the fat , and wash them very cleane , and so put them in a bucket of faire water , and let them lye foure and twentie houres , and in that time the oftner you shift them in faire water it will be the better ; then set them on the fire in two gallons of water , or somewhat lesse , and let them boyle very softly , continually taking off the scumme and fat which riseth ; and when the liquour is more then halfe boyled away , put into it a pinte and a halfe of white wine , and as it boyleth there will come a foule scumme upon it , take it off still cleane , and when the ielly is boyled enough , you may know , for your fingers will sticke to the spoone ; then take it from the fire , and with a cullender take out all the bones and flesh , and when the ielly is almost cold , beat the whites of sixe egges , and put into it , and set it on the fire againe , and so let it boyle till it be cleare : then straine it through a cleane cloth into a bason , and so let it stand all night long ; the next morning put it into a skellet , and put to it a pound of sugar , halfe an ounce of cinamon broken in peeces , one ounce of nutmegs , an ounce of ginger bruised , and a good quantitie of large mace ; boyle all these together till it taste of the spices as much as you desire , and when it is almost cold , take the whites of six egs , and beat them , and put into it , and set it on the fire , and when it riseth wilde it in halfe a pint of white wine ; then strain it through a jelly bag . to stay the flux . take date stones , and beat them to fine powder , and take the quantity of one of them , and drink it with posset drink , or beere ; use these two or three mornings together , and after as often as you finde occasion ; this is very good . in the month of may gather of the reddest oak leaves you can get , and still them , and when need requireth make pap thereof , mingled with milk or fine flower , suger , and cinamom , as oft as your stomack serveth to eat it . to make green ink. take greene bice and grinde it with gum water , and if you will have it a sadder green , put a little saffron to the grinding . to make blew ink. tae fine flower , and grinde it with a little chalk , and allum , and then put it in a violl . for an ague . take a handfull of hartstong that groweth in the field , and a handfull of bay salt , and beat them both together in a morter , and lay this to both the wrists . a water good against the plangs , or to be given after a surfet . take red sage , celendine , rosemary , hearbegrace , wormwood , mugwort , pimpernell , dragons , scabious , egrimony , rosa solis , and balme , of e●ch a handfull , or like quantity by weight ; wash and shake them in a cloth ; then shred and put them into a gallon of white wine , with a quarter of an ounce of gentian roots , and as much of angelica roots ; let it stand two dayes and two nights close covered , and then distill it at your pleasure , and stop the glasse very close in which you keep the same . to avoyd urine that is stopped with the stone . take as much black sope as a walnut , temper it with eight or ten leaves of english saffron , spread it upon a round leather as big as the palme of your hand , and cover the navell of your belly therewithall , and it shall cause you to make water . for the stone and strangury . take the filmes that is within the mawes of geese , and let them bee purely dried , and then make powder thereof , and drink it with stale ale , and it will help him with gods grace . proved . for scald heads . take green coperas , and mingle it with creame till it bee turned yellow , and let it stand three or foure dayes : then take primrose roots , leaves and all , with may butter , and beat the roots and leaves in the butter , and boyle them together with a little beere and butter , and let it touch no salt . to cure an old vlcer . take a quart of the strongest ale that is to be gotten , or brewed , halfe a pint of raw honey , two ounces of roch allum beaten , halfe a pint of sallet oyle , and the quantitie of a tennis ball of common washing sope , one ounce of stone pitch beaten ; one ounce of rosin beaten , two ounces of yellow waxe : boyle all these together , and straine them through a thin linnen cloth ; and this will cure any old vlcer . a water to cleanse , and mundifie old rotten sores and ulcers . take a wine pint of stilled water of planten , as much white wine ; put therein two ounces of roch allum , a dramme of verdigrease , a dramme of mercurie sublimed : boyle all these together , and keepe them in a thicke glasse being stoped with waxe very close that the strength go not out ; this will cleanse and mundifie old sores ▪ it will also heale a fistula if you use a siering , so that the water may come to the bottome of the sore . the medicine of medicines proved for the stone . take a quantity of eg-shels , wash them cleane ; those are the best whereout chickens are come ; dry them very dry in an oven , or betweene two tile-stones ; then make powder thereof , searce it , and mingle it with sugar , or powder of licoras to give it taste , and let him use it as often as hee needeth , morning and evening , either with rhenish wine , white wine , or stale ale , a spoonfull of the powder at a time , and use to make water in a cleane bason , and so you shall see the deliverance hereof . a precious water for the sight . take smallage , fennell , rew , verveine , egrimony , daffadill , pimpernell , and sage , and still them with breast milk together with five drams of frankincense , and drop of it in your eyes each night : often proved . for the fluxe to stay it . take the yolke of an egge , and beat it , then mixe with it one grated nutmegge , and lay it on an hot tyle stone to bake , and eate thereof fasting , and before supper , and after meales , and it will stay it . often proved to be excellent . a good powder for the gout . take fine ginger the weight of two groats , and enula-campane-roots dryed , the weight of foure groats , of liquorish the weight of eight groats , of sugar-candy three ounces ; beat all these into a powder , searce them fine , and then mingle them together , and drinke thereof morning and evening , and all times of the day . approved . a speciall medicine for the collicke . take horehound halfe an handfull , of sage , and hysope of either as much , twelve leaves of betony , of centaury sixe crops , one alexander-root , foure penie weight of enula-campana roots powdered , spikenard of spaine one penie worth ; seethe all these in three quarts of fine wort to a pottle , and draw it through a linnen cloth , and take three spoonfuls at once morning and evening . to take away rednesse of burning of the eyes . take the white of an egge , and beat it very well with a spoonfull or two of red rose-water , then put thereto the pap of a rosted apple , mingle them well together , and spread it upon a little flaxe ; so lay it on the eye , binding it on with a linnen cloth . for the rheume in the eyes . take the white of an egge , and so much bolearmoniacke as will thicken it , and spread it on a round plaister of sheeps leather , and lay it on the temples on that side the rheume is . the oyntment for the same . take lapis tutiae and burne it in a fire-shovell of quicke coales , quench it in a poringer of womans milke , do so halfe a score times , then grinde it in a cleane morter till it be very fine powder , then mingle it with fresh barrows grease till it looke russet : anoint your eyes with a little of it when you go to bed . for deafenesse . take rew , and rub it betweene the palmes of your hands untill it be so brused that you may make thereof a tent ; then dip it in sweet sallet oyle , and put in each eare one , so that you may pull them forth againe . this doe for seven or eight dayes , and change the tent every day . take a quarter of a pinte of angelica water , of cardus benedictus water , and of white wine , of either a like quantity : mingle them together , dividing the same into two equall parts ; drink it in two severall mornings : then the next night after the taking of the second draught of water , take the fish of an oyster , and put it into a fayre linnen cloth , and stop the same into the eare that is thickest of hearing , and lie on that side as long as you can : in the morning pick that eare as cleane as you can , and after that take a draught of the best ale you can get , with a toast of houshold bread toasted very dry , a reasonable quantity of nutmegs ; use the same every morning for five or six dayes , fasting after the taking hereof two houres , every time you take it . for the cough of the lungs . take two handfuls of rosemary , and strip it of the stalk , one of hissop , and seethe them in a pottle of running water , till it come to a quart , and then put a quarter of a pound of fine sugar , and let it seethe a little , and scum it , drink it morning and evening . a present remedie for all manner aches , and bruises in the bones . take a good quantitie of wallwort , and a certaine quantity of balme , and smallach , and stamp them , and take a pound of may butter , and temper them very well together , then make them into round bals , and let them lye for the space of eight dayes after , and then stampe them againe as you did before : then take it , and fry it , and straine it , and put it into an earthen pot : this will helpe the bruise , be it never so blacke . for burning , or scalding . to take out the fire , beat onyons very small , and binde them to the place . to heale it , take halfe a pound of sheeps suet , as much sheeps dung , a quarter of a pound of the inner rinde of an elder-tree , and a little housleeke : fry them altogether , and straine it , and use it as a plaister , or make a serecloth of it , and apply it to the grieved part . for burstnesse of old , or young . take nine red snailes , lay them betweene two tyles of clay , so that they creepe not nor slide away , and bake them in the hot embers , or in an oven , till they may be powdered , then take the powder of one of the snailes , and put it in white wine , and let the patient drinke it in the morning at his rising , and fast two houres after , and drinke these nine snailes in eighteene dayes , that is , every other day one . and if the sicknesse be so old that it will not heale in eighteene dayes , begin againe , and drinke other nine snailes , and he shall be whole . probatum est . a salve for all sores . take a pound of sheepes-tallow , and a pound of turpentine , and a pound of virgin-waxe , a pint of sallet oyle , a quarter of a pound of rosin : take also bugle , smallach , and plantaine halfe the quantitie of the other , or so much as will make a pint just : boyle all these together upon a soft fire of coales , alwayes stirring it till a third part be consumed ; then take it from the fire , and straine it through a new canvas cloth into an earthen pot . for bleeding . take a blacke toade in may , drie it betweene two tile stones , and hang it in sarcenet about the parties necke . to procure sleepe . take betony , roseleaves , vinegar , nutmeg , and the crummes of rye-bread : put this in a cloth warme to the poll of the head . for the cough . two handfuls of last saverie , steepe it five dayes in white wine vineger , put into the vineger halfe an ounce of pepper , at the five dayes end draine out the vineger , and as soone as the bread is drawne , set them in a pewter dish into the oven , and stop it up , and let them stand all night . in the morning take them out of the oven and powder them . take of this powder and drinke it with sacke , so much of it as will lye on a three-pence . a gargill for the ●vula . take a pint of good strong ale , and as much sacke , and a good quantitie of long pepper , and bruise it grossely , and boyle it from a quart to a pinte , and let the parties gargle their mouthes , and throats as warme as they may suffer it . if the pallat of the mouth be downe , it will fetch it up . for deafnesse very excellent good . take the hoofes of the neats feet after they be sodden , and hold them in a cloth so warme as may be to your eare , divers times together one after another . they will last to be warmed in the same they were sodden in some three or foure dayes without sowring . finis . mathematicall recreations. or, a collection of many problemes, extracted out of the ancient and modern philosophers as secrets and experiments in arithmetick, geometry, cosmographie, horologiographie, astronomie, navigation, musick, opticks, architecture, statick, mechanicks, chemistry, water-works, fire-works, &c. not vulgarly manifest till now. written first in greeke and latin, lately compi'ld in french, by henry van etten, and now in english, with the examinations and augmentations of divers modern mathematicians whereunto is added the description and use of the generall horologicall ring: and the double horizontall diall. invented and written by william oughtred. récréation mathématique. english. 1653 approx. 447 kb of xml-encoded text transcribed from 177 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2005-12 (eebo-tcp phase 1). a48262 wing l1790 estc r217635 99829293 99829293 33730 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a48262) transcribed from: (early english books online ; image set 33730) images scanned from microfilm: (early english books, 1641-1700 ; 1992:7) mathematicall recreations. or, a collection of many problemes, extracted out of the ancient and modern philosophers as secrets and experiments in arithmetick, geometry, cosmographie, horologiographie, astronomie, navigation, musick, opticks, architecture, statick, mechanicks, chemistry, water-works, fire-works, &c. not vulgarly manifest till now. written first in greeke and latin, lately compi'ld in french, by henry van etten, and now in english, with the examinations and augmentations of divers modern mathematicians whereunto is added the description and use of the generall horologicall ring: and the double horizontall diall. invented and written by william oughtred. récréation mathématique. english. oughtred, william, 1575-1660. aut [40], 286, [17] p. : ill. printed for william leake, at the signe of the crown in fleetstreet, between the two temple gates, london : m d c liii. [1653] translation of: jean leurechon. recreation mathematique. henry van etten is a pseudonym of jean leurechon. with an added engraved title page reading: mathematicall recreations or a collection of sundrie excellent problemes out of ancient and moderne phylosophers. "the description and use of the double horizontall dyall" has separate title page dated 1652; register is continuous. running title reads: mathematicall recreation. reproduction of the original in the british library. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 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that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng science -problems, exercises, etx. -early works to 1800. mathematics -problems, exercises, etc. -early works to 1800. fireworks -early works to 1800. scientific recreations -early works to 1800. sundials -early works to 1800. 2005-02 tcp assigned for keying and markup 2005-05 spi global keyed and coded from proquest page images 2005-06 jonathan blaney sampled and proofread 2005-06 jonathan blaney text and markup reviewed and edited 2005-10 pfs batch review (qc) and xml conversion mathematicall recreations . or , a collection of many problemes , extracted out of the ancient and modern philosophers , as secrets and experiments in arithmetick , geometry , cosmographie , horologiographie , astronomie , navigation , musick , opticks , architecture , stati●k , mechanicks , chemistry , water-works , fire-works , &c. not vulgarly manifest till now . written first in greeke and latin , lately compi'ld in french , by henry van etten , and now in english , with the examinations and augmentations of divers modern mathematicians whereunto is added the description and use of the generall horologicall ring : and the double horizontall diall . invented and written by william oughtred . london : printed for william leake , at the signe of the crown in fleetstreet , between the two temple gates , mdcliii . on the frontispice and booke . all recreations do delight the minde , but these are best being of a learned kinde : here art and nature strive to give content , in shewing many a rare experiment , which you may read , & on their schemes here look both in the frontispice , and in the book . upon whose table new conceits are set , like dainty dishes , thereby for to whet and winne your judgement , with your appetite to taste them , and therein to taka delight . the senses objects are but dull at best , but art doth give the intellect a feast . come hither then , and here i will describe , what this same table doth for you provide . here questions of arithmetick are wrought , and hidden secrets unto light are brought , the like it in geometrie doth unfold , and some too in cosmographie are told : it divers pretty dyals doth descrie , with strange experiments in astronomie , and navigation , with each severall picture , in musick , opticks , and in architecture : in statick , machanicks , and chymistrie , in water-works , and to ascend more hie , in fire-works , like to joves artillerie . all this i know thou in this book shalt finde , and here 's enough for to content thy minde . for from good authors , this our author drew these recreations , which are strange , and true so that this book 's a centre , and t is fit , that in this centre ; lines of praise should meet w. mathematicall recreations or a collection of sundrie excellent problemes out of ancient & moderne phylosophers both vsefull and recreatiue printed for william leake and are to be solde at the crowne in fleet streete betweene the two temple gates . to the thrice noble and most generous lo. the lo. lambert verreyken , lo. of hinden , wolverthem , &c. my honourable lo. amongst the rare and curious propositions which i have learned out of the studies of the mathematicks in the famous university of pont a mousson , i have taken singular pleasure in certaine problemes no lesse ingenious than recreative , which drew me unto the search of demonstrations more difficult and serious ; some of which i have amassed and caused to passe the presse , and here dedicate them now unto your honour ; not that i account them worthy of your view , but in part to testifie my affectionate desires to serve you , and to satisfie the curious , who delight themselves in these pleasant studies , knowing well that the nobilitie , and gentrie rather studie the mathematicall arts , to content and satisfie their affections , in the speculation of such admirable experiments as are extracted from them , than in hope of gaine to fill their purses . all which studies , and others , with my whole indevours , i shall alwayes dedicate unto your honour , with an ardent desire to be accounted ever , your most humble and obedient nephew and servant , h. van etten . by vvay of advertisement . five or six things i have thought worthy to declare before i passe further . first , that i place not the speculative demonstrations with all these problems , but content my self to shew them as at the fingers end : which was my plot and intention , because those which understand the mathematicks can conceive them easily ; others for the most part will content themselves onely with the knowledge of them , without seeking the reason . secondly , to give a greater grace to the practice of these things , they ought to be concealed as much as they may , in the subtiltie of the way ; for that which doth ravish the spirits is , an admirable effect , whose cause is unknowne : which if it were discovered , halfe the pleasure is l●st ; therefore all the finenesse consists in the dexterity of the act , concealing the meanes , and changing often the streame . thirdly , great care ought to be had that one deceive not himselfe , that would declare by way of art to deceive another : this will make the matter contemptible to ignorant persons , which will rather cast the fault upon the science , than upon him that shewes it : when the cause is not in the mathematicall principles , but in him that failes in the acting of it . fourthly , in certaine arithmeticall propositions they have onely their answers as i found them in sundry authors , which any one being studious of mathematicall learning , may finde their originall , and also the way of their operation . fifthly , because the number of these problemes , and their dependances are many , and intermixed , i thought it convenient to gather them into a table : that so each one according to his fancie , might make best choise of that which might best please his palate , the matter being not of one nature , nor of like subtiltie : but whosoever will have patience to read on , shall finde the end better than the beginning . to the reader . it hath been observed by many , that sundry fine wits as well amongst the ancient as moderne , have sported and delighted themselves upon severall things of small consequence , as upon the foot of a fly , upon a straw , upon a point , nay upon nothing ; striving as it were to shew the greatnesse of their glory in the smalnesse of the subject : and have amongst most solid and artificiall conclusions , composed and produced sundry inventions both philosophicall and mathematicall , to solace the minde , and recreate the spirits , which the succeeding ages have imbraced , and from them gleaned and extracted many admirable , and rare conclusions ; judging that borrowed matter often-times yeelds praise to the industry of its author . hence for thy use ( courteous reader ) i have with great search and labour collected also , and heaped up together in a body of these pleasant and fine experiments to stirre up and delight the affectionate , ( out of the writings of socrates , plato , aristotle , demosthenes , pythagoras , democrates , plinie , hyparchus , euclides , vitruvius , diaphantus , pergaeus , archimedes , papus alexandrinus , vitellius , ptolomaeus , copernicus , proclus , mauralicus , cardanus , valalpandus , kepleirus , gilbertus , tychonius , dureirus , josephus , clavius , gallileus maginus , euphanus tyberill , and others ) knowing art imitating nature that glories alwayes in the variety of things , which she produceth to satisfie the minde of curious inquisitors . and though perhaps these labours to some humourous persons may seeme vaine , and ridiculous , for such it was not undertaken : but for those which intentively have desired and ●ought after the knowledge of those things , it being an invitation and motive to the search of greater matters , and to imploy the minde in usefull knowledge , rather than to be busied in vaine pamphlets , play-books , fruitlesse legends , and prodigious histories that are invented out of fancie , which abuse many noble spirits , dull their wits , & alienate their thoughts from laudable and honourable studies . in this tractate thou maist therefore make choise of such mathematicall problemes and conclusions as may delight thee , which kinde of learning doth excellently adorne a man ; seeing the usefulnesse thereof , and the manly accomplishments it doth produce , is profitable and delightfull for all sorts of people , who may furnish and adorne themselves with abundance of matter in that kinde , to help them by way of use , and discourse . and to this we have also added our pyrotechnie , knowing that beasts have for their object only the surface of the earth ; but hoping that thy spirit which followeth the motion of fire , will abandon the lower elements , and cause thee to lift up thine eyes to soare in an higher contemplation , having so glittering a canopie to behold , and these pleasant and recreative fires ascending may cause thy affections also to ascend . the whole whereof we send forth to thee , that desirest the scrutability of things ; nature having furnished us with matter , thy spirit may easily digest them , and put them finely in order , though now in disorder . a table of the particular heads of this book , contracted according to the severall arts specified in the title-page . experiments of arithmetick . page 1 , 2 , 3 , 16 , 19 , 22 , 28 , 33 , 39 , 40 , 44 , 45 , 51 , 52 , 53 , 59 , 60 , 69 , 71 , 77 , 83 , 85 , 86 , 89 , 90 , 91 , 124 , 134 , 135 , 136 ▪ 137 , 138 , 139 , 140 , 178 179 , 181 , 182 , 183 , 184 , 185 , 188 , 208 , 210 , 213. experiments ●n geometrie . pag. 12 , 15 , 24 , 26 , 27 , 30 , 35 , 37 , 41 , 42 , 47 , 48 , 49 , 62 , 65 , 72 , 79 , 82 , 113 , 117 , 118 , 119 , 214 , 215 , 217 , 218 , 234 , 235 , 236 , 239 , 240. experiments in cosmographie . pag. 14 , 43 , 75 , 106 , 107 , 219 , 220 , 225 , 227 , 228 , 229 , 230 , 232. experiments in horologiographie . pag. 137 , 166 , 167 , 168 , 169 , 171 , 234. experiments in astronomie . pag. 220 , 221 , 222 , 223 , 224. experiments in navigation . pag. 105 , 233 , 234 , 237 , 238. experiments in musick . pag. 78 , 87 , 126. experiments in opticks . pag. 6 , 66 , 98 , 99 , 100 , 102 , 129 , 131 , 141 , 142 , 143 , 144 , 146 , 149 , 151 , 152 , 153 , 155 , 156 , 157 , 158 , 160 , 161 , 162 , 163 , 164 , 165. experiments in architecture . pag. 16 , 242 , 243. experiments in staticke . pag. 27 , 30 , 32 , 71 , 199 , 200 , 201 , 283 , 204 , 205 , 207. experiments in machanicks . pag. 56 , 58 , 68 , 88 , 95 , 108 , 110 , 128 , 173 , 174 , 176 , 246 , 248 , 258 , 259. experiments in chymistrie . pag. 198 , 255 , 256 , 257 , 260 , 262 , 263 , 264. experiments in water-workes . pag. 190 , 191 , 192 , 193 , 194 , 196 , 247 , 249 , 250 , 252 , 253. experiments in fireworkes . from page , 265. to the end . finis . a table of the contents , and chiefe points conteined in this book . problem . ii. how visible objects that are without , and things that passe by , are most lively represented to those that are within . page 6 prob. 1 of finding of numbers conceived in the minde . 1 , 2 , 3 prob. 5 of a geographicall garden-plot fit for a prince or some great personage . 14 prob. 37 any liquid substance , as water or wine , placed in a glasse , may be made to boile by the motion of the finger , and yet not touching it . 54 prob. 3 how to weigh the blow of ones fist , of a mallet , a hatchet or such like . 9. prob. 30 two severall numbers being taken by two sundry persons , how subtilly to discover which of those numbers each of them took . 46 prob. 4 that a staffe may be broken ▪ placed upon two glasses , without hurting of the glasses . 12 prob. 7 how to dispose lots that the 5 , 6 , 9 , &c. of any number of persons may escape . 16 prob. 13 how the weight of smoke of a combustible body , which is exhaled , may be weighed . 27 prob. 12 of three knives which may be so disposed to hang in the aire , and move upon the point of a needle . 27 prob. 17 of a deceitfull bowle , to bowle withall . 32 prob. 16 a ponderous or heavy body may be supported in the aire without any one touching it . 30 prob. 18 how a peare , or apple , may be parted into any parts , without breaking the rinde thereof . 33 prob. 15 of a fine kinde of dore which opens and shuts on both sides . 30 prob. 9 how the halfe of a vessell which containes 8 measures may be taken , being but onely two other measures , the one being 3 , and the other 8 measures . 22 prob. 8 three persons having taken each of them severall things , to finde which each of them hath taken . 19 prob. 6 how to dispose three staves which may support each other in the aire . 15 prob. 14 many things being disposed circular ( or otherwise ) to finde which of them any one thinks upon . 28 prob. 19 to finde a number thought upon without asking questions . 33 prob. 11 how a milstone or other ponderosity may hang upon the point of a needle without bowing , or any wise breaking of it . 26 prob. 20 and 21 how a body that is uniforme and inflexible may passe through a hole which is round , square and triangular ; or round , square and ovall-wise , and exactly fill those severall holes . 35 , 37 prob. 10 how a stick may stand upon ones finger , or a pike in the middle of a court without falling . 24 prob. 22 to finde a number thought upon after another manner than those which are formerly delivered . 39 prob. 23 to finde out many numbers that sundry persons or any one hath thought upon . 40 prob. 24 how is it that a man in one & the same time may have his head upward , and his feet upward , being in one and the same place ? 4● prob. 25 of a ladder by which two men ascending at one time , the more they ascend , the more they shal be asunder , notwith standing the one be as high as the other . 42 prob. 26 how is it that a man having but a rod or pole of land , doth brag that he may in a right line passe from place to place 3000 miles . 42 prob. 27 how is it that a man standing upright , and looking which way he will , he looketh true north or south . 43 prob. 28 to tell any one what number remaines after certaine operations being ended , without asking any question . 44 prob. 29 of the play with two severall things . 45 prob. 31 how to describe a circle that shall touch 3 points placed howsoever upon a plaine , if they be not in a right line . 47 prob. 32 how to change a circle into a square forme . 48 prob. 33 with one and the same compasses , and at one and the same extent or opening , how to describe many circles concentricall , that is , greater or lesser one than another . 49 prob. 34 any number under 10. being thought upon , to finde what numbers they were . 51 prob , 35 of the play with the ring . 52 prob. 36 the play of 3 , 4 , or more dice . 53 prob. 38 of a fine vessell which holds wine or water being cast into it at a certain height , but being filled higher it will runne all out of its owne accord . 56 prob. 39 of a glasse very pleasant . 58 prob. 40. if any one should hold in each hand as many pieces of money as in the other , how to finde how much there is . 59 prob. 41 many dice being cast , how artificially to discover the number of the points that may arise . 60 prob. 42 two metals as gold and silver or of other kinde , weighing alike , being privately placed into two like boxes , to finde in which of them the gold or silver is . 62 prob. 43 two globes of divers metals ( as one gold the other copper ) yet of equall weight , being put in a box as b.g. to finde in which end the gold or copper is . 65 prob. 44 how to represent divers sorts of rainbowes here below . 66 prob. 45 how that if all the powder in the world were inclosed in a bowle of paper or glasse , and being fired on all parts , it could not break that bowle . 68 prob. 46 to finde a number which being divided by 2. there will remaine 1. being divided by 3. there will remaine 1. and so likewise being divided by 4 , 5 , or 6. there will still remaine one , but being divided by 7 will remaine nothing . 69 prob. 47 one had a certaine number of crownes , and counting them by 2 and 2 , there rested 1. counting them by 3 , and 3 , there rested 2. counting them by 4 , and 4 , there rested 3. counting them by 5 , and 5 , there rested 4. counting them by 6 , and 6 , there rested 5. but counting them by 7 and 7 , there rested nothing , how many crownes might he have ? 71 prob. 48 how many sorts of weights in the least manner must there be to weigh all sorts of things betweene one pound and 121 pound , and so unto 364 pound ? 71 prob. 49 of a deceitfull balance which being empty seems to be just , because it hangs in aequilibrio , notwithstanding putting 12 pound in one ballance , and 11 in the other , it will remaine in aequilibrio . 72 prob. 50 to heave or lift up a bottle with a straw . 74 prob. 51 how in the middle of a wood or desert , without the sight of the sun , starres , shadow , or compasse , to finde out the north , or south , or the 4 cardinal points of the world , east , west , &c. 75 prob. 52 three persons having taken counters , cards , or other things , to finde how much each one hath taken . 7● prob. 53 how to make a consort of musick of many parts with one voice or one instrument onely . 78 prob. 54 to make or describe an oval form , or that which is neare resembled unto it at one turning , with a paire of common compasses . 79 prob. 55 of a purse difficult to be opened . 80 prob. 56 whether is it more hard and admirable without compasses to make a perfect circle , or being made to finde out the centre of it ? 82 prob. 56 any one having taken 3 cards , to finde how many points they containe . 83 prob. 57 many cards placed in divers ranks , to finde which of those cards any one hath thought . 85 prob. 58 many cards being offered to sundry persons to finde which of those cards any one thinketh upon . 86 prob. 59 how to make an instrument that helps to heare , as gallileus made to help to see . 87 prob. 60 of a fine lamp which goeth not out , though one carries it in ones pocket , or being rolled on the ground will still burne . 88 prob. 61 any one having thought a card amongst many cards , how artificially to discover it out . 89 prob. 62 three women a , b , c. carried apples to a market to sell : a had 20. b had 30. c 40. they sold as many for a penny one as the other , and brought home one as much money as another , how could this be ? 90 prob. 63 of the properties of some numbers . 91 prob. 64 of an excellent lamp which serves or furnisheth it selfe with oile , and burnes a long time . 95 prob. 65 of the play at keyles or nine-pins . 97 prob. 66 of spectacles of pleasure of spectacles which give severall colours to the visage . 98 of spectacles which make a towne seeme to be a city , one armed man as a company , and a piece of gold as many pieces . 99 how out of a chamber to see the objects which passe by according to the lively perspective . 100 of gallileus admirable optick-glasse , which helps one to see the beginning and ending of eclipses , the spots in the sunne , the starres which move about the planets , and perspicuously things far remote . of the parts of gallileus his glasse . 102 prob. 67 of the magnes and needles touched therewith . how rings of iron may hang one by another in the aire . 103 of mahomets tombe which hangs in the aire by the touch of the magnes . 104 how by the magnes only to finde out north and south 105 of a secrecie in the magnes , for discovering things farre remote . 106 of finding the poles by the magnes 107 prob. 68 of the properties of aeolipiles or bowles to blow the fire . 108 prob. 69 of the thermometer , or that which measures the degrees of heat and cold by the aire . 110 of the proportion of humane bodies , of statues , of colosses , or huge jmages and monstrous giants . 113 of the commensuration of the parts of the bodie the one to the other in particular , by which the lion was measured by his claw , the giant by his thumbe , and hercules by his foot . 115 , 116 of statues or colosses , or huge images ; that mount athos metamorphosed by dynocrites into a statue , in whose hand was a towne able to receive ten thousand men . 117 of the famous colossus at rhodes which bad 70 cubits in height , and loaded 900. camels , which weighed 1080000 l. 118 of nero his great colossus which had a face of 12 foot large . 119 of monstrous giants of the giant og and goliah . 119 , 120 of the carkasse of a man found which was in length 49 foot ; and of that monster found in creet , which had 46. cubits of height . 120 of campesius his relation of a monster of 300 foot found in sicile , whose face according to the former proportion should be 30 foot in length . 121 prob. 71 of the game at the palme , at trap , at bowles , paile-maile , and others . 122 prob. 72 of the game of square formes . 124 prob. 73 how to make the string of a viol sensibly shake without any one touching it . 126 prob. 74 of a vessell which containes 3 severall kindes of liquor , all put in at one bung-hole , and drawne out at one tap severally without mixture . 128 prob. 75 of burning-glasses . archimedes his way of burning the ships of syracuse . 129 of proclus his way , and of concave and sphericall glasses which burne , the cause and demonstration of burning with glasses . 131 of maginus his way of setting fire to powder in a mine by glasses . 131 of the examination of burning by glasses . 133 prob. 76 of pleasant questions by way of arithmetick . of the asse and the mule. 134 of the number of souldiers that fought before old troy. 135 of the number of crownes that two men had . 136 about the houre of the day . 137 of pythagoras schollers . 137 of the number of apples given amongst the graces and the muses . 138 of the testament or last will of a dying father . 138 of the cups of croesus . 139 of cupids apples . 139 of a mans age. 140 of the lion of bronze placed upon a fountaine with his epigram . ibid. prob. 77 in opticks , excellent experiments . principles touching reflections . 141 experiments upon flat and plaine glasses . 142 how the images seeme to sink into a plaine glasse , and alwayes are seene perpendicular to the glasse , an● also inversed . 143 the things which passe by in a street may by help of a plaine glasse be seen in a chamber , and the height of a tower or tree observed . 143 how severall candles from one candle are represented in a plaine glasse , and glasses alternately may be seene one within another , as also the back-parts of the body as well as the fore-parts are evidently represented . 144 how an image may be seene to hang in the aire by help of a glasse : and writing read or easily understood . 146 experiments upon gibbous , or convex sphericall glasses . how lively to represent a whole city , fortification , or army , by a gibbous glasse . 147 how the images are seen in concave glasses . 149 how the images are transformed by approaching to the centre of the glasse , or point of concourse ; and of an exceeding light that a concave glasse gives by help of a candle . 151 how the images , as a man , a sword , or hand , doth come forth out of the glasse . 152 , 153 of strange apparitions of images in the aire , by help of sundry glasses . 152 , 154 of the wonderfull augmentation of the parts of mans body comming neare the point of inflammation , or centre of the glasse . 155 how writing may be reverberated from a glasse upon a vvall , and read. 156 how by help of a concave glasse to cast light into a campe , or to give a perspective light to pyoneers in a mine , by one candle only . 156 how excellently by help of a concave glasse and a candle placed in the centre , to give light to read by . 157 of other glasses of pleasure . 158 of strange deformed representations by glasses ; causing a man to have foure eyes , two mouthes , two noses , two heads . of glasses which give a colour to the visage , and make the face seeme faire and foule . 160 prob. 78 how to shew one that is suspicious , what is in another chamber or roome , notwithstanding the interposition of that wall . 160 corolary , 1. to see the besiegers of a place , upon the rampa●●t of a fortification 161 corolary 2. and 3. notwithstanding the interposition of vvalls and chambers , by help of a glasse things may be seen , which passe by . 162 prob. 79 how with a musket to strike a marke not looking towards it , as exactly as one aimed at it . 162 how exactly to shoot out of a mu●ket to a place which is not seene , being hindred by some obstacle or other interposition . 163 prob. 80 how to make an image to be seen hanging in the aire , having his head downward . 164 prob. 81. how to make a company of representative souldiers seeme to be as a regiment , or how few in number may be multiplyed to seem to be many in number . 165 corolarie . of an excellent delightfull cabinet made of plaine glasses . 165 prob. 82 of fine and pleasant dyalls in horologiographie . of a dyall of herbs for a garden . 166 of the dyall upon the finger and hand , to finde what of the clock it is . 167 of a dyall which was about an obelisk at rome . 168 of dyals with glasses . 168 of a dyall which hath a glasse in the place of the stile . 169 of dyals with water , which the ancients use● 171 prob. 83 of shooting out of cannons or great artillery . how to charge a cannon without powder . 173 to finde how much time the bullet of a cannon spends in the aire before it falls to the ground . 174 how it is that a cannon shooting upward , the bullet flies with more violence , than being shot point blanke , or shooting downeward . 174 vvhether is the discharge of a cannon so much the more violent , by how much it hath the more length ? 176 prob. 84 of prodigious progressions , and multiplications of creatures , plants , fruits , numbers , gold , silver , &c. of graines of mustardseed , and that one graine being sowne , with the increase thereof for 20 yeares will produce a heap greater than all the earth a hundred thousand times . 178 of pigges , and that the great turke with all his revenne , is not able to maintaine for one yeare , a sow with all her increase for 12 yeares . 179 of graines of corne , and that 1 graine with all its increase for 12 yeares , will amount to 244140625000000000000 graines , which exceeds in value all the treasures in the world. 183 of the wonderfull increase af sheepe . 182 of the increase of cod-fish . 182 of the progressive multiplication of soules ; that from one of noahs sonnes , from the flood unto nimrods monarchie , should be produced 111350 soules . 183 of the increase of numbers in double proportion , and that a pin being doubled as often as there are weekes in the yeare , the number of pinnes that should arise is able to load 45930 ships of a thousand tunne apiece , which are worth more than tenne hundred thousand pounds a day . 183 , 184 of a man that gathered apples , stones , or such like upon a condition . 185 of the changes in bells , in musicall instruments , transmutation of places , in numbers , letters , men and such like ▪ 185 of the wonderfull interchange of the letters in the alphabet : the exceeding number of men , and time to expresse the words that may be made with these letters , and the number of books to comprehend them . 187 , 188 of a servant hired upon certaine condition , that he might have land lent him to sowe one graine of corne with its increase for 8 yeares time , which amounted to more than four hundred thousand acres of land. 188 prob. 85 of fountaines , hydriatiques ; stepticks , machinecks , and other experiments upon water , or other liquor . first , how water at the foot of a mountaine may be made to ascend to the top of it , and so to descend on the other side of it 190 secondly , to finde how much liquor is in a vessell , onely by using the tap-hole . 191 thirdly , how is it , that a vessell is said to hold more water at the foot of a mountaine , then at the top of it 191 4 how to conduct water from the top of one mountaine to the top of another 192 5 of a fine fountaine which spouts water very high and with great violence , by turning of a cock 193 6 of archimedes screw which makes water ascend by descending . 194 7 of a fine fountaine of pleasure . 196 8 of a fine watering pot for gardens . 197 9 how easily to take wine out of a vessell at the bung hole without piercing a hole in the vessell . 198 10 how to measure irregular bodies by help of water . 198 11 to finde the weight of water . 199 12 to finde the charge that a vessell may carry , as ships , boats or such like . 200 13 how comes it that a ship having safely sailed in the vast ocean , and being come into the port or harbour , will sinke down right . 200 14 how a grosse body of metall may swim upon the water . 201 15 how to weigh the lightnesse of the aire . 203 16 being given a body , to mark it about , and shew how much of it will sink in the water , or swim above the water . 204 17 to finde how much severall metalls or other bodies do weigh lesse in the water than in the aire . 204 18 how is it that a ballance having like weight in each scale , and hanging in aequilibrio in the aire , being removed from that place ( without diminishing the weights in each balance , or adding to it ) it shall cease to hang in aequilibrio sensibly , yea by a great difference of weight . 205 19 to shew what waters are heavier one than another , and how much . 206 20 how to make a pound of water weigh as much as 10 , 20 , 30 , or a hundred pound of lead , nay as much as a thousand or ten thousand pound weight . 207 prob. 86. of sundry questions of arithmetick , and first of the number of sands calculated by archimedes and clavius . 208 2 divers metalls being melted together in one body , to finde the mixture of them . 210 3 a subtile question of three partners about equality of wine and vessels . 213 4 of a ladder which standing upright against a wall of 10 foot high , the foot of it is pulled out 6 foot from the wall upon the pavement , how much hath the top of the ladder descended . 214 prob. 87 witty suits or debates between caius and sempronius , upon the forme of figures , which geometricians call isoperimeter , or equall in circuit , or compasse . 214 1 incident : of changing a field of 6 measures square , for a long rectrangled fiel of 9 measures in length and 3 in breadth : both equall in circuit but not in quantity . 215 2 incident : about two sacks each of them ho●ding but a bushell , and yet were able to hold 4 bushels . 217 3 incident : sheweth the deceit of pipes which conveygh water , that a pipe of two inches diameter , doth cast out foure times as much water as a pipe of one such diameter . 218 7 heapes of corne of 10 foot every way , is not as much as one heap of corne of 20 foot every way . 218 prob. 88 of sundry questions in matter of cosmographie , and astronomy . in what place the middle of the earth is supposed to be . 219 of the depth of the earth , and height of the heavens , and the compasse of the world , how much . 219 how much the starry firmament , the sun , and the moone are distant from the centre of the earth . 220 how long a mill-stone would be in falling to the centre of the earth from the superficies , if it might have passage thither . 220 how long time a man or a bird may be in compassing the whole earth . 220 if a man should ascend by supposition 20 miles every day : how long it would be before he approach to the moone . 221 the sunne moves more in one day than the moone in 20 dayes . 221 if a milstone from the orbe of the sun should descend a thousand miles in an houre how long it would be before it come to the earth . 221 of the sunnes quick motion , of more than 7500 miles in one minute . 221 of the rapt and violent motion of the starry firmament , which if a horseman should ride every day 40 miles , he could not in a thousand yeares make such a distance as it moves every houre . 221 to finde the circle of the sunne by the fingers . 223 prob. 93 of finding the new and full moone in each moneth . 224 prob. 94 to finde the latitude of countreys . 225 prob. 95 of the climates of countreys , and how to finde them . 225 prob. 96 of longitude and latitude of the places of the earth , and of the starres of the heavens . 227 to finde the longitude of a countrey . 228 of the latitude of a countrey . 229 to finde the latitude of a countrey . 230 to finde the distance of places . 230 of the longitude , latitude , declination , and distance of the starres . 231 how is it that two horses or other creatures comming into the world at one time , and dying at one and the same instant , yet the one of them to be a day older than the other ? 232 certaine fine observations . in what places of the world is it that the needle hangs in aequilibrio , and verticall ? 233 in what place of the world is it the sun is east or west but twice in the yeare ? 233 in what place of the world is it that the sunnes longitude from the equinoctiall paints and altitude , being equall , the sunne is due east or west ? that the sunne comes twice to one point of the compasse in the forenoone or afternoone . 233 that in some place of the world there are but two kindes of winde all the yeare . 233 two ships may be two leagues asunder under the equinoctiall , and sayling north at a certaine parallell they will be but just halfe so much . 233 to what inhabitants , and at what time the sunne will touch the north-part of the horizon at midnight . 234 how a man may know in his navigation when he is under the equinoctiall . 234 at what day in the yeare the extremitie of the styles shadow in a dyall makes a right line . 234 what height the sunne is of , and how far from the zenith , or horizon , when a mans shadow is as long as his height . 234 prob. 97 to make a triangle that shall have three right angles . 234 prob. 98 to divide a line in as many parts as one will , without compasses or without seeing of it . 235 prob. 99 to draw a line which shall incline to another line , yet never meet against the axiome of parallells . 236 prob. 100 to finde the variation of the compasse by the sunne shining . 237 prob. 101 to know which way the winde is in ones chamber without going abroad . 238 prob. 102 how to draw a parallel sphaericall line with great ease . 239 prob. 103 to measure an height onely by help of ones hat. 240 prob. 104 to take an height with two strawes . 240 in architecture how statues or other things in high buildings shall beare a proportion to the eye below either equall , double , &c. 242 prob. 106 of deformed figures which have no exact proportion , where to place the eye to see them direct . 243 prob. 107 how a cannon that hath shot may be covered from the battery of the enemy . 244 prob. 108 of a fine lever , by which one man alone may place a cannon upon his carriage . 245 prob. 109 how to make a clock with one wheele 246 of water-workes . prob. 110 how a childe may draw up a hogshead of water with ease . 247 prob. 111 of a ladder of cords to cary in ones pocket , by which he may mount a wall or tower alone . 248 prob. 112 of a marvelous pump which drawes up great quantity of water . 249 prob. 113 how naturally to cause water to ascend out of a pit. 250 prob. 114 how to cast water out of a fountaine very high . 252 prob. 115 how to empty the water of a pit by help of a cisterne . 253 prob. 116 how to spout out water very high . 253 prob. 117 how to re-animate simples though brought a thousand miles . 255 prob. 118 how to make a perpetuall motion . 255 prob. 119 of the admirable invention of making the philosophers tree , which one may see to grow by little and little . 256 prob. 120 how to make the representation of the great world 257 prob. 121 of a cone , or pyramidall figure that moves upon a table 258 prob. 122 how an anvill may be cleaved by the blow of a pistoll . 258 prob. 123 how a capon may be rosted in a mans travells at his sa●●le-bowe . 259 prob. 124 how a candle may be made to burne three times longer than usually it doth 259 prob. 125 how to draw wine out of water 260 prob. 126 of two marmouzets , the one of which lights a candle , and the other blowes it out . 261 prob. 127 how to make wine fresh without ice or snow in the height of summer . 262 prob. 128 to make a cement which lastes as marble , resisting aire and water . 262 prob. 129 how to melt metall upon a shell with little fire . 263 prob. 130 of the hardning of iron and steele . 263 prob. 131 to preserve fire as long as you will , imitating the inextinguible fire of the vestales . 264 finis . ad authorem d.d. henricum van etenium , alumnum academiae ponta mousson . ardua walkeri sileant secreta profundi , desinat occultam carpere porta viam . itala cardani mirata est lampada docti terra , syracusium graecia tota senem : orbi terrarum , ptolemaei clepsydra toti , rara dioptra procli , mira fuêre duo , anglia te foveat doctus pont-mousson alumnum : quidquid naturae , qui legis , hortus habet . docta , coronet opus doctum , te sit tua docto digna , syracusii , arca , corona , viri . arca syracusiis utinam sit plumbea servis , aurea sed dominis , aurea tota suis. mathematical recreation . problem i. to finde a number thought upon . bid him that he quadruple the number thought upon , that is , multiply it by 4 , and unto it bid him to adde 6 , 8 , 10 , or any number at pleasure : and let him take the halfe of the sum , then ask how much it coms to , for then if you take away half the number from it which you willed him at first to add to it , there shall remain the double of the number thought upon . example the number thought upon 5 the quadruple of it 20 put 8 unto it , makes 28 the halfe of it is 14 take away halfe the number added from it , viz 4 , the rest is 10 the double of the number thought upon , viz. 10 another way to finde what number was thought upon . bid him which thinketh double his number , and unto that double adde 4 , and bid him multiply that same product by 5 , and unto that product bid him adde 12 , and multiply that last number by 10 ( which is done easily by setting a cypher at the end of the number ) then ask him the last number or product , and from it secretly subtract 320 , the remainder in the hundreth place , is the number thought upon . example . the number thought upon 7 for which 700 account onely but the number of the hundreds viz. 7. so have you the number thought upon . his double 14 for which 700 account onely but the number of the hundreds viz. 7. so have you the number thought upon . to it add 4 , makes 18 for which 700 account onely but the number of the hundreds viz. 7. so have you the number thought upon . which multiplyed by 5 makes 90 for which 700 account onely but the number of the hundreds viz. 7. so have you the number thought upon . to which add 12 makes 102 for which 700 account onely but the number of the hundreds viz. 7. so have you the number thought upon . this multiplyed by 10 which is only by adding a cypher to it , makes 1020 for which 700 account onely but the number of the hundreds viz. 7. so have you the number thought upon . from this subtract 320 for which 700 account onely but the number of the hundreds viz. 7. so have you the number thought upon . rest 700 for which 700 account onely but the number of the hundreds viz. 7. so have you the number thought upon . to finde numbers conceived upon , otherwise than the former . bid the party which thinks the number , that he triple his thought , and cause him to take the half of it : ( if it be odde take the least half , and put one unto it : ) then will him to triple the half , and take half of it as before : lastly , ask him how many nines there is in the last half , and for every nine , account four in your memory , for that shall shew the number thought upon , if both the triples were even : but if it be odde at the first triple , and ev●n at the second , for the one added unto the least halfe keep one in memory : if the first triple be even , and the second odde , for the one added unto the least halfe keepe two in memory ; lastly , if at both times in tripling , the numbers be odde , for the two added unto the least halfes , keep three in memory , these cautions observed , and added unto as many fours as the party sayes there is nines contained in the last halfe , shall never fail you to declare or discern truly what number was thought upon . example . the number thought upon 4 or 7 the triple 12 or 21 the half thereof 6 or 10 , one put to it makes 11 the triple of the halfe 18 or 33 the halfe 9 or 1● , one put to it makes 17 the number of nines in the last halfe 1 or 1 the first 1. representeth the 4. number thought upon , and the last 1. with the caution makes 7. the other number thought upon . note . order your method so that you be not discovered , which to help , you may with dexterity and industry make additions ▪ substractions , multiplications , divisions , &c. and instead of asking how many nines there is , you may ask how many eights tens , &c. there is , or subtract 8.10 . &c. from the number which remains , for to finde out the number thought upon . now touching the demonstrations of the former directions , and others which follow , they depend upon the 2 , 7 , 8 , and 9 , books of the elements of euclide : upon which 2. book & 4. proposition this may bee extracted , for these which are more learned for the finding of any number that any one thinketh on . bid the party that thinks , that he break the number thought upon into any two parts , and unto the squares of the parts , let him adde the double product of the parts , then ask what it amounteth unto , so the root quadrat shall be the number thought upon . the number thought upon 5 , the parts suppose 3 and 2. the square of 3 makes 9 the sum of these three nūbers 25 , the squa●e root of which is 5 , the number thought upon the square of 2 makes 4 the sum of these three nūbers 25 , the squa●e root of which is 5 , the number thought upon the product of the parts . viz. 3 by 2 makes 6 , which 6 doubled makes 12 the sum of these three nūbers 25 , the squa●e root of which is 5 , the number thought upon or more compendiously it may be delivered thus . break the number into two parts , and to the product of the parts , adde the square of half the difference of the parts , then the root quadrat of the aggregate is halfe the number conceived . examination . the problems which concern arithmetick , we examine not , for these are easie to any one which hath read the grounds and principles of arithmetick , but we especially touch upon that , which tends to the speculations of physick , geometry , and optickes , and such others which are of more difficulty , and more principally to be examined and considered . problem ii. how to represent to those which are in a cham●er that which is without , or all that which passeth by , it is pleasant to see the beautifull and goodly representation of the heavens intermixed with clouds in the horizon , upon a woody scituation , the motion of birds in the aire , of men and other creatures upon the ground , with the trembling of plants , tops of trees , and such like : for every thing will be seen within even to the life , but inversed : notwithstanding , this beautifull paint will so naturally represent it self in such a lively perspective , that hardly the most accurate painter can represent the like . but here note , that they may be represented right two manner of wayes ; first , with a concave glasse : secondly , by help of another convex glasse , disposed or placed between the paper and the other glasse : as may be seen here by the figure . now i will add here only by passing by , for such which affect painting and portraiture , that this experiment may excellently help them in the lively painting of things perspectivewise , as topographicall cards , &c. and for philosophers , it is a fine secret to explain the organ of the sight , for the hollow of the eye is taken as the close chamber , the ball of the apple of the eye , for the hole of the chamber , the crystaline humor at the small of the glasse , and the bottome of the eye , for the wall or leafe of paper . examination . the species being pressed together or contracted doth not perform it upon a wall , for the species of any thing doth represent it selfe not only in one hole of a window , but in infinite holes , even unto the whole sphere , or at least unto a hemisphere ( intellectuall in a free medium ) if the beams or reflections be not interposed , and by how much the hole is made less to give passage to the species , by so much the more lively are the images formed . in convexe , or concave glasses the images will be disproportionable to the eye , by how much they are more concave , or convexe , & by how much the parts of the image comes neer to the axis , for these that are neer are better proportioned then these which are farther off . but to have them more lively and true , according to the imaginary conicall section , let the hole be no greater than a pins head made upon a piece of thin brasse , or such like , which hole represents the top of the cone , and the base thereof the term of the species : this practice is best when the sun shines upon the hole , for then the objects which are opposite to that plaine will make two like cones , and will lively represent the things without in a perfect inversed perspective , which drawn by the pensill of some artificiall painter , turn the paper upside down , and it will be direct and to the life . but the apparences may be direct , if you place another hole opposite unto the former , so that the spectator be under it ; or let the species reflect upon a concave glass , and let that glas reflect upon a paper or some white thing . problem iii. to tell how much waighs the blow of ones fist , of a mallet , hatchet , or such like , or resting without giving the blow scaliger in his 331 exercise against cardan , relates that the mathematicians of maximillian the emperour did propose upon a day this question , and promised to give the resolution ; notwithstanding ●caliger delivered it not , and i conceive it to be thus . take a balance , and let the fist , the mallet , or hatchet rest upon the scale , or upon the beam of the balance , and put into the other scale as much weight as may counterpoyse it ; then charging or laying more waight into the scale , and striking upon the other end , you may see how much one blow is heavier than another , and so consequently how much it may waigh for as aristotle saith , the motion that is made in striking adds great waight unto it , and so much the more , by how much it is quicker : therefore in effect , if there were placed a thousand mallets , or a thousand pounde waight upon a stone , nay , though it were exceedingly pressed down by way of a vice , by levers , or other mechanick engine , it would be nothing to the rigor and violence of a blow . is it not evident that the edge of a knife laid upon butter , and a hatchet upon a leafe of paper , without striking makes no impression , or at least enters not ; but striking upon the wood a little , you may presently see what effect it hath , which is from the quicknesse of the motion , which breaks and enters without resistance , if it be extream quick , as experience shews us in the blows of arrows , of cannons , thunder-boults , and such like . examination . this problem was extracted from scaliger , who had it from aristotle , but somwhat refractory compiled , & the strength of the effect he says depends only in the violence of the motion ; then would it follow that a little light hammer upon a piece of wood being quickly caused to smite , would give a greater blow , and do more hurt than a great sledge striking soft ; this is absurd , and contrary to experience : therefore it consists not totally in the motion , for if two severall hammers , the one being 20 times heavier than the other , should move with like quickness , the effect would be much different , there is then some thing else to be considered besides the motion which scaliger understood not , for if one should have asked him , what is the reason that a stone falling from a window to a place neer at hand , is not so forceable as if it fell farther 〈◊〉 when a bullet flying out of a peece and striking the mark neer at hand 〈◊〉 not make such an effect as striking 〈…〉 that scaliger and 〈…〉 this subiect ▪ would not be less troubled to resolve this , than they have been in that . problem iv. how to break a staffe which is laid upon two glasses full of water , without breaking the glasses , spilling the water , or upon two reeds or straws without breaking of them . in like manner may you doe upon two reeds , held with your hands in the aire without breaking them ▪ thence kitchin boyes often break bones of mutton upon their hand , or with a napkin without any hurt , in only striking upon the middle of the bone with a knife . now in this act , the two ends of the staffe in breaking slides away from the glasses , upon which they were placed ; hence it commeth that the glasses are no wise indangered , no more than the knee upon which a staffe is broken , forasmuch as in breaking it presseth not : as aristotle in his mechanick questions observeth . examination . it were necessary here to note , that this thing may be experimented , first , without glasses , in placing a small slender staffe upon two props , and then making tryall upon it , by which you may see how the staffe will either break , bow , or depart from his props , and that either directly or obliquely : but why by this violence , that one staffe striking another , ( which is supported by two glasses ) will be broken without offending the glasses , is as great a difficulty to be resolved as the former . problem v. how to make a faire ge●graphic●ll card in a garden plot , fit for a prince , or great personage . it is usuall amongst great men to have faire geographicall maps ▪ large cards , and great globes , that by them they may as at once have a view of any place of the world , and so furnish themselves with a generall knowledge , not only of their own kingdoms form , scituation , longitude , latitude , &c. but of all other places in the whole universe , with their magnitudes , positions , climats , and distances . now i esteem that it is not unworthy for the meditations of a prince , seeing it carries with it many profitable and pleasant contentmen●s : if such a card or map by the advice and direction of an able mathematician were geographically described in a garden plot form , or in some other convenient place , and instead of which generall description might particularly and artificially be prefigured his whole kingdoms and dominions , the mountains and hils being raised like small hillocks with turfs of earth , the valleys somwhat concave , which will be more agreeable and pleasing to the eye , than the description in plain maps and cards , within which may be presented the towns , villages , castles , or other remarkable edifices in small green mo●●e banks , or spring-work proportionall to the pl●tform , the forrests and woods represented according to their form and capacity , with herbs and stoubs , the great rivers , lakes , and ponds to dilate themselves according to their course from some artificiall fountain made in the garden to passe through chanels ; then may there be composed walks of pleasure , ascents , places of repose , adorned with all variety of delightfull herbs and flowers , both to please the eye or other senses . a garden thus accommodated shall farre exceed that of my lord of verulams specified in his ●ssayes ; that being only for delight and pleasure , this may have all the properties of that , and also for singular use , by which a prince may in little time personally visit his whole kingdom , and in short time know them distinctly : and so in like manner may any particular man geographically prefigure his own possession or heritage . problem vi. how three staves , knives , or like bodies , may be conceived to hang in the aire , without being supported by any thing but by themselves . take the first staffe ab , raise up in the aire the end b , and upon him cros-wise place the staffe cb , then lastly , in triangle wise place the third staffe ef ▪ in such manner that it may be under ab , and yet upon cd . i say that these staves so disposed cannot fall , and the space cbe is made the stronger , by how much the more it is pressed downe , if the staves break not , or sever themselves from the triangular forme : so that alwayes the center of gravitie be in the center of the triangle : for ab is supported by ef , and ef is held up by cd , and cd is kept up from falling by ab , therefore one of these staves cannot fall , and so by consequence none . problem vii . how to dispose as many men , or other things in such sort , that rejecting , or casting away the 6 , 9 , 10 part , unto a certain number , there shall remaine these which you would have . ordinarily the proposition is delivered in this wise : 15 christians and 15 turkes being at sea in one shippe , an extreame tempest being risen , the pilot of the shippe saith , it is necessary to cast over board halfe of the number of persons to disburthen the shippe , and to save the rest : now it was agreed to be done by lot , and therefore they consent to put themselves in rank , counting by nine and nine , the ninth person should alwayes be cast into the sea , untill there were halfe throwne over board ; now the pilote being a christian indeavoured to save the christians , how ought he therefore to dispose the christians , that the lot might fall alwayes upon the turkes , and that none of the christians be in the ninth place ? the resolution is ordinarily comprehended in this verse . populeam virgam mater regina ferebat . for having respect unto the vowels , making a one , e two , i three , o foure , and u five : o the first vowell in the first word sheweth that there must be placed 4. christians ; the next vowel u , signifieth that next unto the 4. christians must be placed 5 turkes , and so to place both christians and turkes according to the quantity and value of the vowels in the words of the verse , untill they be all placed : for then counting from the first christian that was placed , unto the ninth , the lot will fall upon a turk , and so proceed . and here may be further noted that this probleme is not to be limited , seeing it extends to any number and order whatsoever , and may many wayes be usefull for captaines , magistrates , or others which have divers persons to punish , and would chastise chiefely the unruliest of them , in taking the 10 , 20 , or 100. person , &c. as we reade was commonly practised amongst the ancient romans : herefore to apply a generall rule in counting the third , 4 , 9 , 10 , &c. amongst 30 , 40 , 50 , persons , and more or lesse ; this is to be observed , take as many units as there are persons , and dispose them in order privately : as for example , let 24 men be proposed to have committed some outrage , 6 of them especially are found accessary : and let it be agreed that counting by 8 and 8 the eight man should be alwayes punished . take therefore first 24 units , or upon a piece of paper write down 24 cyphers , and account from the beginning to the eighth , which eighth mark , and so continue counting alwayes marking the eighth , untill you have markt 6 , by which you may easily perceive how to place those 6 men that are to be punished , and so of others . it is supposed that josephus the author of the jewish history escaped the danger of death by help of this problem ; for a worthy author of beliefe reports in his eighth chapter of the third book of the destruction of jerusalem , that the town of jotapata being taken by main force by vespatian , josephus being governour of that town , accompanyed with a troop of forty souldiers , hid themselves in a cave , in which they resolved rather to famish than to fall into the hands of vespatian : and with a bloudy resolution in that great distresse would have butchered one another for sustenance , had not josephus perswaded them to die by lot and order , upon which it should fall : now seeing that josephus did save himselfe by this art , it is thought that his industry was exercised by the helpe of this problem , so that of the 40 persons which he had , the third was alwayes killed . now by putting himselfe in the 16 or 31 place he was saved , and one with him which he might kill , or easily perswade to yeild unto the romans . problem . viii . three things , and three persons proposed , to finde which of them hath either of these three things . let the three things be a ring , a piece of gold , and a piece of silver , or any other such like , and let them be known privately to your self by these three vowels a , e , i , or let there be three persons that have different names , as ambrose , edmond , and john , which privately you may note or account to your selfe once known by the aforesaid vowels , which signifie for the first vowel 1 , for the second vowell 2 , for the third vowell 3. now if the said three persons should by the mutuall consent of each other privately change their names , it is most facill by the course and excellencie of numbers , distinctly to declare each ones name so interchanged , or if three persons in private , the one should take a ring , the other a piece of gold , and the third should take a piece of silver ; it is easie to finde which hath the gold , the silver , or the ring , and it is thus done . take 30 or 40 counters ( of which there is but 24 necessary ) that so you may conceale the way the better , and lay them down before the parties , and as they sit or stand , give to the first 1. counter , which signifieth a , the first vowell ; to the second 2. counters , which represent e , the second vowel ; and to the third 3. counters , which stand for i , the third vowell : then leaving the other counters upon the table , retire apart , and bid him which hath the ring , take as many counters as you gave him , and he that hath the gold , for every one that you gave him , let him take 2 , and he that hath the silver for every one that you gave him , let him take 4. this being done , consider to whom you gave one counter , to whom two , and to whom three ; and mark what number of counters you had at the first , for there are necessarily but 24. as was said before , the surpluse you may privately reject . and then there will be left either 1.2.3.5.6 or 7. and no other number can remaine , which if there be , then they have failed in taking according to the directions delivered : but if either of these numbers do remaine , the resolution will be discovered by one of these 6 words following , which ought to be had in memory , viz. salve , certa , anima , semita , vita , quies· 1. 2. 3. 5. 6. 7. as suppose 5. did remaine , the word belonging unto it is semita , the vowels in the first two syllables are e and i , vvhich shevveth according to the former directions , that to vvhom you gave 2 counters , he hath the ring ( seeing it is the second vovvell represented by tvvo as before ) and to vvhom you gave the 3. counters , he hath the gold , for that i represents the third vovvel , or 3. in the former direction , and to vvhom you gave one counter , he hath the silver , and so of the rest : the variety of changes , in vvhich exercise , is laid open in the table follovving . rest men hid rest men hid 1 1 a 5 1   2 e 2   3 i 3   2 1 e 6 1   2 a 2   3 i 3   3 1 a 7 1   2 i 2   3 e 3   this feat may be done also without the former words by help of the circle a. for having divided the circle into 6 parts , write 1. within and 1. vvithout , 2. vvithin and 5. vvithout , &c. the first 1.2.3 . vvhich are vvithin vvith the numbers over them , belongs to the upper semicircle ; the other numbers both vvithin and vvithout , to the under semicircle ; now if in the action there remaineth such a number which may be found in the upper semicircle without , then that which is opposite within shews the first , the next is the second , &c. as if 5 remains , it shews to whom he gave 2 , he hath the ring ; to whom you gave ● , he hath the gold , &c. but if the remainder be in the under semicircle , that which is opposite to it is the first ; the next backwards towards the right hand is the second ; as if 3 remains , to whom you gave 1 he hath the ring , he that had 3 he had the gold , &c. problem ix . how to part a vessel which is full of wine conteining eight pints into two equall parts , by two other vessels which conteine as much as the greater vessell ; as the one being 5 pints , and the other 3 pints . let the three vessels be represented by abc , a being full , the other two being empty ; first , poure out a into b until it be full , so there will be in b 5 pints , and in a but 3 pints : then poure out of b into c untill it be full : so in c shall be 3 pints , in b 2 pints , and in a 3 pints , then poure the wine which is in c into a , so in a will be 6 pints , in b 2 pints , and in c nothing : then poure out the wine which is in b into the pot c , so in c there is now 2 pints , in b nothing , and in a 6 pints , . lastly , poure out of a into b untill it be full , so there will be now in a only 1 pint in b 5 pints , and in c 2 pints . but it is now evident , that if from b you poure in unto the pot c untill it be full , there wil remain in b 4 pints , and if that which is in c , viz. 3 pints be poured into the vessell a , which before had 1 pint , there shall be in the vessel a , but halfe of its liquor that was in it at the first , viz. 4 pints as was required . otherwise poure out of a into c untill it be full , which pour into b , then poure out of a into c again untill it be full , so there is now in a onely 2 pints , in b 3 , and in c 3 , then pour from c into b untill it be full , so in c there is now but 1 pint , 5 in b , and 2 in a : poure all that is in b into a , then poure the wine which is in c into b , so there is in c nothing , in b onely 1 pint , and in 7 a 7 pints : lastly , out of a fill the pot c , so there will remain in a 4 pints , or be but halfe full : then if the liquor in c be poured into b , it will be the other half . in like manner might be taken the half of a vessell which conteins 12 pints , by having but the measures 5 and 7 , or 5 and 8. now such others might be proposed , but we omit many , in one and the same nature . problem . x. to make a stick stand upon the tip of ones finger , without falling . fasten the edges of tvvo knives or such like of equall poise , at the end of the stick , leaning out somevvhat from the stick , so that they may counterpoise one another ; the stick being sharp at the end , and held upon the top of the finger , vvill there rest vvithout supporting : if it fall , it must fall together , and that perpendicular or plumb-wise , or it must fall side-wise or before one another ; in the first manner it cannot : for the centre of gravitie is supported by the top of the finger : and seeing that each part by the knives is counterpoised , it cannot fall sidevvise , therefore it can fall no vvise . in like manner may great pieces of timber , as joists , &c be supported , if unto one of the ends be applied convenient proportionall counterpoises , yea a lance or pike , may stand perpendicular in the aire upon the top of ones finger : or placed in the midst of a court by help of his centre of gravitie . examination . this proposition seems doubtfull ; for to imagine absolutely , that a pike , or such like , armed with two knives , or other things , shall stand upright in the aire , and so remain without any other support , seeing that all the parts have an infinite difference of propensity to fall ; and it is without question that a staff so accommodated upon his centre of gravity , but that it may incline to some one part without some remedy be applied , and such as is here specified in the probleme will not warrant the thing , nor keep it from falling ; and if more knives should be placed about it , it should cause it to fall more swiftly , forasmuch as the superiour parts ( by reason of the centricall motion ) is made more ponderous , and therefore lesse in rest . to place therefore this prop really , let the two knives , or that which is for counterpoise , be longer always then the staffe , and so it will hang together as one body : and it will appear admirable if you place the centre of gravity , neer the side of the top of the finger or point ; for it will then hang horizontall , and seem to hang onely by a touch , yet more strange , if you turn the point or top of the finger upside down . problem xi . how a milstone or other ponderosity , may be supported by a small needle , without breaking o● any wise bowing the same . let a needle be set perpendicular to the horizon , and the center of gravitie of the stone be placed on the top of the needle : it is evident that the stone cannot fall , forasmuch as it hangs in aequilibra , or is counterpoysed in all parts alike ; and moreover it cannot bow the needle more on the one side then on the other , the needle will not therefore be either broken or bowed ; if otherwise then the parts of the needle must penetrate and sinke one with another : that which is absurd and impossible to nature ; therefore it shall be supported . the experiments which are made upon trencher plates , or such like lesser thing doth make it most credible in greater bodies . but here especially is to be noted , that the needle ought to be uniforme in matter and figure , and that it be erected perpendicular to the horizon , and lastly , that the center of gravity be exactly found . problem xii . to make three knives hang and move upon the point of a needle . fit the three knives in form of a ballance , and holding a needle in your hand , and place the back of that , knife which lyes cross-wise to the other two , upon the point of the needle : as the figure here sheweth you ; for then in blowing softly upon them , they will easily turne and move upon the point of the needle with ●ou falling . problem xiii . to finde the weight of smoak , which is exhaled of any combustible body whatsoever . let it be supposed that a great heape of fagots , or a load of straw weighing 500 pound should be fired , it is evident that this grosse substance will be all inverted into smoak and ashes : now it seems that the smoak weighs nothing ; seeing it is of a thin substance now dilated in the aire , notwithstanding if it were gathered and reduced into the thickest that it was at first , it would be sensibly weighty : weigh therefore the ashes which admit 50 pound , now seeing that the rest of the matter is not lost , but is exhaled into smoake , it must necessarily be , that the rest of the weight ( to wit ) 450 pound , must be the weight of the smoak required . examination . now although it be thus delivered , yet here may be noted , that a ponderosity in his own medium is not weighty : for things are said to be weighty , when they are out of their place , or medium , and the difference of such gravity , is according to the motion : the smoak therefore certainly is light being in its true medium ( the aire , ) if it should change his medium , then would we change our discourse . problem xvi . many things being disposed circular , ( or otherwise ) to finde which of them , any one thinks upon ▪ suppose that having ranked 10 things , as abcdefghik , circular ( as the figure sheweth ) and that one had touched or thought upon g , which is the 7 : ask the party at what letter he would begin to account ( for account he must , otherwise it cannot be done ) which suppose , at e which is the 5 place , then add secretly to this 5 , 10 ( which is the number of the circle ) and it makes 15 , bid him account 15 backward from e , beginning his account with that number hee thought upon , so at e he shal account to himself 7 , at d account 8 , at c account 9 , &c. so the account of 15 wil exactly fall upon g , the thing or number thought upon : and so of others : but to conceal it the more , you may will the party from e to account 25 , 35 , &c. and it will be the same . there are some that use this play at cards , turned upside downe , as the ten simple cards , with the king and queen , the king standing for 12 , and the queene for 11 , and so knowing the situation of the cards : and thinking a certain houre of the day : cause the party to account from what card he pleaseth : with this proviso , that when you see where he intends to account , set 12 to that number , so in counting as before , the end of the account shall fall upon the card : which shall denote or shew the houre thought upon , which being turned up will give grace to the action , and wonder to those that are ignorant in the cause . problem xv. how to make a door or gate , which shall open on both sides . all the skill and subtilty of this , rests in the artificiall disposer of foure plates of iron , two at the higher end , and two at the lower end of the gate : so that one side may move upon the hooks or hinges of the posts , and by the other end may be made fast to the gate , and so moving upon these hinges , the gate will open upon one side with the aforesaid plates , or hooks of iron : and by help of the other two plates , will open upon the other side . problem xvi . to shew how a ponderosity , or heavy thing , may be supported upon the end of a staffe ( or such like ) upon a table , and nothing holding or touching it . take a pale which hath a handle , and fill it full of water ( or at pleasure : ) then take a staffe or stick which may not rowle upon the table as ec , and place the handle of the pale upon the staffe ; then place another staffe , or stick , under the staffe ce , which may reach from the bottom of the pale unto the former staffe ce , perpendicular wise : which suppose fg , then shall the pale of water hang without falling , for if it fall it must fall perpendicularly , or plumbe wise : and that cannot be seeing the staffe ce supports it , it being parallel to the horizon and susteined by the table , and it is a thing admirable that if the staffe ce were alone from the table , and that end of the staffe which is upon the table were greater and heavier than the other : it would be constrained to hang in that nature . examination . now without some experience of this probleme , a man would acknowledge either a possibility or impossibity ; therefore it is that very touchstone of knowledge in any thing , to discourse first if a thing be possible in nature , and then if it can be brought to experience and under sence without seeing it done . at the first , this proposition seems to be absurd , and impossible . notwithstanding , being supported with two sticks , as the figure declareth , it is made facile : for the horizontall line to the edge of the table , is the centre of motion ; and passeth by the centre of gravity , which necessarily supporteth it . problem xvii . of a deceitfull bowle to play withall . make a hole in one side of the bowle , and cast molten lead therein , and then make up the hole close , that the knavery or deceit be not perceived : you will have pleasure to see , that notwithstanding the bowle is cast directly to the play , how it wil turn away side-wise : for that on that part of the bowle which is heavier upon the one side then on the other , it never will go truly right , if artificially it be not corrected ; which will hazard the game to those which know it not : but if it be known that the leady side in rolling be always under or above , it may go indifferently right ; if otherwise , the weight will carry it always side-wise . problem . xviii . to part an apple into 2.4 . or 8. like parts , without breaking the rinde . passe a needle and threed under the kinde of the apple , and then round it with divers turnings , untill you come to the place where you began : then draw out the threed gently , and part the apple into as many parts as you think convenient : and so the parts may be taken out between the parting of the rind , and the rind remaining alwayes whole . problem xix . to finde a number thought upon without asking of any question , certaine operations being done . bid him adde to the number thought ( as admit 15 ) halfe of it , if it may be , if not the greatest halfe that exceeds the other but by an unite , which is 8 ; and it makes 23. secondly , unto this 23. adde the halfe of it if it may be , if not , the greatest halfe , viz. 12. makes 35. in the meane time , note that if the number thought upon cannot be halfed at the first time , as here it cannot , then for it keep 3 in the memory , if at the second time it will not be equally halfed , reserve 2 in memory , but if at both times it could not be equally halved , then may you together reserve five in memory : this done , cause him from the last summe , viz. 35. to subtract the double of the number thought , viz. 30. rest 5. will him to take the halfe of that if he can , if not , reject 1. and then take the halfe of the rest , which keep in your memory : then will him to take the halfe againe if he can , if not , take one from it , which reserve in your memory , and so perpetually halveing untill 1. remaine : for then mark how many halfes there were taken , for the first halfe account 2 , for the second 4 , for the third 8 , &c. and adde unto those numbers the one 's which you reserved in memory , so there being 5 remaining in this proposition , there were 2 halfings : for which last ! account 4 , but because it could not exactly be halved without rejecting of 1. i adde the 1 therefore to this 4 , makes 5 , which halfe or summe alwayes multiplied by 4 , makes 20. from which subtract the first 3 and 2 , because the halfe could not be formerly added , leaves 15 , the number thought upon . other examples . the number thought upon . the number thought 12 the halfe of it 6 the summe 18 the halfe of it 9 the summe of it 27 the double of the number , 24 which taken away , rests 3 the halfe of it 1 for which account 2 and 1 put to it because the 3 could not be halfed , makes 3 this multiplied by 4 makes 12 the number thought 79 the greatest halfe 40 3 the summe 119 the greatest halfe of which is 60 2 the summe of it is 179 the double of 79 is 158 which taken from it , rests 21 the lesser half 10. which halve :   the halfe of this is 5 which makes   the half of this is 2 which is 10   the half of this is 1 , with 10 and 11 is 21.   this 21 which is the double of the last halfe with the remainder being multiplied by 4. makes 84 , from which take the aforesaid 3 and 2 , ●●st 79 , the number thought upon .   problem . xx. how to make an uniforme , & an inflexible body , to passe through two small holes of divers formes , as one being circular , and the other square , quadrangular , and triangular-wise , yet so that the holes shall be exactly filled . this probleme is extracted from geometricall observations , and seemes at the first somewhat obscure , yet that which may be extracted in this nature , will appeare more difficult and admirable . now in all geometricall practises , the lesser or easier problemes do alwayes make way to facilitate the greater : and the aforesaid probleme is thus resolved . take a cone or round pyramide , and make a circular hole in some board , or other hard material , which may be equall to the bases of the cone , and also a triangular hole , one of whose sides may be equall to the diameter of the circle , and the other two sides equall to the length of the cone : now it is most evident , that this conicall or pyramidall body , will fill up the circular hole , and being placed side-wise will fill up the triangular hole . moreover , if you cause a body to be turned , which may be like to two pyramides conjoyned , then if a circular hole be made , whose diameter is equal to the diameter of the cones conjoyned , and a quadrangular hole , whose sloping sides be equall to the length of each side of the pyramide , and the breadth of the hol equal to the diameter of the circle , this conjoyned pyramide shall exactly fill both the circular hole , and also the quadrangle hole . problem . xxi . how with one uniforme body or such like to fill three severall holes : of which the one is round , the other a just square , and the third an ovall forme ? this proposition seemes more subtill then the former , yet it may be practised two wayes : for the first , take a cylindricall body as great or little as you please : now it is evident that it will fill a circular hole , which is made equall to the basis of it , if it be placed downe right , and will also fill a long square ; whose sides are equall unto the diameter and length of the cylinder , and acording to pergeus , archimedes , &c. in their cylindricall demonstrations , a true ovall is made when a cylinder is cut slopewise , therefore if the oval have breadth equall unto the diameter of the basis of the cylinder , & any length whatsoever : the cylinder being put into his owne ovall hole shall also exactly fill it . the second way is thus , make a circular hole in some board , & also a square hole , the side of which square may be equall to the diameter of the circle : and lastly , make a hole oval-wise , whose breadth may be equal unto the diagonall of the square ; then let a cylindricall body be made , whose basis may be equall unto the circle , and the length equall also to the same : now being placed downe right shall fall in the circle , and flat-wise will fit the square hole , and being placed sloping-wise will fill the ovall . examination . you may note upon the last two problemes farther , that if a cone be cut ecliptick-wise , it may passe through an issoc●●● triangle through many scalen triangles , and through an ellipsis ; and if there be a cone cut scalen-wise , it will passe through all the former , only for the ellipsis place a circle : and further , if a solid colume be cut ecliptick-wise it may fill a circle , a square , divers parallelogrammes , and divers ellipses , which have different diameters . problem xxii . to finde a number thought upon ●fter another manner , then what is formerly delivered bid him that he multiply the number thought upon , by what number he pleaseth , then bid him divide that product by any other number , and then multiply that quotient by some other number ; and that product againe divide by some other , and so as often as he will : and here note , that he declare or tell you by what number he did multiply & divide now in the same time take a number at pleasure , and secretly multiply and divide as often as he did : then bid him divide the last number by that which he thought upon . in like manner do yours privately , then will the quotient of your divisor be the same with his , a thing which seemes admirable to those which are ignorant of the cause . now to have the number thought upon without seeming to know the last quotient , bid him adde the number thought upon to it , and aske him how much it makes : then subtract your quotient from it , there will remaine the number thought upon for example , suppose the number thought upon were 5 , multiply it by 4 makes 20. this divided by 2 , the quotient makes 10 , which multiplyed by 6 , makes 60 , and divided by 4 , makes 1● . in the same time admit you think upon 4 , which multiplied by 4 , makes 16 , this divided by 2 , makes 8 , which multiplied by 6 makes 48 , and divided by 4 makes 1● ; then divide 1● by the number thought , which was 5 , the quotient is ● ; divide also 12 by the number you took , viz. 4 , the quotient is also 3. as was declared ; therefore if the quo●ient ● be added unto the number thought , viz. ● , it makes 8 , which being known , the number thought upon is also knowne . problem xxiii . to finde out many numbers that sundry persons , or one man hath thought upon . if the multitude of numbers thought upon be odde , as three numbers , five numbers , seven , &c. as for example , let 5 numbers thought upon be these ● 2 , 3 , 4 , 5 , 6. bid him declare the sum of the first and second , which will be 5 , the second and third , which makes 7 , the third and fourth , which makes 9 , the fourth and fifth , vvhich makes 11 , and so alvvayes adding the tvvo next together , aske him hovv much the first and last makes together , vvhich is 8. then take these summes , and place them in order , and adde all these together , vvhich vvere in the odde places : that is the first , third , and fifth , viz. 5 , 9 , ● , makes 22. in like manner adde all these numbets together , vvhich are in the even places , that is in the second and fourth places , viz. 7 and 1● makes 18 , substract this from the former 22 , then there vvill remaine the double of the first number thought upon , viz. 4. which known , the rest is easily known : seeing you know the summe of the first and second ; but if the multitude of numbers be even as these six numbers , viz. 2 , ● , 4 , 5 , 6 , 7 , cause the partie to declare the summe of each two , by antecedent and consequent , and also the summe of the second and last , which will be 5 , 7 , 9 , 11 , 13 , 10 , then adde the odde places together , except the first , that is 9 , and 13 , makes 22 , adde also the even places together , that is 7 , 11 , 10 , which makes 28 , substract the one from the other , there shall remaine the double of the second number thought upon , which known all the rest are knowne . problem xxiv . how is it that a man in one and the same time , may have his head upward , and his feet upward , being in one and the same place ? the answer is very facill , for to be so he must be supposed to be in the centre of the earth : for as the heaven is above on every side , coelum undique sursum , all that which looks to the heavens being distant from the centre is upward ; and it is in this sense that ma●●olyeus in his cosmographie , & first dialogue , reported of one that thought he was led by one of the muses to hell , where he saw lucifer sitting in the middle of the world , and in the centre of the earth , as in a throne : having his head and feet upward . problem . xxv . of a ladder by which two men ascending at one time ; the more they ascend , the more they shall be asunder , notwithstanding one being as high as another this is most evident , that if there were a ladder halfe on this side of the centre of the earth , and the other halfe on the other side : and that two at the centre of the world at one instant being to ascend , the one towards us , and the other towards our antipodes , they should in ascending go farther and farther , one from another ; notwithstanding both of them being of like height . problem . xxvi . how it is that a man having but a rod or pole of land , doth bragge that he may in a right line passe from place to place above 3000 miles . the opening of this is easie , forasmuch as he that possesseth a rod of ground possesseth not only the exterior surface of the earth , but is master also of that which extends even to the centre of the earth , and in this wise all heritages & possessions are as so many pyramides , whose summets or points meet in the centre of the earth , and the basis of them are nothing else but each mans possession , field , or visible quantity ; and therefore if there were made or imagined so to be made , a descent to go to the bottome of the heritage , which would reach to the centre of the earth ; it would be above 3000 miles in a right line as before . problem . xxvii . how it is , that a man standing upright , and looking which way he will , he looketh either true north or true south . this happeneth that if the partie be under either of the poles , for if he be under the north-pole , then looking any way he looketh south , because all the meridians concurre in the poles of the world , and if he be under the south-pole , he looks directly north by the same reason . problem xxviii . to tell any one what number remaines after certaine operations being ended , without asking any question . bid him to think upon a number , and will him to multiply it by what number you think convenient : and to the pro●●ct bid him adde what number you please , or 〈◊〉 that secretly you consider , that it ma● be divided by that which multiplied , and 〈…〉 divide the sum by the number which he 〈…〉 by , and substract from this quotient the number thought upon : in the same time divide apart the number which was add●d by that which multiplied , so then your quotient shall be equall to his remainder , wherefore without asking him any thing , you shall tell him what did remaine , which will seem strange to him that knoweth not the cause : for example , suppose he thought 7 , which multiplied by 5 makes 35 , to which adde 10 , makes 45 , which divided by 5 , yields 9 , from which if you take away one the number thought , ( because the multiplier divided by the divisor gives the quotient 1 , ) the rest will be two , which will be also proved , if 10 the number which was added , were divided by 5 , viz. 2. problem xxix . of the play with two severall things . it is a pleasure to see and consider how the science of numbers doth furnish us , not only 〈…〉 recreate the spirits , but also 〈…〉 knowledge of admirable things , 〈…〉 measure be shewen in this 〈…〉 the meane time to produce alwayes some of them : suppose that a man hold divers things in his hand , as gold and ●ilver ▪ and in one hand he held the gold , and in the other hand he held the silver : to know subtilly , and by way of divination , or artificially in which hand the gold or silver is ; attribu●e t● the gold , or suppose it have a certaine price , and so likewise attribute to the silver another price , conditionally that the one be odd , and the other even : as for example , bid h●m that the gold be valued at 4 crownes , or shillings , and the silver at ● crownes , or 3 shillings , or any other number , so that one be odde ▪ and the other even , as before ; then bid him triple that which is in the right hand , & double that which is in the left hand , and bid him adde these two products together , and aske him if it be even or odde ; if it be even , then the gold is in the right hand ; if odde , the gold is in the left hand . problem . xxx . two numbers being proposed unto two severall parties , to tell which of these numbers is taken by each of them . as for example : admit you had proposed unto two men whose names were peter and john , two numbers , or pieces of money , the one even , and the other odde , as 10. and 9. and let the one of them take one of the numbers , and the other partie take the other number , which they place privately to themselves : how artificially , according to the congruity , and excellency of numbers , to finde which of them did take 10. and which 9. without asking any qustion : and this seems most subtill , yet delivered howsoever differing little from the former , and is thus performed : take privately to your selfe also two numbers , the one even , and the other odde , as 4. and 3. then bid peter that he double the number which he took , and do you privately double also your greatest number ; then bid john to triple the number which he hath , and do you the like upon your last number : adde your two products together , & mark if it be even or odde , then bid the two parties put their numbers together , and bid them take the halfe of it , which if they cannot do , then immediately tell peter he took 10. and john 9. because the aggregate of the double of 4. and the triple of 3. makes odde , and such would be the aggregate or summe of the double of peters number and johns number , if peter had taken 10. if otherwise , then they might have taken halfe , and so john should have taken 10. and peter 9. as suppose peter had taken 10. the double is 20. and the triple of 9. the other ●umber is 27. which put together makes 47. odde : in like manner the double of your number conceived in minde , viz. 4. makes 8. and the triple of the 3. the other number , makes 9. which set together makes 17. odde . now you cannot take the halfe of 17 , nor 47. which argueth that peter had the greater number , for otherwise the double of 9. is 18. & the triple of 10. is 30. which set together makes 48. the halfe of it may be taken : therefore in such case peter the took lesse number : and john the greater , and this being don cleanly carries much grace with it . problem . xxxi . how to describe a circle that shall touch 3 : points placed howsoever upon a plaine , if they be not in a right line . let the three points be a.b.c. put one foot of the compasse upon a. and describe an arch of a circle at pleasure : and placed at b. crosse that arch in the two points e. and f. and placed in c. crosse the arch in g. and h. then lay a ruler upon g.h. and draw a line , and place a ruler upon e. and f. cut the other line in k ▪ so k is the centre of the circumference of a circle , which will passe by the said three points a.b.c. or it may be inverted , having a circle drawne ; to finde the centre of that circle , make 3. points in the circumference , and then use the same way : so shall you have the centre , a thing most facill to every practitioner in the principles of geometrie . problem . xxxii . how to change a circle into a square forme ? m●ke a circle upon past-board or other materiall , as the circle a.c.d.e. of which a. is the centre ; then cut it into 4 quarters , and dispose them so , that a. at the centre of the circle may alwayes be at the angle of the square , and so the foure quarters of the circle being placed so , it will make a perfect square , whose side a.a. is equall to the diameter b.d. now here is to be noted that the square is greater then the circle by the vacuity in the middle , viz. m. problem . xxxiii . with one and the same comp●sses , and at one and the same extent , or opening , how to describe many circles concentricall , that is , greater or lesser one then another ? it is not without cause that many admire how this proposition is to be resolved ; yea in the judgement of some it is thought impossible : who consider not the industrie of an ingenious geometrician , who makes it possible , and that most facill , sundry wayes ; for in the first place if you make a circle upon a fine plaine , and upon the centre of that circle , a small pegge of wood be placed , to be raised up and put downe at pleasure by help of a small ho●e made in the centre , then with the same opening of the compasses , you may describe circles concentricall , that is , one greater or lesser than another ; for the higher the center is lifted up , the lesser the circle will be . secondly , the compasse being at that extent upon a gibus body , a circle may be described , which will be lesse than the former , upon a plaine , and more artificially upon a globe , or round bowle : and this againe is most obvious upon a round pyramide , placing the compasses upon the top of it , which will be farre lesse than any of the former ; and this is demonstrated by the 20. prop. of the first of euclids , for the diameter ● . d. is lesse than the line ad.a.e. taken together , and the lines ad.ae. being equall to the diameter bc. because of the same distance or extent of opening the compasses , it followes that the diameter e.d. and all his circles together is much lesse than the diameter , and the circle bc. which was to be performed . problem xxxiv . any numbers under 10. being thought upon , to finde what numbers they were . let the first number be doubled , and unto it adde 5. and multiply that summe by 5. and unto it adde 10. and unto this product add the next number thought upon ; multiply this same againe by 10. and adde unto it the next number , and so proceed : now if he declare the last summe ; marke if he thought but upon one figure , for then subtract only 35. from it , and the first figure in the place of tennes is the number thought upon : if he thought upon two figures , then subtract also the said ●5 . from his last summe , and the two figures which remaine are the number thought upon : if he thought upo● three figures , then subtract 350. and then the first three figures are the numbers thought upon , &c. so if one thought upon these numbers 5.7.9.6 . double the first , makes 1● . to which adde 5. makes 15. this multiplied by 5. makes 75. to which adde 1● . makes 85. to this adde the next number , viz. 7. makes 92. this multiplied by 10. makes 920. to which adde the next number , viz. 9. makes 929. which multiplied by 10. makes 9290. to which adde 6. makes 9296. from which subtract 3500. resteth 5796. the foure numbers thought upon . now because the two last figures are like the two numbers thought upon : to conceale this , bid him take the halfe of it , or put first 12. or any other number to it , and then it will not be so open . problem . xxxv . of the play with the ring . amongst a company of 9. or 10. persons , one of them having a ring , or such like : to finde out in which hand : upon which finger , & joynt it is ; this will cause great astonishment to ignorant spirits , which will make them beleeve that he that doth it works by magick , or witchcraft : but in effect it is nothing else but a nimble act of arithmetick , founded upon the precedent probleme : for first it is supposed that the persons stand or sit in order , that one is first , the next second , &c. likewise there must be imagined that of these two hands the one is first , and the other second : and also of the five fingers , the one is first , the next is second , and lastly of the joynts , the one is as 1. the other is as 2. the other as 3. &c. from whence it appeares that in performing this play there is nothing else to be done than to think 4. numbers : for example , if the fourth person had the ring in his left hand , and upon the fifth finger , and third joynt , and i would divine and finde it out : thus i would proceed , as in the 34 problem : in causing him to double the first number : that is , the number of persons , which was 4. and it makes 8. to which add 5. makes 13. this multiplied by 5. makes 65. put 10. to it , makes 75. unto this put ● . for the number belonging to the left hand , and so it makes 77. which multiplied by 10. makes 770. to this adde the number of the fingers upon which the ring is , viz. 5. makes 775. this multiplied by 10. makes 7750. to which adde the number for the joynt upon which the ring is , viz the third joynt , makes 7●53 . to which cause him to adde 14. or some other number , to conceale it the better : and it makes 7767. which being declared unto you , substract 3514 ▪ and there will remaine 4.2.5.3 . which figures in order declares the whol mystery of that which is to be known : 4. signifieth the fourth person , 2. the left hand , 5. the fifth finger , and 3. the third joynt of that finger . problem . xxxvi . the play of 34. or more dice . that which is said of the two precedent problemes may be applied to this of dice ( and many other particular things ) to finde what number appeareth upon each dice being cast by some one , for the points that are upon any side of a dice are alwayes lesse than 10 and the points of each side of a dice may be taken for a number thought upon : therefore the rule will be as the former : as for example , one having thrown three dice , and you would declare the numbers of each one , or how much they make together , bid him double the points of one of the dice , to which bid him adde 5 , then multiply that by 5. and to it adde 10 , and to the summe bid him adde the number of the second dice : and multiply that by 10 : lastly , to this bid him adde the number of the last dice , and then let him declare the whole number : then if from it you subtract ●50 . there will remaine the number of the three dice throwne . problem . xxxvii . how to make water in a glasse seeme to boyle and sparkle ? take a glasse neere full of water or other liquor ; and setting one hand upon the foot of it , to hold it fast : turne slightly one of the fingers of your other hand upon the brimme , or edge of the glasse ; having before privately wet your finger : and so passing softly on with your finger in pressing a little : for then first , the glasse will begin to make a noyse : secondly , the parts of the glasse will sensibly appeare to tremble , with notable rarefaction and condensation : thirdly , the water will shake , seeme to boyle : fourthly , it will cast it selfe out of the glasse , and leap out by small drops , with great astonishment to the standers by ; if they be ignorant of the cause of it , which is onely in the rarefaction of the parts of the glasse , occasioned by the motion and pressure of the finger . examination . the cause of this , is not in the rarefaction of the parts of the glasse , but it is rather in the quick locall motion of the finger , for reason sheweth us that by how much a body draweth nearer to a quality , the lesse is it subject or capable of another which is contrary unto it ? now condensation , and rarefaction are contrary qualities , and in this probleme there are three bodies considered , the glasse , the water , and the aire , now it is evident that the glasse being the most solid , and impenitrable body , is lesse subject and capable of rarefaction than the water , the water is lesse subject than the aire , and if there be any rarefaction , it is rather considerable in the aire then in the water , which is inscribed by the glasse , and above the water , and rather in the water then in the glasse : the agitation , or the trembling of the parts of the glasse to the sense appeares not : for it is a continued body ; if in part , why then not in the whole ? and that the water turnes in the glasse , this appeares not , but only the upper contiguous parts of the water : that at the bottome being lesse subiect to this agitation , and it is most certaine that by how much quicker the circular motion of the finger upon the edge of the glasse is , by so much the more shall the aire be agitated , and so the water shall receive some apparant affection more or lesse from it , according to that motion : as we see from the quicknesse of winde upon the sea , or c●lme thereof , that there is a greater or lesser agitation in the water ; and for further examination , we leave it to the search of those which are curious . problem . xxxviii . of a fine vessell which holds wine or water , being cast in●o it at a certaine height , but being filled higher , it will runne out of its owne accord . let there be a vessell a.b.c.d. in the middle of which place a pipe ; whose ends both above at e , and below at the bottom of the vessell as at ● ▪ are open ; let the end ● be somewhat lower than the brimme of the glasse : about this pipe , place another pipe as h. l , which mounts a little above e and let it most diligently be closed at h , that no aire enter in thereby , and this pipe at the bottome may have a small hole to give passage unto the water ; then poure in water or wine , and as long as it mounts not above e , it is safe ; but if you poure in the water so that it mount above it , farewell all : for it will not cease untill it be all gone out ; the same may be done in disposing any crooked pipe in a vessell in the manner of a faucet or funnell , as in the figure h , for fill it under h , at pleasure , and all will go well ; but if you fill it unto h. you will see fine sport , for then all the vessell will be empty incontinent , and the subtiltie of this will seeme more admirable , if you conceale the pipe by a bird , serpent , or such like , in the middle of the glasse . now the reason of this is not difficult to those which know the nature of a cock or faucet ; for it is a bowed pipe , one end of which is put into the water or liquor , and sucking at the other end untill the pipe be full , then will it run of it selfe , and it is a fine secret in nature to see , that if the end of the pipe which is out of the water , be lower then the water , it will run out without ceasing : but if the mouth of the pipe be higher then the water or levell with it , it will not runne , although the pipe which is without be many times bigger than that which is in the water : for it is the property of water to keep alwayes exactly levell ▪ examination . here is to be noted , that if the face of the water without be in one and the same plaine , with that which is within , though the outtermost pipe be ten times greater than that which is within ; the water naturally will not runne , but if the plaine of the water without be any part lower then that which is within , it will freely runne : and here may be noted further , that if the mouth of the pipe which is full of water , doth but only touch the superficies of the water within , although the other end of the pipe without be much lower than that within , the water it will not run at all : which contradicts the first ground ; hence we gather that the pressure or ponderosity of the water within , is the cause of running in some respect . problem . xxxix . of a glasse very pleasant . sometimes there are glasses which are made of a double fashion , as if one glasse were within another , so that they seem but one , but there is a little space between them . no● poure wine or other liquor between the two edges by help of a tunnell , into a little hole left to this end , so vvill there appeare tvvo fine delusions or fallacies ; for though there be not a drop of wine vvithin the hollovv of the glasse , it vvill seem to those vvhich behold it that it is an ordinary glasse full of wine , and that especially to those vvhich are side-vvise of it , and if any one move it , it vvill much confirme it , because of the motion of the wine ; but that vvhich vvill give most delight , is that , if any one shall take the glasse , and putting it to his mouth shall think to drink the wine , instead of vvhich he shall sup the aire , and so vvill cause laughter to those that stand by , vvho being deceived , vvill hold the glass to the light , & thereby considering that the raies or beames of the light are not reflected to the eye , as they vvould be if there vvere a liquid substance in the glasse , hence they have an assured proofe to conclude , that the hollovv of the glasse is totally empty . problem . xl. if any one should hold in each hand , as many pieces of money as in the other , how to finde how much there is ? bid him that holds the money that he put out of one hand into the other vvhat number you think convenient : ( provided that it may be done , ) this done , bid him that out of the hand that he put the other number into , that he take out of it as many as remaine in the other hand , and put it into that hand : for then be assured that in the hand which was put the first taking away : there will be found just the double of the number taken away at the first . example , admit there were in each hand 12 shi●lings or counters , and that out of the right hand you bid him take 7. and put it into the left : and then put into the right hand from the left as many as doth remaine in the right , which is 5. so there will be in the left hand ●4 , which is the double of the number taken out of the right hand , to wit 7. then by some of the rules before delivered , it is easie to finde how much is in the right hand , viz. 10. problem . xli . many dice being cast , how artificially to discover the number of the points that may arise . svppose any one had cast three dice secretly , bid him that he adde the points that were upmost together : then putting one of the dice apart , unto the former summe adde the points which are under the other two , then bid him throw these two dice , and mark how many points a paire are upwards , which adde unto the former summe : then put one of these dice away not changing the side , mark the points which are under the other dice , and adde it to the former summe : lastly , throw that one dice , and whatsoever appeares upward adde it unto the former summe ; and let the dice remaine thus : this done , comming to the table , note what points do appeare upward upon the three dice , which adde privately together , and unto it adde ●1 or 3 times 7 : so this addition or summe shall be equall to the summe which the party privately made of all the operations which he formerly made . as if he should throw three dice , and there should appeare upward 5 , 3 , 2. the sum of them is 10. and setting one of them apart , ( as 5. ) unto 10 , adde the points which are under 3 and 2 , which is 4 and 5 , and it makes 19. then casting these two dice suppose there should appeare 4 and 1 , this added unto 19 makes 24. and setting one of these two dice apart as the 4. unto the former 24 , i adde the number of points which is under the other dice , viz. under 1 , that is 6 , which makes 30. last of all i throw that one dice , and suppose there did appeare 2 , which i adde to the former 30 , and it makes 32 , then leaving the 3 dice thus , the points which are upward will be these , 5 , 4 , 2 unto which adde secretly 21 , ( as before was said ) so have you 32 , the same number whi●h he had ; and in the same manner you may practise with 4 , 5 , 6 , or many dice or other bodies , observing only that you must adde the points opposite of the dice ; for upon which depends the whole demonstration or secret of the play ; for alwayes that which is above and underneath makes 7. but if it make another number , then must you adde as often that number . problem . xlii . two mettals , as gold and silver , or of other kin●● weighing alike , being privately placed into two like boxes , to finde which of them the gold or silver is in . but because that this experiment in water hath divers accidents , and therefore subject to a caution ; and namely , because the matter of the chest , mettall or other things may hinder . behold here a more subtill and certaine invention to finde and discover it out without weighing it in the water ▪ now experience and reason sheweth us that two like bodies or magnitudes of equall weight , and of divers mettalls , are not of equal quantity : and seeing that gold is the heaviest of all mettalls , it will occupie less roome or place ; from which will follow that the like weight of lead in the same forme , will occupie or take up more roome or place . now let there be therefore presented two globes or chests of wood or other matter alike , & equall one to the other , in one of which in the middle there is another globe or body of lead weighing 12. l. ( as c , ) and in the other a globe or like body of gold weighing 12 pound ( as b. ) now it is supposed that the wooden globes or chests are of equall weight , forme , and magnitude : and to discover in which the gold or lead is in , take a broad paire of compasses , and clip one of the coffers or globes somewhat from the middle , as at d. then fix in the chest or globe a small piece of iron between the feet of the compasses , as ek , at the end of which hang a vveight g , so that the other end may be counterpoysed , and hang in aequilibrio : and do the like to the other chest or globe . novv if that the other chest or globe being clipped in like distance from the end , and hanging at the other end the same weight g. there be found no difference ; then clip them nearer tovvards the middle , that so the points of the compasse may be against some of the mettall vvhich is inclosed ; or just against the extremitie of the gold as in d , and suppose it hang thus in aequilibrio ; it is certaine that in the other coffer is the lead ; for the points of the compasses being advanced as much as before , as at f , vvhich takes up a part of the lead , ( because it occupies a greater place than the gold ) therefore that shall help the vveight g. to vveigh , and so vvill not hang in aequilibrio , except g be placed neare to f. hence vve may conclude , that there is the lead ; and in the other chest or globe , there is the gold. examination . if the two boxes being of equall magnitude weighed in the aire be found to be of equall weight , they shall necessarily take up like place in the water , and therefore weigh also one as much as another : hence there is no possibilitie to finde the inequalitie of the mettalls which are inclosed in these boxes in the water : the intention of archimedes was not upon contrary mettalls inclosed in 〈…〉 boxes , but consisted of comparing metta●●● , simple in the water one with another : therefore the inference is false and absurd . problem . xliii . two globes of diverse mettalls , ( as one gold , and the other copper ) yet of equall weight being put into a box , as bg , to finde in which end the gold or copper is . this is discovered by the changing of the places of the tvvo bovvles or globes , having the same counterpoyse h to be hung at the other side , as in n. and if the gold vvhich is the lesser globe , vvere before the nearest to the handle d● , having novv changed his place vvill be farthest from the handle de , as in k. therefore the centre of gravity of the two globes taken together , shall be farther separate from the middle of the handle ( under which is the centre of gravity of the box ) than it was before , and seeing that the handle is alwayes in the middle of the box , the vveight n. must be augmented ▪ to keep it in equil●●●● and by this way one may knovv , that if at the second time , the counterpoise be too light , it is a signe that the gold is farthest off the handle , as at the first triall it vvas nearest . problem . xliiii . how to represent diverse sorts of rainebowes here below ? the rainbovve is a thing admirable in the vvorld , vvhich ravisheth often the eyes and spirits of men in consideration of his rich intermingled colours vvhich are seen under the clouds , seeming as the glistering of the starres , precious stones , and ornaments of the most beauteous flovvers : some part of it as the resplendent stars , or as a rose , or burning cole of fire ▪ in it one may see dyes of sundry sorts , the violet , the blew , the orange , the saphir , the jacinct , and the emerald colours , as a lively plant placed in a green soile : and as a most rich treasure of nature , it is a high work of the sun who casteth his raies or beames as a curious painter drawes strokes with his pensill , and placeth his colours in an exquisite situation ; and solomon saith , eccles. 43. it is a chiefe and principall work of god. notwithstanding there is left to industrie how to represent it from above , here below , though not in perfection , yet in part , with the same intermixture of colours that is above . have you not seen how by oares of a boate it doth exceeding quickly glide upon the water with a pleasant grace ? aristotle sayes , that it coloureth the water , and makes a thousand atomes , upon which the beames of the sunne reflecting , make a kinde of coloured rainbowe : or may we not see in houses or gardens of pleasure artificiall fountaines , which poure forth their droppie streames of water , that being between the sunne and the fountaine , there will be presented as a continuall rainbowe ? but not to go farther , i will shew you how you may do it at your doore , by a fine and facill experiment . take water in your mouth , and turne your back to the sunne , and your face against some obscure place , then blow out the water which is in your mouth , that it may be sprinkled in small drops and vapours : you shall see those atomes vapours in the beames of the sunne to turne into a faire rainebowe , but all the griefe is , that it lasteth not , but soone is vanished . but to have one more stable and permanent in his colours : take a glasse full of water , and expose it to the sunne , so that the raies that passe through strike upon a shadowed place , you will have pleasure to see the fine forme of a rainebovve by this reflection . or take a trigonall glasse or crystall glasse of diverse angles , and look through it , or let the beames of the sunne passe through it ; or vvith a candle let the appearances be received upon a shadovved place : you vvill have the same contentment . problem xlv . how that if all the powder in the world were in closed within a bowle of paper or glasse , and being fired on all parts , it could not break that bowle ? if the bowle and the powder be uniforme in all his parts , then by that means the powder would presse and move equally on each side , in which there is no possibility whereby it ought to begin by one side more than another . now it is impossible that the bowle should be broken in all his parts : for they are infinite . of like fineness or subtiltie may it be that a bowle of iron falling from a high place upon a plaine pavement of thin glasse , it were impossible any wise to break it ; if the bowle were perfectly round , and the glasse flat and uniforme in all his parts ▪ for the bowle would touch the glasse but in one point , which is in the middle of infinite parts which are about it : neither is there any cause why it ought more on one side than on another , seeing that it may not be done with all his sides together ; it may be concluded as speaking naturally , that such a bovvle falling upon such a glasse vvill not break it . but this matter is meere metaphysicall , and all the vvorkmen in the vvorld cannot ever vvith all their industrie make a bovvle perfectly round , or a glasse uniforme . problem . xlvi . to finde a number which being divided by 2 , there will remaine 1 , being divided by 3 , there will remaine 1 ; and so likewise being divided by 4 , 5 , or 6 , there would still remaine 1 ; but being didivided by 7 , there will remaine nothing . in many authors of arithmetick this probleme is thus proposed : a vvoman carrying egges to market in a basket , met an unruly fellovv who broke them : who vvas by order made to pay for them : and she being demanded what number she had , she could not tell : but she remembred that counting them by 2 & 2 , there remained 1 ▪ likewise by 3 and 3 by 4 and 4 , by 5 and 5 , by 6 and 6 ; there still remained 1. but when she counted them by 7 and 7 , there remained nothing : now how may the number of egges be discovered ? finde a number which may exactly be measured by 7 , and being measured by 2 , 3 , 4 , 5 , and 6 ; there vvill still remaine a unite ▪ multiply these numbers together , makes 720 , to which adde 1 ; so have you the number , viz. 721. in like manner 301 vvill be measured by 2 , 3 , 4 , 5 , 6 ; so that 1 remaines : but being measured by 7 , nothing vvill remaine ; to vvhich continually adde 220 , and you have other numbers vvhich vvill do the same : hence it is doubtfull vvhat number she had , therefore not to faile , it must be knovvn vvhether they did exceed 400 , 800 , &c. in vvhich it may be conjectured that it could not exceed 4 or 5 hundred , seeing a man or vvoman could not carry 7 or 8 hundred egges , therefore the number vvas the former ●01 . vvhich she had in her basket : vvhich being counted by 2 and 2 , there vvill remaine 1 , by 3 and 3 , &c. but counted by 7 and 7 , there vvill remaine nothing . problem . xlvii . one had a certaine number of crownes , and counting them by 2 and 2 , there rested 1. counting them by 3 and 3 , there rested 2. counting them by 4 and 4 , there rested 3. counting them by 5 and 5 , there rested 4. counting them by 6 & 6 , there rested 5. but counting them by 7 and 7 , there remained nothing : how many crownes might he have ? this question hath some affinitie to the precedent , and the resolution is almost in the same manner : for here there must be found a number , vvhich multiplied by 7 , and then divided by 2 , 3 , 4 , 5 , 6 ; there may alvvayes remaine a number lesse by 1 than the divisor : novv the first number vvhich arrives in this nature is 119 , unto vvhich if 420 be added , makes 539 , vvhich also vvill do the same : and so by adding 420 , you may have other numbers to resolve this proposition . problem . xlviii . how many sorts of weights in the least manner must there be to weigh all sorts of things between 1 pound and 40 pound , and so unto 121 , & 364 pound . to vveigh things betvveen 1 and 40 , take numbers in triple proportion , so that their summe be equall , or somewhat greater than 40 , as are the numbers 1 3.9.27 . i say that with ● such weights , the first being of 1 pound , the second being 3 pound , the third being 9 pound , and the fourth being 27 : any weight between 1 and 40 pound may be weighed . as admit to weigh 21 pound , put unto the thing that is to be weighed the 9 pound weight , then in the other ballance put 27 pound and 3 pound , which doth counterpoise 21 pound and 9 pound , and if 20 pound were to be weighed , put to it in the ballance 9 and 1 , and in the other ballance put 27 and 3 , and so of others in the same manner take those 5 weights , 1 , 3 , 9 , 27 ▪ 81 , you may weigh with them between 1 pound , and 121 pound : and taking those 6 weights ▪ as 1 , 3 , 9 , 2● , 81 , 243 , you may weigh even from 1 pound unto 364 pound : this depends upon the property of continued proportionals , the latter of which containing twice all the former . problem . xlix . of a deceitfull ballance which being c●●●ty seemes i● be just , because it hangs in aequilibrio : not●ithstanding putting 12 pound in one ballance , and 11 in the other , it will remaine in aequilibrio . aristotle maketh mention of this ballance in his mechanick questions , and saith , that the merchants of purpose in his time used them to deceive the world : the subtiltie or craft of which is thus , that one arme of the ballance is longer then another , by the same proportion , that one weight is heavier then another : as if the beame were 23 inches long , and the handle placed so that 12 inches should be on one side of it , and 11 inches on the other side : conditionally that the shorter end should be as heavy as the longer , a thing easie to be done : then afterwards put into the ballance two unequal weights in such proportion as the parts of the beame have one unto another , which is 12 to 11 , but so that the greater be placed in the ballance which hangs upon the shorter part of the beame , and the lesser weight in the other ballance : it is most certaine that the ballances will hang in aequilibrio , which will seem most sincere and just ; though it be most deceitfull , abominable , and false . the reason of this is drawne from the experiments of archimedes , who shewes that two unequall weights will counterpoyse one another , when there is like proportion betweene the parts of the beame ( that the handle separates ) and the vveights themselves : for in one and the same counterpoise , by hovv much it is farther from the centre of the handle , by so much it seems heavier , therefore if there be a diversitie of distance that the ballances hang from the handle , there must necessarily be an ineqality of weight in these ballances to make them hang in aequilibrio , and to discover if there be deceit , change the weight into the other ballance , for as soone as the greater vveight is placed in the ballance that hangs on the longer parts of the beame : it vvill vveigh dovvne the other instantly . problem . l. to heave or lift up a bottle with a straw . take a stravv that is not bruised , bovv it that it make an angle , and put it into the bottle so that the greatest end be in the neck , then the reed being put in the bovved part vvil cast side-vvise , and make an angle as in the figure may be seen : then may you take the end vvhich is out of the bottle in your hand , and heave up the bottle , and it is so much surer , by how much the angle is acuter or sharper ; and the end which is bowed approacheth to the other perpendicular parts which come out of the bottle . problem . li. how in the middle of a wood or desert , without the sight of the sunne , starres , shadow or compasse , to finde out the north or south , or the foure cardinall points of the world , east , west , & c ? it is the opinion of some , that the windes are to be observed in this : if it be hot , the south is found by the windes that blow that way , but this observation is uncertaine and subject to much error : nature will help you in some measure to make it more manifest than any of the former , from a tree thus : cut a small tree off , even to the ground , and mark the many circles that are about the sap or pith of the tree , which seem nearer together in some part than in other , which is by reason of the suns motion about the tree : for that the humiditie of the parts of the tree towards the south by the heat of the sun is rarified , and caused to extend : and the s●n not giving such heat towards the north-part of the tree , the sap is lesser rarefied , but condensed ; by which the circles are nearer together on the north-part , than on the south-part : therefore if a line be drawne from the widest to the narrowest part of the circles , it shall shew the north & south of the world . another experiment may be thus : take a small needle , such as women work with : place it gently downe flatwise upon still water , and it will not sink , ( which is against the generall tenet that iron will not swimme ) which needle will by little and little turne to the north and south-points . but if the needle be great and will not swim , thrust it through a small piece of cork , or some such like thing , and then it will do the same : for such is the property of iron when it is placed in aequilibrio , it strives to finde out the poles of the world or points of north and south in a manner as the magnes doth . examination . here is observable , that the moisture which aideth to the growth of the tree , is dilated and rarefied by the meridionall heat , and contracted by the septentrionall cold : this rarefaction works upon the part of the humour or moisture that is more thinne , which doth easily dissipate and evaporate : which evaporation carries a part of the salt with it ; and because that solidation or condensation , so that there is left but a part of the nourishment which the heat bakes up and consumes : so contrarily on the other side the condensation and restrictive quality of the moisture causeth lesse evaporation and perdition : and so consequently there remaines more nourishment , which makes a greater increase on that side than on the other side : for as trees have their growth in winter , because of their pores and these of the earth are shut up : so in the spring when their pores are open , and when the sappe and moisture is drawne by it , there is not such cold on the north-side that it may be condensed at once : but contrarily to the side which is south , the heat may be such , that in little time by continuance , this moisture is dissipated greatly : and cold is nothing but that which hardneth and contracteth the moisture of the tree , and so converteth it into wood . problem . lii . three persons having taken counters , cards , or other things , to finde how much each one hath taken . cause the third party to take a number which ma● be divided by 4 , and as often as he takes 4 , let the second party take 7 , and the first take 13 , then cause them to put them all together , and declare the summe of it ; which secretly divide by 3 , and the quotient is the double of the number which the third person did take . or cause the third to give unto the second and first , as many as each of them hath ; then let the second give unto the first and third , as many as each of them hath ; lastly , let the third give unto the second and first , as many as each of them hath ; and then aske how much one of them hath ; ( for they will have then all alike , ) so halfe of that number is the number that the third person had at the first : which knowne all is knowne . problem . liii . how to make a consort of musick of many parts with one voyce , or one instrument only ? this probleme is resolved , so that a finger or player upon an instrument , be neare an echo which answereth his voice or instrument ; and if the echo answereth but once at a time , he may make a double ; if twice , then a triple , if three times , then an harmonie of foure parts , for it must be such a one that is able to exercise both tune and note as occasion requires . as when he begins ut , before the echo answer , he may begin sol , and pronounce it in the same tune that ●he echo answereth , by which meanes you ●ave a fifth , agreeable consort of musick : then in the same time that the echo followeth , to sound the second note sol , he may sound forth another sol higher or lower to make an eight , the most perfect consort of musick , and so of others , if he will continue his voice with the echo , and sing alone with two parts . now experience sheweth this to be true , which often comes to passe in many churches , making one to beleeve that there are many more parts in the musick of a quire , then in effect truly there are because of the resounding and multiplying of the voic● , and redoubling of the quire. problem . liiii . t● make or describe an ovall form , or that which neare resembles unto it , at one turning with a paire of common compasses . there are many fine wayes in geometricall practices , to make an ovall figure or one neare unto it , by severall centres : any of which i will not touch upon , but shew how it may be done promptly upon one centre only . in which i will say nothing of the ovall forme , which appeares , when one describeth circles with the points of a common compasses , somewhat deep upon a skinne stretched forth hard : which contracting it selfe in some parts of the skinne maketh an ovall forme . but it will more evidently appeare upon a columne or cylinder : if paper be placed upon it , then with a paire of compasses describe as it were a circle upon it , which paper afterwards being extended , will not be circular but ovall-wise : and a paire of compasses may be so accommodated , that it may be done also upon a plaine thus . as let the length of the ovall be h. k , fasten 2 pinnes or nailes neare the end of that line as f. g , and take a threed which is double to the length of g. h , or f. k , then if you take a compasse which may have one foot lower than another , with a spring between his legges : and placing one foot of this compasse in the centre of the ovall , and guiding the threed by the other foot of the compasses , and so carrying it about : the spring will help to describe and draw the ovall forme . but in stead of the compasses it may be done with ones hand only , as in the figure may appeare . problem . lv. of a pu●se difficult to be opened . it is made to shut and open with rings : first at each side there is a strap or string , as ab . and cd , at the end of which are 2 rings , b & d , and the string cd passeth through the ring b , so that it may not come out againe ; or be parted one from another : and so that the ring b , may slide up and downe upon the string cd , then over the purse , there is a piece of leather efgh , which covers the opening of the purse , and there is another piece of leather ae , which passeth through many rings : which hath a slit towards the end i , so great that the string bc may slide into it : now all the cunning or craft is how to make fast or to open the purse , which consists in making the string bc slide through the side at i , therefore bring down b to i , then make the end i passe through the ring b , and also d with his string to passe through the slit i , so shall the purse be fast , and then may the strings be put as before , and it will seem difficult to discover how it was done . now to open the purse , put through the end i through the ring b , and then through the slit i , by which you put through the string dc , by this way the purse will be opened . problem . lvi . whether it is more hard and admirable without compasses to make a perfect circle , or being made to finde out the centre of it ? it is said that upon a time past , two mathematicians met , and they would make tryall of their industry : the one made instantly a perfect circle without compasses , and the other immediately pointed out the centre thereof with the point of a needle ; now which is the chiefest action ? it seems the first , for to draw the most noblest figure upon a plaine table without other help than the hand , and the minde , is full of admiration ; to finde the centre is but to finde out only one point , but to draw a round , there must be almost infinite points , equidistant from the centre or middle ; that in conclusion it is both the circle and the centre together . but contrarily it may seem that to finde the centre is more difficult , for what attention , vivacitie , and subtiltie must there be in the spirit , in the eye , in the hand , which will chuse the true point amongst a thousand other points ? he that makes a circle keeps alwayes the same distance , and is guided by a halfe distance to finish the rest ; but he that must finde the centre , must in the same time take heed to the parts about it , and choose one only point which is equall distant from an infinite of other points which are in the circumference ; which is very difficult . aristotle confirmes this amongst his morals , and seems to explaine the difficultie which is to be found in the middle of vertue ; for it may want a thousand wayes , and be farre separated from the true centre of the end of a right mediocritie of a vertuous action ; for to do well it must touch the middle point which is but one , and there must be a true point which respects the end , and that 's but one only . now to judge which is the most difficult , as before is said , either to draw the round or to finde the centre , the round seems to be harder than to finde the centre , because that in finding of it , it is done at once , and hath an equall distance from the whole ; but , as before , to draw a round there is a visible point imagined , about which the circle is to be drawne . i esteeme that it is as difficult therefore , if not more , to make the circle without a centre , as to finde the middle or centre of that circle . problem . lvii . any one having taken 3 cards , to finde how many points they containe this is to be exercised upon a full pack of cards of 52 , then let one choose any three at pleasure secretly from your sight , and bid him secretly account the points in each card , and will him to take as many cards as will make up 15 to each of the points of his cards , then will him to give you the rest of the cards , for 4 of them being rejected , the rest shew the number of points that his three cards which he took at the first did conteine . as if the 3 cards were 7 , 10 , and 4 ; now 7 wants of 15 , 8. take 8 cards therefore for your first card : the 10 wants of 15 ▪ 5 , take 5 cards for your second card : lastly 4 wants of 15 , 11 , take 11 cards for your third card , & giving him the rest of the cards , there will be 25 ; from which take 4 , there remaines 21 , the number of the three cards taken , viz. 7 , 10 , and 4. whosoever would practise this play with 4 , 5 , 6 , or more cards , and that the whole number of cards be more or lesse than 52 ; and that the terme be 15 , 14 , 12 , &c , this generall rule ensuing may serve : multiply the terme by the number of cards taken at first : to the product adde the number of cards taken , then subtract this summe from the whole number of cards ; the remainder is the number which must be subtracted from the cards , which remaines to make up the game : if there remaine nothing after the subtraction , then the number of cards remaining doth justly shew the number of points which were in the cards chosen . if the subtraction cannot be made , then subtract the number of cards from that number , and the remainder added unto the cards that did remaine , the summe will be the number of points in the cards taken , as if the cards were 7 , 10 , 5 , 8 , and the terme given were 12 ; so the first wants 5 , the second wants 2 , the third wants 7 , and the fourth wants 4 cards , which taken , the party gives you the rest of the cards : then secretly multiply 12 by 4 , makes 48 ; to which adde 4 , the number of cards taken makes 52 , from which 52 should be taken , rest nothing : therefore according to the direction of the remainder of the cards which are 30 , is equall to the points of the foure cards taken , viz. 7 , 10 , 5 , 8. againe , let these five cards be supposed to be taken , 8 , 6 , 10 , 3 , 7 ; their differences to 15 , the termes are 7 , 9 , 5 , 12 , 8 , which number of cards taken , there will remaine but 6 cards : then privately multiply 15 by 5 , makes 75 , to which adde 5 makes 80 , from this take 52 the number of cards , rest 28 , to vvhich add the remainder of cards , make 34. the summe with 8 , 6 , 10 , 3 , 7. problem . lvii . many cards placed in diverse ranks , to finde which of these cards any one hath thought . take 15 cards , and place them in 3 heaps in rank-wise , 5 in a heap : now suppose any one had thought one of these cards in any one of the heaps , it is easie to finde vvhich of the cards it is , and it is done thus ; ask him in vvhich of the heaps it is , vvhich place in the middle of the other tvvo ; then throvv dovvne the cards by 1 and 1 into three severall heaps in rank-vvise , untill all be cast dovvne , then aske him in which of the rankes his card is , which heap place in the middle of the other two heaps alwayes , and this do foure times at least , so in putting the cards altogether , look upon the cards , or let their back be towards you , and throw out the eight card , for that was the card thought upon without faile . problem . lviii . many cards being offered to sundry persons , to finde which of these cards any one thinketh upon . admit there were 4 persons , then take 4 cards , and shew them to the first , bid him think one of them , and put these 4 away , then take 4 other cards , and shew them in like manner to the second person , and bid him think any one of these cards , and so do to the third person , and so the fourth , &c. then take the 4 cards of the first person , and dispose them in 4 rankes , and upon them the 4 cards of the second person , upon them also these of the third person , and lastly , upon them these of the fourth person , then shew unto eaeh of these parties each of these ranks , and aske him if his card be in it which he thought , for infallibly that vvhich the first partie thought upon vvill be in the first rank , and at the bottome , the card of the second person vvill be in the second ranke , the card of the third thought upon will be in the third rank , and the fourth mans card will be in the fourth rank , and so of others , if there be more persons use the same method . this may be practised by other things , ranking them by certaine numbers : allotted to pieces of money , or such like things . problem . lix . how to make an instrument to help hearing , as galileus made to help the sight ? think not that the mathematickes ( which hath furnished us with such admirable helps for seeing ) is wanting for that of hearing , it s well knowne that long trunks or pipes make one heare well farre off , and experience shewes us that in certaine places of the orcades in a hollow vault , that a man speaking but softly at one corner thereof , may be audibly understood at the other end : notwithstanding those which are between the parties cannot heare him speak at all : and it is a generall principle , that pipes do greatly help to strengthen the activitie of naturall causes : we see that 〈◊〉 contracted in a pipe , burnes 4 or 5 foot high , which would scarce heat , being in the open aire : the rupture or violence of water issuing out of a fountaine , shewes us that vvater being contracted into a pipe , causeth a violence in its passage . the glasses of galeileus makes us see how usefull pipes or trunkes are to make the light and species more visible , and proportionable to our eye . it is said that a prince of italy hath a faire hall , in which he can with facility heare distinctly the discourses of those which walk in the adjacent gardens , which is by certaine vessels and pipes that answer from the garden to the hall. vitruvius makes mention also of such vessels and pipes , to strengthen the voice and action of comedians : and in these times amongst many noble personages ▪ the new kinde of trunkes are used to help the hearing , being made of silver , copper , or other resounding materiall ; in funnell-wise putting the widest end to him which speaketh , to the end to contract the voice , that so by the pipe applied to the eare it may be more uniform and lesse in danger to dissipate the voice , and so consequently more fortified . problem . lx. of a fine lamp which goes not out , though one carry it in ones pocket : or being rolled upon the ground will still burne . it must be observed that the vessell in which the oile is put into , have two pinnes on the sides of it , one against another , being included within a circle : this circle ought to have two other pinnes , to enter into another circle of brasse , or other solid matter : lastly , this second circle hath two pinnes , which may hang within some box to containe the whole lamp , in such manner , that there be 6 pinnes in different position : now by the aid of these pegges or pinnes , the lamp that is in the middle will be alwayes well situated according to his centre of gravity , though it be turned any way : though if you endeavour to turne it upside downe , it will lie levell ▪ which is pleasant and admirable to behold to those which know not the cause : and it is facil from his to make a place to rest quiet in , though there be great agitation in the outvvard parts . problem . lxi . any one having thought a card amongst many cards , how artificially to discover it out ? take any number of cards as 10 , 12 , &c. and open some 4 or 5 to the parties sight , and bid him think one of them , but let him note vvhether it be the first , second , third , &c. then vvith promptness learn vvhat number of cards you had in your hands , and take the other part of the cards , and place them on the top of these you hold in your hand ; and having done so , aske him whether his card were the first , second , &c. then before knowing the number of cards that were at the bottome , account backwards untill you come to it : so shall you easily take out the card that he thought upon . problem . lxii . three women ab.c. carried apples to a marke to sell , a had 20 , b 30 ▪ and c 40 , they sold as many for a penny , the one as the other : and brought home one as much money as another , how could this be ? the answer to the probleme is easie ▪ as suppose at the beginning of the market : a ▪ sold her apples at a penny an apple : and sold but 2. which was 2 pence , and so she had 18 left : but b. sold 17. which was 17 pence , and so had 13 left : c. sold 32. which was 32 pence , and so had 8 apples left ▪ then a said she would not sell her apples so cheap , but would sell them for 3 pence the peece , which she did : and so her apples came to 54 pence , and b having left but 13 apples sold them at the same rate , which came to 39 pence : and lastly ▪ c. had but 8 apples , which at the same rate came to 24 pence : these summes of money which each others before received come to 56 pence , and so much each one received ; and so consequently brought home one as much as another . problem . lxiii . of the properties of some numbers . first , any two numbers is just the summe of a number , that have equall distance from the halfe of that number ▪ the one augmenting , and the other diminishing , as 7 and 7 , of 8 and ● , of 9 and 5 , of 10 and 4 , of 11 and 3 , of 12 and 2 , of 13 and ● . as the one is more than the halfe , the other is lesse . secondly , it is difficult to finde two numbers whose summe and product is alike , ( that is ) if the numbers be multiplied one by another , and added together , will be equall , which two numbers are 2 and 2 , for to multiply 2 by 2 makes 4 , and adding 2 unto 2 makes the same : this property is in no other two whole numbers , but in broken numbers there are infinite , whose summe and product will be equall one to another . as clavius shewes upon the 36 pro. of the 9t h book of euclide . thirdly , the numbers 5 and 6 are called circular numbers , because the circle turnes to the point from whence it begins : so these numbers multiplied by themselves , do end alwayes in 5 and 6 , as 5 times 5 makes 25 , that againe by 5 makes 125 , so 6 times 6 makes 36 , and that by 6 makes 216 , &c. fourthly , the number 6 , is the first which arithmeticians call a perfect number , that is , whose parts are equall unto it , so the 6 part of it is 1 , the third part is 2 , the halfe is 3 , which are all his parts : now 1 , 2 , and 3 , is equall to 6. it is wonderfull to conceive that there is so few of them , and how rare these numbers are ▪ 50 of perfect men : for betwixt 1 & 1000000000000 numbers there is but ten , that is ; 6 , 28 , 486. 8128. 120816. 2096128. 33550336. 536854528. 8589869056 , & 137438691328 ▪ with this admirable property , that alternately they end all in 6 and 8 , & the twentieth perfect number is 151115727451553768931328. fiftly , the number 9 amongst other priviledges carries with it an excellent property : for take what number you will , either in grosse or in part , the nines of the whole or in its parts rejected , and taken simply will be the same , as ●7 it makes 3 times 9 , so vvhether the nines be rejected of 27 , or of the summe of 2 and 7 , it is all one , so if the nines vvere taken avvay of 240. it is all one , if the nines vvere taken avvay of 2 , 4 , and 0 ; for there vvould remaine 6 in either ; and so of others . sixtly , 11 being multiplied by 2 , 4 , 5 , 6 , 7 , 8 , or 9 , will end and begin with like numbers ; so 11 multiplied by 5 makes 55 , if multiplied by 8 , it makes 88 , &c. seventhly , the numbers 220 and 284 being unequall , notwithstanding the parts of the one number do alwayes equalize the other number : so the aliquot parts of 220 are 110 , 54 , 44 , 22 , 20 , 11 , 10 , 5 , 4 , 2 , 1 , which together makes 284. the aliquot parts of 284 , are 142 , 71 , 4 , 2 , 1. which together makes 220 , a thing rare and admirable , and difficult to finde in other numbers . i● one be taken from any square number which is odde , the square o● halfe of it being added to the first square , will make a square number . the square of halfe any even number + . 1 being added to that even number makes a square number , and the even number taken from it leaves a square number . if odde numbers be continually added from the unitie successively , there will be made all square numbers , and if cubick numbers be added successively from the unitie , there will be likewise made square numbers . problem . lxiv . of an excellent lamp , which serves or furnisheth it selfe with oile , and burnes a long time . i speak not here of a common lamp which ca●danus writes upon in his book de subtilita●● , for that 's a little vessell in columne-wise , which is full of oile , and because there is but one little hole at the bottome neare the weeke or match ; the oile runnes not , for feare that there be emptinesse above : when the match is kindled it begins to heat the lamp , and rarefying the oile it issueth by this occasion : and so sends his more airie parts above to avoid vacuitie . it is certaine that such a lampe the atheniaus used , which lasted a whole yeare without being touched : which was placed before the statue of minerva , for they might put a certaine quantitie of oile in the lamp cd , and a match to burne without being consumed : such as the naturalists write of , by which the lamp will furnish it selfe , and so continue in burning : and here may be noted that the oile may be poured in , at the top of th● vessell at a little hole , and then made fast againe that the aire get not in . problem . lxv . of the play at keyles or nine pinnes . you will scarce beleeve that with one bowle and at one blow playing freely , one may strike downe all the keyles at once : yet from mathematicall principles it is easie to be demonstrated , that if the hand of him that playes were so well assured by experience , as reason induceth one thereto ; one might at one blow strike downe all the keyles , of at least 7 or 8 , or such a number as one pleaseth . for they are but 9 in all disposed or placed in a perfect square , having three every way . let us suppose then that a good player beginning to play at 1 somewhat low , should so strike it , that it should strike down the keyles 2 and 5 , and these might in their violence strike downe the keyles 3 , 6 , and 9 , and the bowle being in motion may strike down the keyle 4 , and 7 ; which 4 keyle may strike the keyle 8 , & so all the 9 keyles may be striken down at once . problem . lxiv . of spectacles of pleasure . simple spectacles of blew , yellow , red or green colour , are proper to recreate the sight , and will present the objects died in like colour that the glasses are , only those of the greene do somewhat degenerate ; instead of shewing a lively colour it will represent a pale dead colour , and it is because they are not dyed greene enough , or receive not light enough for greene : and colour these images that passe through these glasses unto the bottome of the eye . examination . it is certaine , that not onely glasses dyed green , but all other glasses coloured , yield the app●arances of objects strong or weak in colour according to the quantity of the dye , more or lesse , as one being very yellow , another a pale yellow ; now all colours are not proper to glasses to give colour , hence the defect is not that they want facultie to receive light , or resist the penetration of the beams ; for in the same glasses those which are most dyed , give alwayes the objects more high coloured and obscure , and those which are lesse dyed give them more pale and cleare : and this is daily made manifest by the painting of glasse , which hinders more the penetration of the light than dying doth , where all the matter by fire is forced into the glasse , leaving it in all parts transparent . spectacles of crystall cut with divers angles diamond-wise do make a marvellous multiplication of the appearances , for looking towards a house it becomes as a towne , a towne becomes like a citie , an armed man seems as a whole company caused solely by the diversity of refractions , for as many plaines as there are on the outside of the spectacle , so many times will the object be multiplied in the appearance , because of diverse images cast into the eye . these are pleasurable spectacles for avaricious persons that love gold and silver , for one piece will seeme many , or one heap of money will seeme as a treasury : but all the mischiefe is , he will not have his end in the enjoying of it , for indeavouring to take it , it will appeare but a deceitfull image , or delusion of nothing . here may you note that if the finger be directed by one and the same ray or beam , which pointeth to one and the same object , then at the first you may touch that visible object without being deceived : otherwise you may faile often in touching that which you see . againe , there are spectacles made which do diminish the thing seen very much , and bring it to a faire perspective forme , especially if one look upon a faire garden plat , a greater walk , a stately building , or great court , the industry of an exquisite painter cannot come neare to expresse the lively forme of it as this glasse will represent it ; you will have pleasure to see it really experimented , and the cause of this is , that the glasses of th●se spectacles are hollow and thinner in the middle , than at the edges by which the visuall angle is made lesser : you may observe a further secret in these spectacles , for in placing them upon a window one may see those that passe to and fro in the streets , without being seen of any , for their property is to raise up the objects that it lookes upon . now i would not passe this probleme without saying something of galileus admirable glasse , for the common simple perspective glasses give to aged men but the eyes or sight of young men , but this of galileus gives a man an eagles eye , or an eye that pierceth the heavens : first it discovereth the spottie and shadowed opacous bodies that are found about the sunne , which darknet and diminisheth the splendor of that beautifull and shining luminary : secondly , it shewes the new planets that accompany saturne and jupiter : thirdly , in venus is seen the new , full , and quartill increase ; as in the moon by her separation from the sunne : fourthly , the artificiall structure of this instrument helpeth us to see an innumerable number of stars , which otherwise are obscured , by reason of the naturall weaknesse of our sight , yea the starres in via lactea are seen most apparantly ; where there seem no starres to be , this instrument makes apparantly to be seen , and further delivers them to the eye in their true and lively colour , as they are in the heavens : in which the splendor of some is as the sunne in his most glorious beauty . this glasse hath also a most excellent use in observing the body of the moone in time of eclipses , for it augments it manifold , and most manifestly shewes the true forme of the cloudy substance in the sunne ; and by it is seene when the shadow of the earth begins to eclipse the moon , & when totally she is over shadowed : besides the celestiall uses which are made of this glasse , it hath another noble property ; it farre exceedeth the ordinary perspective glasses , which are used to see things remote upon the earth , for as this glasse reacheth up to the heavens and excelleth them there in his performance , so on the earth it claimeth preheminency , for the objects which are farthest remote , and most obscure , are seen plainer than those which are neere at hand , scorning as it were all small and triviall services , as leaving them to an inferiour help : great use may be made of this glass in discovering of ships , armies , &c. now the apparell or parts of this instrument or glasse , is very meane or simple , which makes it the more admirable ( seeing it performes such great service ) having but a convex glasse thickest in the middle , to unite and amasse the rayes , and mak the object the greater : to the augmenting the visuall angle , as also a pipe or trunk to amasse the species , and hinder the greatness of the light which is about it : ( to see well , the object must be well inlightened , and the eye in obscurity ; ) then there is adjoyned unto it a glasse of a short sight to distinguish the rayes , which the other would make more confused if alone . as for the proportion of those glasses to the trunk , though there be certaine rules to make them , yet it is often by hazard that there is made an excellent one there being so many difficulties in the action , therefore many ought to be tryed , seeing that exact proportion , in geometricall calculation cannot serve for diversity of sights in the observation . problem . lxvii . of the adamant or magnes , and the needles touched therewith . who would beleeve if he saw not with his eyes , that a needle of steel being once touched with the magnes , turnes not once , not a yeare ▪ but as long as the world lasteth ; his end towards the north and south , yea though one remove it , and turne it from his position , it will come againe to his points of north and south . who would have ever thought that a brute stone black and ill formed , touching a ring of iron , should hang it in the aire , and that ring support a second , that to support a third , and so unto 10 , 12 , or more , according to the strength of the magnes ; making as it vvere a chaine without a line , without souldering together , or without any other thing to support them onely ; but a most occult and hidden vertue , yet most evident in this effect , which penetrateth insensibly from the first to the second , from the second to the third , &c. what is there in the world that is more capable to cast a deeper astonishment in our minds than a great massie substance of iron to hang in the aire in the middest of a building without any thing in the world touching it , only but the aire ? as some histories assure us , that by the aid of a magnes or adamant , placed at the roof of one of the turkish synagogues in meca : the sepulchre of that infamous mah●met rests suspended in the aire ; and plinie in his naturall historie writes that the architect or democrates did begin to vault the temple of a●sin●e in alexandria , with store of magnes to produce the like deceit , to hang the sepulchre of that goddesse likewise in the aire . i should passe the bounds of my counterpoise , if i should divulge all the secrets of this stone , and should expose my selfe to the laughter of the world : if i should brag to shew others the cause how this appeareth , than in its owne naturall sympathy , for why is it that a magnes with one end will cast the iron away , & attract it with the other ? from whence commeth it that all the magnes is not proper to give a true touch to the needle , but only in the two poles of the stone : which is known by hanging the stone by a threed in the aire untill it be quiet , or placed upon a peece of cork in a dish of water , or upon some thinne board , for the pole of the stone will then turne towards the poles of the world , and point out the north and south , and so shew by which of these ends the needle is to be touched ? from whence comes it that there is a variation in the needle , and pointeth not out truly the north and south of the world , but only in some place of the earth ? how is it that the needle made with pegges and inclosed within two glasses , sheweth the height of the pole , being elevated as many degrees as the pole is above the horizon ? what 's the cause that fire and garlick takes away the propertie of the magnes ? there are many great hidden mysteries in this stone , which have troubled the heads of the most learned in all ages ; and to this time the world remaines ignorant of declaring the rrue cause thereof . some say , that by help of the magnes persons which are absent may know each others minde , as if one being here at london , and another at prague in germany : if each of them had a needle touched with one magnes , then the vertue is such that in the same time that the needle which is at prague shall move , this that is at london shall also ; provided that the parties have like secret notes or alphabets , and the observation be at a set houre of the day or night ; and when the one party will declare unto the other , then let that party move the needle to these letters which will declare the matter to the other , and the moving of the other parties needle shall open his intention . the invention is subtile , but i doubt whether in the world there can be found so great a stone ▪ or such a magnes which carries with it such vertue : neither is it expedient , for treasons would be then too frequent and open . examination . the experimentall difference of rejection , and attraction proceeds not from the different nature of stones , but from the quality of the iron ; and the vertue of the stone consisteth only , and especially in his poles , which being hanged in the aire , turnes one of his ends alwayes naturally towards the south , and the other towards the north : but if a rod of iron be touched with one of the ends thereof , it hath the like property in turning north and south , as the magnes hath : notwithstanding the end of the iron rod touched , hath a contrary position , to that end of the stone that touched it ; yet the same end will attract it , and the other end reject it : and so contrarily this may easily be experimented upon two needles touched with one or different stones , though they have one and the same position ; for as you come unto them apply one end of the magnes neare unto them , the north of the one will abhorre the north of the other , but the north of the one will alwayes approach to the south of the other : and the same affection is in the stones themselves . for the finding of the poles of the magnes , it may be done by holding a small needle between your fingers softly , and so moving it from part to part over the stone untill it be held perpendicular , for that shall be one of the poles of the stone which you may marke out ; in like manner finde out the other pole : now to finde out which of those poles is north or south , place a needle being touched with one of the poles upon a smooth convex body , ( as the naile of ones finger or such like , ) and marke which way the end of the needle that was touched turneth : if to the south , then the point that touched it was the south-pole , &c. and it is most certain and according to reason and experience : that if it be suspended in aequilibrio in the aire , or supported upon the water , it will turne contrary to the needle that toucheth it ; for then the pole that was marked for the south shall turne to the north , &c. problem . lxviii . of the properties of aeolipiles or bowels to blow the fire . these are concave vessels of brass or copper or other material , which may indure the , fire : having a small hole very narrow , by which it is filled with water , then placing it to the fire , before it be hot there is no effect seen ; but assoone as the heat doth penetrate it , the water begins to rarefie , & issueth forth with a hidious and marvelous force ; it is pleasure to see how it blowes the fire with great noise . novv touching the forme of these vessels , they are not made of one like fashion : some makes them like a bovvle , some like a head painted representing the vvinde , some make them like a peare : as though one vvould put it to rost at the fire , vvhen one vvould have it to blovv , for the taile of it is hollovv , in forme of a funnell , having at the top a very little hole no greater than the head of a pinne . some do accustome to put vvithin the aeolipile a crooked funnell of many foldings , to the end that the vvinde that impetuously rolles ▪ to and fro vvithin , may imitate the noise of thunder . others content themselves vvith a simple funnell placed right upvvard , somevvhat vvider at the top than elsevvhere like a cone , vvhose basis is the mouth of the funnell : and there may be placed a bovvle of iron or brasse , vvhich by the vapours that are cast out vvill cause it to leap up , and dance over the mouth of the aeolipile . lastly , some apply near to the hole smal windmils , or such like , vvhich easily turne by reason of the vapours ; or by help of tvvo or more bovved funnels , a bowle may be made to turne● these aeolipiles are of excellent use for the melting of mettalls and such like . now it is cunning and subtiltie to fill one of these aeolipiles with water at so little a hole , and therefore requires the knowledge of a philosopher to finde it out : and the way is thus . heat the aeolipiles being empty , and the aire which is within it will become extreamely rarefied ; then being thus hot throw it into water , and the aire will begin to be condensed : by which meanes it will occupie lesse roome , therefore the water will immediately enter in at the hole to avoide vacuitie : thus you have some practicall speculation upon the aeolipile . problem . lxix . of the thermometer : or an instrument to measure the degrees of heat and cold in the aire . this instrument is like a cylindricall pipe of glasse , which hath a little ball or bowle at the toppe ▪ the small end of which is placed into a vessell of water below , as by the figure may be seene . then put some coloured liquor into the cylindricall glasse , as blew , red , yellow , green , or such like : such as is not thick . this being done the use may be thus . those that will determine this change by numbers and degrees , may draw a line upon the cylinder of the thermometer ; and divide it into 4 degrees , according to the ancient philosophers , or into 4 degrees according to the physicians , dividing each of these 8 into 8 others : to have in all 64 divisions , & by this vvay they may not only distinguish upon vvhat degree the vvater ascendeth in the morning , at midday , & at any other houre : but also one may knovv hovv much one day is hotter or colder than another : by marking hovv many degrees the vvater ascendeth or descendeth , one may compare the hottest and coldest dayes in a vvhole year together vvith these of another year : againe one may knovv hovv much hotter one roome is than another , by vvhich also one might keep a chamber , a furnace , a stove , &c. alvvayes in an equalitie of heat , by making the vvater of the thermometer rest alvvayes upon one & the same degree : in brief , one may judge in some measure the burning of fevers , and neare unto what extension the aire can be rarefied by the greatest heat . many make use of these glasses to judge of the vveather : for it is observed that if the vvater fall in 3 or 4 hours a degree or thereabout , that raine insueth ; and the vvater vvill stand at that stay , untill the vveather change : marke the water at your going to bed , for if in the morning it hath descended raine followeth , but if it be mounted higher , it argueth faire weather : so in very cold weather , if it fall suddenly , it is snow or some sleekey weather that wiil insue , problem . lxx . of the proportion of humane bodies of statues , of colossus or huge images , and of monstrous giants . pythagoras had reason to say that man is the measure of all things . first , because he is the most perfect amongst all bodily creatures , & according to the maxime of philosophers , that which is most perfect and the first in rank , measureth all the rest . secondly , because in effect the ordinary measure of a foot , the inch , the cubit , the pace , have taken their names and greatnesse from humane bodies . thirdly , because the symmetrie and concordancie of the parts is so admirable , that all workes which are well proportionable , as namely the building of temples , of shippes , of pillars , and such like pieces of architecture , are in some measure fashioned and composed after his proportion . and we know that the arke of noah built by the commandement of god , was in length 300 cubits , in breadth 50 cubits , in height or depth 30 cubits , so that the length containes the breadth 6 times , and 10 times the depth : now a man being measured you will finde him to have the same proportion in length , breadth , and depth . vilalpandus treating of the temple of solomon ( that chieftaine of works ) was modulated all of good architecture , and curiously to be observed in many pieces to keep the same proportion as the body to his parts : so that by the greatnesse of the work and proportionable symmetrie , some dare assure themselves that by knowledge of one onely part of that building , one might know all the measures of that goodly structure . some architects say that the foundation of houses , and basis of columnes , are as the foot ; the top , and roofe as the head ; the rest as the body : those which have beene somewhat more curious , have noted that as in humane bodies , the parts are uniforme , as the nose , the mouth , &c. these which are double are put on one side or other , with a perfect equality in the same architecture . in like manner , some have been yet more curious than solid ; comparing all the ornaments of a corinth to the parts of the face , as the brow , the eyes , the nose , the mouth ; the rounding of pillars , to the vvrithing of haire , the channells of columnes , to the fouldings of vvomens robes , &c. novv building being a vvork of the best artist , there is much reason vvhy man ought to make his imitation from the chiefe vvork of nature ; vvhich is man. hence it is that vitru●ius in his third book , and all the best architectes , treate of the proportion of man ; amongst others albert durens hath made a whole book of the measures of mans body , from the foot to the head , let them read it who wil , they may have a prefect knowledge thereof : but i will content my selfe and it may satisfie some with that which followeth . first , the length of a man well made , which commonly is called height , is equall to the distance from one end of his finger to the other : when the armes are extended as wide as they may be . secondly , if a man have his feet and hands extended or stretched in forme of s. andrews crosse , placing one foot of a paire of compasses upon his navill , one may describe a circle which will passe by the ends of his hands and feet , and drawing lines by the termes of the hands and feet , you have a square within a circle . thirdly , the breadth of man , or the space which is from one side to another ; the breast , the head , and the neck , make the 6 part of all the body taken in length or height . fourthly , the length of the face is equall to the length of the hand , taken from the small of the arme , unto the extremity of the longest finger . fiftly , the thicknesse of the body taken from the belly to the back ; the one or the other is the tenth part of the whole body , or as some will have it , the ninth part , little lesse . sixtly , the height of the brow , the length of the nose , the space between the nose and the chinne , the length of the eares , the greatnesse of the thumbe , are perfectly equall one to the other . what would you say to make an admirable report of the other parts , if i should reckon them in their least ? but in that i desire to be excused , and will rather extract some conclusion upon ▪ that which is delivered . in the first place , knowing the proportion of a man , it is easie to painters , image-makers , &c. perfectly to proportionate their work ; and by the same is made most evident , that which is related of the images and statues of greece , that upon a day diverse workmen having enterprised to make the face of a man , being severed one from another in sundry places , all the parts being made and put together , the face was found in a most lively and true proportion . secondly , it is a thing most cleare , that by the help of proportion , the body of hercules was measured by the knowledge of his foot onely , a lion by his claw , the giant by his thumb , and a man by any part of his body . for so it was that pythagoras having measured the length of hercules foot , by the steps which were left upon the ground , found out all his height : and so it was that phidias having onely the claw of a lion , did figure and draw out all the beast according to his true type or forme , so the exquisite painter timantes , having painted a pygmey or dwarfe , which he measured with a fadome made with the inch of a giant , it was sufficient to know the greatnesse of that giant to be short , we may by like methode come easily to the knowledge of many fine antiquities touching statues , colossus , and monstrous giants , onely supposing one had found but one only part of them , as the head , the hand , the foot or some bone mentioned in ancient histories . of statues , of colossus , or huge images . vitruvius relates in his second book , that the architect dinocrates was desirous to put out to the world some notable thing , went to alexander the great , and proposed unto him a high and speciall piece of work which he had projected : as to figure out the mount athos in forme of a great statue , which should hold in his right hand a towne capable to receive ten thousand men : and in his left hand a vessell to receive all the water that floweth from the mountaine , which with an ingine should cast into the sea. this is a pretty project , said alexander , but because there was not field-roome thereabout to nourish and reteine the citizens of that place , alexander was wise not to entertaine the designe . now let it be required of what greatnesse this statue might have been , the towne in his right hand , and the receiver of water in his left hand if it had been made . for the statue , it could not be higher than the mountaine it selfe , and the mountaine was about a mile in height plumb or perpendicular ; therefore the hand of this statue ought to be the 10th part of his height , which would be 500 foot , and so the breadth of his hand would be 250 foot , the length now multiplyed by the breadth , makes an hundred twenty five thousand square feet , for the quantitie of his hand to make the towne in , to lodge the said 10 thousand men , allowing to each man neere about 12 foot of square ground : now judge the capacitie of the other parts of this collossus by that which is already delivered . secondly , plinie in his 34 book of his natural history , speakes of the famous colossus that was at rhodes , between whose legges a shippe might passe with his sailes open or displayed , the statue being of 70 cubits high : and other histories report that the sarasens having broken it , did load 900 camels with the mettal of it , now what might be the greatnesse and weight of this statue ? for answer , it is usually allowed for a camels burthen 1200 pound weight , therefore all the collosus did weigh 1080000 pound weight , which is ten hundred and fourescore thousand pound vveight . novv according to the former rules , the head being the tenth part of the body , this statues head should be of 7 cubits , that is to say , 10 foot and a halfe , and seeing that the nose , the brovv , and the thumbe , are the third part of the face , his nose vvas 3 foot and a halfe long , and so much also vvas his thumbe in length : novv the thicknesse being alvvayes the third part of the length , it should seem that his thumb was a foot thick at the least . thirdly , the said plinie in the same place reports that nero did cause to come out of france into italy , a brave and bold statue-maker called zenodocus , to erect him a colossus of brasse , which was made of 120 foot in height , which nero caused to be painted in the same height . now would you know the greatnesse of the members of this colossus , the breadth would be 20 foot , his face 12 foote , his thumb and his nose 4 foot , according to the proportion before delivered . thus i have a faire field or subject to extend my selfe upon , but it is upon another occasion that it was undertaken , let us speak therefore a word touching the giants , and then passe away to the matter . of monstrous giants . you will hardly beleeve all that which i say touching this , neither will i beleeve all that which authors say upon this subject : notwithstanding you nor i cannot deny but that long ago there have been men of a most prodigious greatnesse ; for the holy vvritings vvitnesse this themselves in deut , chap. 3. that there vvas a certaine giant called og , of the town of rabath , vvho had a bed of iron , the length thereof vvas 9 cubits , and in breadth 4 cubits . so in the first of kings chap. 17. there is mention made of goliah , vvhose height vvas a palme and 6 cubits , that is more then 9 foot , he was armed from the head to the foot , and his curiat onely with the iron of his lance , weighed five thousand and six hundred shekels , which in our common weight , is more than 233 pound , of 12 ounces to the pound : now it is certaine , that the rest of his armes taking his target , helmet , bracelets , and other armour together , did weigh at the least 5 hundred pound , a thing prodigious ; seeing that the strongest man that now is , can hardly beare 200 pound , yet this giant carries this as a vesture without paine . solinus reporteth in his 5 chap. of his historie , that during the grecians warre after a great overflowing of the rivers , there was found upon the sands the carcase of a man , whose length was 33 cubits , ( that is 49 foot and a halfe ) therefore according to the proportion delivered , his face should be 5 foot in length , a thing prodigious and monstrous . plinie in his 7. book and 16 chap. saith , that in the isle of crete or candie , a mountaine being cloven by an earth-quake , there was a body standing upright , which had 46 cubits of height : some beleeve that it was the body of orion or othus , ( but i think rather it was some ghost or some delusion ) whose hand should have beene 7 foot , and his nose two foot and a half long . but that which plutarch in the l●fe of sertorius reports of , is more strange , who saith , that in timgy a morative towne , where it is thought that the giant antheus was buried , sertorius could not beleeve that which was reported of his prodigious greatnesse , caused his sepulchre to be opened , and found that his body did containe 60 cubits in length , then by proportion he should be 10 cubits or 15 foot in breadth ; 9 foot for the length of his face , 3 foot for his thumb , which is neare the capacitie of the colossus at rhodes . but behold here a fine fable of symphoris campesius , in his book intituled hortus gallicus , who sayes that in the kingdome of sicilie , at the foot of a mountaine neare trepane , in opening the foundation of a house , they found a cave in which was ●aid a giant , which held in stead of a staffe a great post like the mast of a ship : and going to handle it , it mouldered all into ashes , except the bones which remained of an exceeding great measure , that in his head there might be easily placed 5 quarters of corn , and by proportion it should seeme that his length was 200 cubits , or 300 foot : if he had said that he had been 300 cubits in length , then he might have made us beleeve that noahs ark was but great enough for his sepulchre . who can believe that any man ever had 20 cubits , or 30 foot in length for his face , and a nose of 10 foot long ? but it is very certaine that there have been men of very great stature , as the holy scriptures before witnesse , and many authours worthy of beliefe relate : josephus acosta in his first book of the indian history , chap. 19. a late writer , reporteth , that at peru was found the bones of a giant , which was 3 times greater than these of ours are , that is 18 foot , for it is usually attributed to the tallest ordinary man in these our times but 6 foot of length ; and histories are full of the description of other giants of 9 , 10 , and 12 foot of height , and it hath been seen in our times some which have had such heights as these . problem . lxxi . of the game at the palme , at trap , at bowles , paile-maile , and others . the mathematickes often findeth place in sundry games to aid and assist the gamesters , though not unknowne unto them , hence by mathematicall principles , the games at tennis may be assisted , for all the moving in it is by right lines and reflections . from whence comes it , that from the appearances of flat or convex glasses , the production and reflection of the species are explained ; is it not by right lines ? in the same proportion one might sufficiently deliver the motion of a ball or bowle by geometrical lines and angles . and the first maxime is thus : when a bowle toucheth another bowle ▪ or when a trapstick striketh the ball , the moving of the ball is made in a right line , which is drawne from the centre of the bowle by the point of contingencie . secondly , in all kinde of such motion ; when a ball or bowle rebounds , be it either against wood , a wall , upon a drumme , a pavement , or upon a racket ; the incident angle is alwayes equall to the angle of reflection . now following these maximes , it is easie to canclude , first , in what part of the wood or wall , one may make the bowle or ball go to reflect or rebound , to such a place as one would . secondly , how one may cast a bowle upon another , in such sort that the first or the second shall go and meet with the third , keeping the reflection or angle of incidence equal . thirly , how one may touch a bowle to send it to what part one pleaseth : such and many other practices may be done . at the exercises at keyls there must be taken heed that the motion slack or diminish by little and little , and may be noted that the maximes of reflections cannot be exactly observed by locall motion , as in the beames of light and of other quallities , whereof it is necessary to supply it by industry or by strength , otherwise one may be frustrated in that respect . problem . lxxii . of the game of square formes . nvmbers have an admirable secrecie , diversly applied , as before in part is shewed , and here i will say something by way of transmutation of numbers . it 's answered thus , in the first forme the men were as the figure a , then each of these 4 souldiers placed themselves at each gate , and removing one man from each angle to each gate , then would they be also 9 in each side according to the figure b. lastly , these 4 souldiers at the gates take away each one his cumrade , and placing two of these men which are at each gate to each angle , there will be still 9 for each side of the square , according to the figure c. in like manner if there were 12 men , how might they be placed about a square that the first side shall have 3 every way , then disordered , so that they might be 4 every way ; and lastly , being transported might make 5 every way ? & this is according to the figures , f. g.h problem . lxxiii . how to make the string of a viole sensibly shake , without any one touching it ? this is a miracle in musick , yet easie to be experimented . take a viole or other instrument , and choose two strings , so that there be one between them ; make these two strings , agree in one and the same tune : then move the viole-bowe upon the greater string , and you shall see a wonder : for in the same time that that shakes which you play upon , the other will likewise sensibly shake without any one touching it ; and it is more admirable that the string which is between them will not shake at all : and if you put the first string to another tune or note , and loosing the pin of the string , or stopping it with your finger in any fret , the other string will not shake : and the same will happen if you take two violes , and strike upon a string of the one , the string of the other will sensibly shake . now it may be demanded , how comes this shaking , is it in the occult sympathie , or is it in the strings being wound up to like notes or tunes , that so easily the other may receive the impression of the aire , which is agitated or moved by the shaking or the trembling of the other ? & whence is it that the viole-bowe moved upon the first string , doth instantly in the same time move the third string , and not the second ? if the cause be not either in the first or second ? i leave to others to descant on . examination . in this examination we have something else to imagine , than the bare sympathie of the cords one to another : for first there ought to be considered the different effect that it produceth by extention upon one and the same cord in capacitie : then what might be produced upon different cords of length and bigness to make them accord in a unisone or octavo , or some consort intermediate : this being naturally examined , it will be facill to lay open a way to the knowledge of the true and immediate cause of this noble and admirable phaenomeny . now this will sensibly appeare when the cords are of equall length and greatnesse , and set to an unisone ; but when the cords differ from their equalitie , it will be lesse sensible : hence in one and the same instrument , cords at a unisone shall excite or shake more than that which is at an octavo , and more than those which are of an intermediate proportionall consort : as for the other consorts they are not exempted , though the effect be not so sensible , yet more in one than in another : and the experiment will seem more admirable in taking 2 lutes , viols , &c. & in setting them to one tune : for then in touching the cord of the one , it will give a sensible motion to the cord of the other : and not onely so but also a harmony . problem . lxxiiii . of a vessell which containes three severall kindes of liquor , all put in at one bung-hole , and drawn out at one tap severally without mixture . the vessell is thus made , it must be divided into three cells for to conteine the three liquors , which admit to be sack , claret , and white-wine : now in the bung-hole there is an engine with three pipes , each extending to his proper cell , into which there is put a broach or funnell pierced in three places , in such sort , that placing one of the holes right against the pipe which answereth unto him , the other tvvo pipes are stopped ; then vvhen it is full , turne the funnel , and then the former hole vvill be stopped , and another open , to cast in other vvine vvithout mixing it vvith the other . novv to dravv out also vvithout mixture , at the bottome of the vessell there must be placed a pipe or broach , vvhich may have three pipes ; and a cock piersed vvith three holes so artificially done , that turning the cock , the whole vvhich ansvvereth to such of the pipes that is placed at the bottom , may issue forth such vvine as belongeth to that pipe , & turning the cock to another pipe , the former hole vvil be stopped ; and so there will issue forth another kinde of wine without any mixtures ; but the cocke may be so ordered that there may come out by it two wines together , or all three kindes at once : but it seems best when that in one vessell and at one cocke , a man may draw severall kindes of wine , and which he pleaseth to drink . problem . lxxv . of burning-glasses . in this insuing discourse i will shew the invention of prom●theus , how to steale fire from heaven , and bring it down to the earth ; this is done by a little round glasse , or made of steele , by which one may light a candle , and make it flame , kindle fire-brands to wake them burne , melt lead , ●inne , gold , and silver , in a little time ▪ with as great ease as though it had been put into a cruzet over a great fire . but this is nothing to the burning of those glasses which are hollow , namely those which are of steele well polished , according to a par●bolicall or ovall section . a sphericall glasse , or that which is according to the segment of a sphere , burnes very effectually about the fourth part of the diameter ; notwithstanding the parabolie and ecliptick sections have a great effect : by which glasses there are also diverse figures represented forth to the eye . the cause of this burning is the uniting of the beames of the sunne , which heat mightily in the point of concourse or inflammation , which is either by transmissi●n or reflection ▪ now it is pleasant to behold when one breatheth in the point of concourse , or throweth small dust there , or sprinkles vapours of hot water in that place ; by which the pyramidall point , or point of inflammation is knowne . now some authors promise to make glasses which shall burne a great distance off , but yet not seen vulgarly produced , of which if they were made , the parabolie makes the greatest eff●ct , and is g●nerally held to be the invention of archimedes or pro●●us . maginus in the 5 chap. of his treatise of sphericall glasses , shewes how one may serve himselfe with a concave glasse , to light fire in the shadow , or neare such a place where the sunne shines not , which is by help of a flat glasse , by which may be made a percussion of the beames of the sun into the concave glasse , adding unto it that it serves to good use to put fi●e to a mine , provided that the combustible matter be well applyed before the concave glasse ; in which he saies true : but because all the effect of the practice depends upon the placing of the glasse and the powder which he speaks not of : i will deliver here a rule more generall . how one may place a burning-glasse with his combust●ble matter in such sort , that at a convenient houre of the day , the sun shining , it shall take fire and burne : now it is certaine that the point of inflammation or burning , is changed as the sun changeth place , and no more nor lesse , than the shadow turnes about the style of a dyall ; therefore have regard to the suns motion , and ●is height and place : a bowle of crystall in the same place that the top of the style is , and the powder or other combustible matter under the meridian , or houre of 12 , 1 , 2 , 3 , &c. or any other houre , and under the suns arch for that day : now the sunne comming to the houre of 12 , to ● , 2 , ● , &c. the sunne casting his beames through the crystall bowle , will fire the materiall or combustible thing , which meets in the point of burning : the like may be observed of other burning-glasses . examination . it is certaine in the first part of this probleme that conicall , ●oncave and sphericall glasses , of what matter soever , being placed to receive the beames of the sun will excite heat , and that heat is so much the greater , by how much it is neere the point of conc●rse or inflamatio● . but that archimedes or proclus d●d fire or burne shipps with such glasses , the ancient histories are silent , yea the selves say nothing : besides the great difficultie that doth oppose it in remotenesse , and the matter that the effect is to work upon : now by a common glasse we fire things neare at hand , from which it seems very facil to such which are lesse read , to do it at a farre greater distance , and so by re●ation some deliver to the world by supposition that which never was done in action : this we say the rather , not to take away the most excellent and admirable effects which are in burning-glasses , but to shew the variety of antiquity , and truth of history : and as touching to burne at a great distance , as is said of some , it is absolutely impossible ; and that the parabolicall and ovall glasses were of archimedes and ●roclus invention is much uncertaine : for besides the construction of such glasses , they are more difficult than the obtuse concave ones are ; and further , they cast not a great heat but neere at hand ; for if it be cast farre off , the effect is little , and the heat weake , or otherwise such glasses must be greatly extended to contract many beames to amasse a sufficient quantity of beames in parabolicall and conicall glasses , the point of inflammation ought to concur in a point , which is very difficult to be done in a due proportion . moreover if the place be farre remote , as is supposed before , such a glasse cannot be used but at a great inclination of the sunne ▪ by which the eff●ct of ●urning is d●min●shed , by reason of the weaknesse of the sunne-beames . and here may be noted in the last part of this probleme , that by r●ason of obstacles if one plaine glasse be not sufficient , a second glasse may be applyed to help it : that so if by one simple reflection it cannot be done , yet by a double reflection the sun-beames may be ●ast into the said caverne or mine , and though the reflected beams in this case be weak ▪ yet upon a 〈◊〉 c●mbustible matter it will not faile to do the effect . problem . lxxvi . containing m●ny ple●sant questions by way of arithmetick● . j will not in●ert i● this probleme that which is drawne from the ●reek epigrams , but proposing the question immediately will give the an●wer also , without ●●aying to shew the manner how they are answered ; in this j will 〈◊〉 be tied to the ●reek tearms , w●●ch j account no● proper to this place , nei●●er to my purpose : ●et t●o●e ●ead that will di●phanta s●●●●biliu● upon eu●li●● and others , and they may be satisf●ed of the 〈…〉 the mule. jt 〈◊〉 ●hat ●he mule and the asse upon a day 〈◊〉 a voyage each of them carried a barrell full of wine : now the las●e asse f●lt her selfe over-loaden , complained and bowed under her burthen ; which th● mule seeing said unto her being angry , ( for it was in the time when beasts spake ) thou great asse , wherefore complainest thou ? if i had but onely one measure of that which thou carriest , i should be loaden twice as much as thou art , and if j should give a measure of my loading to thee , yet my burthen would be as much as thine . now how many measures did each of them carry ? answer , the mule did carry 7 measures , and the asse 5 measures : for if the mule had one of the measures of the asses loading , then the mule would have 8 measures , which is double to 4 , and giving one to the asse , each of them would have equall burthens : to wit , 6 measures apiece . of the number of souldiers that fought before old troy. homer being asked by he●iodus how many grecian souldiers came against troy ? who answered him thus ; the grecians , said homer , made 7 fires , or had 7 kitchins , and before every fire , or in every kitchin there were 50 broaches turning to rost a great quantitie of flesh , and each broach had meat enough to satisfie 900 men : now judge how many men there might be . answer , 315000. that is , three hundred and fifteen thousand men , which is cleare by multiplying 7 by 50 , and the product by 900 makes the said 315000. of the number of crownes that two men had . john and peter had certaine number of crowns : john said to peter , if you give me 10 of your crownes , i shall have three times as much as you have : but peter said to j●hn , if you give me 10 of your crownes i shall have 5 times as much as you have : how much had each of them ? answere , john had 15 crownes and 5 sevenths of a crowne , and peter had 18 crownes , and 4 sevenths of a crowne . for if you adde 10 of peters crownes to those of johns , then should john have 25 crownes and 5 sevenths of a crowne , which is triple to that of peters , viz. 8 ▪ and 4 sevenths : and john giving 10 to peter , peter should have then 28 crownes , and 4 sevenths of a crowne , which is quintupla , or 5 times as much as john had left , viz. 5 crownes and 5 sevenths . in like manner two gamesters playing together , a and b ▪ after play a said to b , give me 2 crownes of thy money , and i shall have twice as much as thou hast : and b said to a , give me 2 crownes of thy money , and i shall have 4 times as much as thou hast : now how much had each ? answer , a had 3 and 5 seventhes , and b had 4 and 6 seventhes . about the houre of the day . some one asked a mathemacian what a clocke it was ; who answered that the rest of the day is foure thirds of that which is past : now judge what a clock it is . answer , if the day were according to the jewes and ancient romanes , which ma●e it alwayes to be 12 houres , it was then the ● houre , and one seventh of an hou●e , so there remained of the whole day 6 , that is , 6 houres , and 6 sevenths of an hour . now if you take the 1 / ● of 5 ● / 7 it is ●2 / 7 or ● and ● 7 , which multipled by 4 makes 6 and 6 / 7 , which is the remainder of the day , as before : but if the day had been 24 houres , then the houre had been 10 of the clock ▪ and two seventhes of an houre , which is found ▪ out by dividing 12 , or 24 by ● . there might have been added many curious propositions in this kinde , but they vvould be too difficult for the most part of people ▪ therefore i have omi●ted them ▪ of pythagoras his schollers . pythagoras being asked what number of schollers he had , ansvvered , that halfe of them studied mathematickes , the fourth part physick , the seventh part rethorick , and besides he had 3 vvomen : novv judge you saith he , hovv many schollers i have . ansvver , he had in all 28 , the halfe of vvhich is 14 , the quarter of which is 7 , and the seventh part of which is which 14 , 7 , and 4 , makes 25 , and the other 3 to make up the 28 , were the 3 women . of the number of apples given amongst the graces and the muses . the three graces carrying apples upon a day , the one as many as the other , met with the 9 muses , who asked of them some of their apples ; so each of the graces gave to each of the muses alike , and the distribution being made , they found that the graces & the muses had one as many as the other : the question is how many apples each grace had , and how many they gave to each muse ? ●o ansvver the qeustion , joyne the number of graces and muses together vvhich makes 12 , and so many apples had each grace : novv may you take the double , triple , &c. of 12 that is 24 , 36 , &c. conditionally , that if each grace had but 12 , then may there be allotted to each muse but one onely ; if 24 , then to each 2 apples , if ●6 , then to each muse 3 apples , and so the distribution being made , they have a like number , that is one as many as the other . of the testament or last will of a dying father . a dying father left a thousand crovvnes amongst his tvvo children ; the one being legitimate , and the other a bastard , conditionally that the fifth part which his legittimate sonne should have , should exceed by 10 , the fourth part of that which the bastard should have : what was each 〈◊〉 part ? answer , the legitimate sonne had 577 crownes and 7 / ● , and the bastard 42● crownes and 2 / 9 now the fifth part of 577 and 7 ninthes is 1●5 , and 5 / 9 , and the fourth part of 422 and ● is 105 and ● which is lesse then ●15 ● by 10 , according to the will of the testator . of the cups of croesus . croesus gave to the temple of the ●ods six cups of gold ▪ which weighed together ●00 drammes , but each cup was heavier one than another by one dram : how much did each of them therefore weigh ? answer , the first weighed 102 drammes and a halfe ; the second 101 drammes and a halfe , the third 100 drammes and ● , the fourth 99 a & halfe , the fifth 98 & a halfe ; and the sixt cup weighed 97 drammes and a halfe ▪ which together makes 600 drams as before . of cupids apples . cvpid complained to his mother that the muses had taken away his apples , clio , said he , took from me the fifth part , euterp the twelfth part , thalia the eighth part , m●lp●meno the twentieth part , erates the seventh part ▪ terpomene the fourth part , polyhymnia took away 30 , vrania 220 , and calliope 300. so there vvere left me but 5 appls , hovv many had he in all at the first ? i ansvver 3●60 . there are an infinite of such like questions amongst the greek epigrams : but it would be unpleasant to expresse them all : i will onely adde one more , and shew a generall rule for all the rest . of a mans age. a man vvas said to passe the sixth part of his life in childe-hood , the fourth part in his youth , the ●hird part in manhood , and 18 yeares besides in old age : what might his age be ? the ansvver is , 72 yeares : vvhich and all others is thus resolved : multiply 1 / ● ▪ ¼ and ⅓ ▪ together , that is , 6 by 4 makes 24 , and that againe by 3 makes 72 , then take the third part of 72 , vvhich is 24 , the fourth part of it , vvhich is 18 , and the sixth part of it vvhich is 12 , these added together make 54 , vvhich taken from 72 , rests 18 this divided by 18 ( spoken in the question ) gives 1 , which multiplied by the summe of the parts , viz. 72 , makes 72 , the ansvver as before . of the lion of bronze placed upon a fountaine with this epigramme . ovt of my right eye if i let vvater passe , i can fill the cisterne in 2 dayes : if i let it passe out of the left eye , it vvill be filled in 3 dayes : if it passe out of my feet , the cistern vvill be 4 dayes a●filling ; but if i let the vvater passe out of my mouth , i can fill the cistern then in 6 houres : in vvhat time should i fill it , if i poure forth the vvater at all the passages at once ? the greeks ( the greatest talkers in the vvorld ) variously apply this question to divers statues , and pipes of fountaines : and the solution is by the rule of ● , by a generall rule , or by ●lgebra . they have also in their anthologie many other questions , but because they are more proper to exercise , than to recreate the spirit , i passe them over ( as before ) with silence . problem . lxxvii . divers excellent and admirable experiments upon glasses . there is nothing in the world so beautifull as light : and nothing more recreative to the sight , than glasses vvhich reflect : therefore i vvill novv produce some experiments upon them , not that vvill dive into their depth ( that vvere to lay open a mysterious thing ) but that vvhich may delight and recreate the spirits : let us suppose therefore these principles , upon which is built the demonstration of the appar●nces which are made ●n all sort of glasses . first , that the rayes or beames , vvhich reflect upon a glasse , make the angle of incident equall to the angle of reflection , by the first theo. of the catoptick of euc. secondly , that in all plain glasses , the images are seen in the perpendicular line to the glasse , as far within the glass as the object is without it . thirdly , in concave , or convex glasses , the images are seen in the right line which passeth from the object and through the centre in the glasse . theo. 17. and 18. and here you are to understand , that there is not meant only those which are simple glasses or glasses of steele , but all other bodies , which may represent the visible image of things by reason of their reflection , as water , marble , mettal , or such like . now take a glasse in your hand and make experiment upon that which followeth . experiment upon flat and plaine glasses . first , a man cannot see any thing in these glasses , if he be not directly and in a perpendicular line before it , neither can he see an object in these glasses , if it be not in such a place , that makes the angle of incidence equall to the angle of reflexion : therefore when a glasse stands upright , that is , perpendicular to the horizon , you cannot see that which is above , except the glasse be placed down flat : and to see that on the right hand , you must be on the left hand , &c. secondly , an image cannot be seen in a glass if it be not raised above the surface of it ; or place a glasse upon a wall , you shall see nothing which is upon the plaine of the wall , and place it upon a table or horizontal plaine , you shall see nothing of that which is upon the table . thirdly , in a plaine glasse all that is seene appeares or seemes to sink behinde the glasse , as much as the image is before the glasse , as before is said . fourthly , ( as in water ) a glasse lying downe flat , or horizontall , towers , trees , men , or any height doth appeare , inversed or upside downe ; and a glasse placed upright , the right hand of the jmage seems to be the left , and the left seems to be the right . fifthly , will you see in a chamber that which is done in the street , without being seen ▪ then a glasse must be disposed , that the line upon which the jmages come on the glasse , make the angle of incidence equall to that angle of reflexion . seventhly , present a candle upon a plaine glasse , and look flaunting upon it , so that the candle and the glasse be neere in a right line , you shall see 3 , 4 , 5 , &c. images , from one and the same candle . eightly , take tvvo plaine glasses , and hold them one against the other , you shall alternately see them oftentimes one vvithin the other , yea vvithin themselves , againe and againe . ninthly , if you hold a plaine glasse behinde your head , and another before your face , you may see the h●nder part of your head , in that glasse vvhich you hold before your face . tenthly , you may have a fine experiment if you place tvvo glasses together , that they make an acute angle , and so the lesser the angle is , the more apparances you shall see , the one direct , the other inversed , the one approaching , and the other retiring . eleventhly , it is a vvonder & astonishment to some , to see within a glasse an image vvithout knovving from vvhence it came , and it may be done many vvayes : as place a glass higher than the eye of the beholder , and right against it is some image ; so it resteth not upon the beholder , but doth cast the image upvvards . then place another object , so that it reflect , or cast the image downeward to the eye of the spectator ▪ without perceiving it being hid behinde something , for then the glasse will represent a quite contrary thing , either that which is before the glasse , or that which is about it , to wit , the other hidden object . twelfthly , if there be ingraved behinde the backside of a glasse , or drawne any image upon it , it will appeare before as an image , without any appearance : o● portraicture to be perceived . examination . this 12 article of ingraving an image behinde the glasse , will be of no great consequence ▪ because the lineaments will seem so obscure , but if there were painted some image , and then that covered according to the usuall covering of glasses behinde , and so made up like an ordinary looking-glasse having an image in the middle , in this respect it would be sufficiently pleasant : and that which would admire the ignorant , and able to exercise the most subtillest , and that principally if the glasse be in an obscure place , and the light which is given to it be somewhat farre off . place a glasse neare the floor of a chamber , & make a hole through the place under the glasse , so that those which are below may not perceive it , and dispose a bright image under the hole so that it may cast his species upon the glasse , and it will cause admiration to those which are below that know not the cause ; the same may be done by placing the image in a chamber adjoyning , and so make it to be seen upon the side of the wall. 14 in these channel-images which shew one side a deaths head , & another side a faire face : and right before some other thing : it is a thing evident , that setting a plaine glasse sidewise to this image you shall see it in a contrary thing , then that which was presented before sidewise . 15 lastly , it is a fine secret to present unto a plaine glasse writing with such industry , that one may read it in the glasse , and yet out of the glasse there is nothing to be known , which will thus happen , if the writing be writ backward : but that which is more strange , to shew a kinde of writing to a plaine glasse , it shall appear another kinde of writing both against sense and forme , as if there were presented to the glasse wel it would shew it met ; if it were written thus miv , and presented to the glasse , it would appeare thus vim ; for in the first , if the glasse ly flat , then the things are inversed that are perpendicular to the glass , if the glass and the object be upright , then that on the right hand , is turned to the left , as in the latter . and here i cease to speak further of these plaine glasses , either of the admirable multiplications , or appearances , which is made in a great number of them ; for to content the sight in this particular , one must have recourse to the cabinets of great personages who inrich themselves with most beautifull ones . experiments upon gibbous , or convex sphericall glasses . if they be in the forme of a bowle , or part of a great globe of glasse , there is singular contentment to contemplate on them . first , because they present the objects lesse and more gracious , and by hovv much more the images are separated from the glasse , by so much the more they diminish in magnitude . secondly , they that shew the images plaiting , or foulding , which is very pleasant , especially when the glasse is placed downe , and behold in it some blanching , feeling , &c. the upper part of a gallerie , the porch of a hall , &c. for they will be represented as a great vessel having more belly in the middle then at the two ends , and posts , and joists of timber will seeme as circles . thirdly , that which ravisheth the spirits , by the eye , and which shames the best perspective painting that a painter can make , is the beautifull contraction of the images , that appeare within the sphericity of these small glasses : for present the glasse to the lower end of a gallarie , or at the corner of a great court full of people , or towards a great street , church , fortification , an army of men , to a whole cittie ; all the faire architecture , and appearances will be seene contracted within the circuit of the glasse with such varietie of colours , and distinctions in the lesser parts , that i know not in the world what is more agreeable to the sight , and pleasant to behold , in which you will not have an exact proportion , but it will be variable , according to the distance of the object from the glasse . exptriments upon hollow , or concave sphericall glasses . i have heretofore spoken how they may burne , being made of glasse , or metall , it remaines now that i deliver some pleasant uses of them , which they represent unto our sight , and so much the more notable it will be , by how much the greater the glasse is , and the globe from whence it is extracted for it must in proportion as a segment of some be made circle or orbe . examination . in this we may observe that a section of 2.3 . or 4. inches in diameter , may be segments of spheres of 2.3 . or 4. foot ● nay of so many fadome , for it is certaine that amongst those which comprehend a great portion of a lesser sphere , and those which comprehend a little segment of a great spheere , whether they be equall or not in section , there will happen an evident difference in one and the same experiment , in the number , situation , quantitie , and figure of the images of one or many different objects , and in burning there is a great difference . maginus , in a little tractate that he had upon these glasses , witnesseth of himselfe that he hath caused many to be polished for sundry great lords of italy , and germanie , which were segments of globes of 2.3 . and 4. foot diameter ; and i wish you had some such like to see the experiments of that which followeth ; it is not difficult to have such made , or bought here in town , the contentment herein would beare with the cost . examination . touching maginus he hath nothing ayded us to the knowledge of the truth by his extract out of vitellius , but left it : expecting it from others , rather than to be plunged in the search of it himselfe , affecting rather the forging of the matter , and composition of the glasses , than geometrically to establish their effects . first therefore in concave glasses , the images are seene sometimes upon the surface of the glasses , sometimes as though they were within it and behinde it , deeply sunk into it , sometimes they are seene before , and without the glasse , sometimes between the object and the glasse ; sometimes in the place of the eye , sometimes farther from the glasse then the object is : which comes to passe by reason of the divers concourse of the beames , and change of the place of the images in the line of reflection . examination . the relation of these appearances passe current amongst most men , but because the curious may not receive prejudice in their experiments , something ought to be said thereof to give it a more lively touch : in the true causes of these appearances , in the first place it is impossible that the image can be upon the surface of the glasse , and it is a principall point to declare truly in which place the image is seen in the glasse those that are more learned in opticall knowledge affirme the contrary , and nature it selfe gives it a certaine place according to its position being alwayes seen in the line of reflection which alhazen , vitellius , and others full of grea● knowledge , have confirmed by their writings : but in their particular they were too much occupied by the authority of the ancients who were not s●fficiently ci●cumspect in experience upon which the principles of this sub●ect ought to be built , an● searched not fully into the true cause of these appearances , seeing they leave unto posterities many 〈◊〉 in their writings , ●nd those that followed them for the most part fell into the like errors . as for the jmages to bid● in the eye ▪ it cannot be but is imp●rtinent and absurd ; but it followeth that , by how much neerer the ob●ect appro●cheth to the glasse , by so much the more the appearances seem to come to the eye : and if the eye be without the point of concourse , and the object also ; as long as the object approacheth thereto , the representation of the image cometh neere the eye , but passing the point of concourse it goes back againe : these appearances thus approaching do not a little astonish those which are ignorant of the cause : they are inversed , if the eye be without the point of concourse untill the object be within , but contrarily if the eye be between the point of concourse and the glasse , then the jmages are direct : and if the eye or the object be in the point of concourse , the glasse will be enlightened and the jmages confused , and if there were but a spark of fire in the said point of concourse , all the glasse would seeme a burning fire-brand , and we dare say it would occurre without chance , and in the night be the most certaine and subtilest light that can be , if a candle were placed there . and whosoever shall enter into the search of the truth of new experiments in this subject without doubt he will confirme what we here speak of : & will finde new lights with a conveniable position to the glasse , he will have reflection of quantities , of truth , and fine secrets in nature , yet not known , which he may easily comprehend if he have but an indifferent sight , and may assure himselfe that the images cannot exceed the fight , nor trouble it , a thing too much absurd to nature . and it is an absolute verity in this science , that the eye being once placed in the line of reflection of any object , and moved in the same line : the obect is seene in one and the same place immutable ; or if the image and the eye move in their owne lines , the representation in the glasse seemes to invest it selfe continually with a different figure . now the image comming thus to the eye , those which know not the secret , draw their sword when they see an image thus to issue out of the glasse , or a pistoll which some one holds behinde : and some glasses will shew a sword wholly drawne out , sepa●ated from the glasse , as though it were in the aire : and it is daily exercised , that a man may touch the image of his hand or his face out of the glasse , which comes out the farther , by how much the glasse is great and the centre remote . examination . now that a pistoll being presented to a glasse behinde a man , should come out of the glasse , and make him afraid that stands before , seeming to shoot at him , this cannot be : for no object whatsoever presented to a concave glasse , if it be not neerer to the g●asse then the eye is it comes not out to the sight of the party ; therefore he needs not feare that which is said to be behinde his back , and comes out of the glasse ; for if it doth come out , it must then necessarily be before his face , so in a concave glasse whose centre is farre remote of a sword , stick , or such like be presented to the glasse , it shall totally be seen to come forth of the glasse and all the hand that holds it . and here generally note that if an image be seen to issue out of the glasse to come towards the face of any one that stands by , the object shall be likewise seen to thrust towards that face in the glass and may easily be knowne to all the standers by : so many persons standing before a glasse , if one of the company take a sword , and would make it issue forth towards any o●her that stands there : let him chuse his image in the gl●sse and carry the sword right towards it and the effect will follow . in like manner ones hand being presented to the glosse as it is thrust towards the centre , s● the representation of it comes towards it , and so the hands will seeme to be united , or to touch one another . from which may be concluded , if such a glasse be placed at the seeling or planching of a hall , so that the face be horizontall and look downward ; one may see under it as it were a man hanging by the feet , and if there were many placed so , one could not enter into that place without great feare or scaring : for one should see many men in the aire as if they were hanging by the feet . examination . touching a glasse tyed at a seeling or planching , that one may see a man hang by the feet in the aire , and so many glasses , many men may be seen : without caution this is very absurd for if the glasse or glasses be not so great that the centre of the sphere upon which it was made , extend not neere to the head of him that is under it , it will not pleasantly appeare , and though the glasse should be of that capacity that the centre did extend so farre , yet will not the images be seene to them which are from the glasse but on●y to those which are under it , or neere unto it : and to them it will not ably appeare , and it would be most admirable to have a gallerie vaulted over with such glasses which would wonderfully astonish any one that enters into it : for a●l the things in the gallery would be seen to hang in the aire , and you could not walk without incountering airie apparitions . secondly , in flat or plaine glasses the image is seen equall to his object , and to represent a whole man , there ought to be a glasse as great as the image is : in convex glasses the images are seen alwayes lesse , in concave glasses they may be seen greater or lesser , but not truly proportionable , by reason the diverse reflexions which contracts or inlargeth the species : when the eye is between the centre and the surface of the glasse ; the image appeares sometimes very great and deformed , and those which have but the appearance of the beginning of a beard on their chinne , may cheare up themselves to see they have a great beard ; those that seeme to be faire will thrust away the glasse with despight , because it will transforme their beauty : those that put their hand to the glasse vvill seeme to have the hand of a giant , and if one puts his finger to the glasse it vvill be seen as a great pyramide of flesh , inversed against his finger . thirdly , it is a thing admirable that the eye being approached to the point of concourse of the glasse , there vvill be seen nothing but an intermixture or confusion : but retiring back a little from that point , ( because the rayes do there meet ▪ ) he shall see his image inversed , having his head belovv and his feet above . fourthly , the divers appearances caused by the motion of objects , either retiring or approaching : whether they turne to the right hand or to the left hand , whether the glasse be hung against a wall , or whether it be placed upon a pavement , as also what may be represented by the mutuall aspect of concave glasses with plaine and convex glasses but i will with silence passe them over , only say something of two rare experiments more as followeth . the first is to represent by help of the sun , such letters as one would upon the front of a house : so that one may read them : maginus doth deliver the way thus . write the letters , saith he , sufficiently bigge , but inversed upon the surface of the glasse , with some kinde of colour , or these letters may be written with wax , ( the easier to be taken out againe : ) for then placing the glasse to the sunne , the letters which are written there will be reverberated or reflected upon the wall : hence it was perhaps that pythagoras did promise with this invention to write upon the moone . in the second place , how a man may sundry wayes help himselfe with such a glasse , with a lighted torch or candle , placed in the point of concourse or inflammation , which is neare the fourth part of the diameter : for by this meanes the light of the candle will be reverberated into the glasse , and vvill be cast back againe very farre by parrallel lines , making so great a light that one may clearly see that vvhich is done farre off , yea in the camp of an enemie : and those which shall see the glasse a farre off , will think they see a silver basin inlightened , or a fire more resplendent then the torch . it is this way that there are made certaine lanthorns which dazell the eyes of those which come against them ; yet it serves singular well to enlighten those which carry them , accommodating a candle with a little hollow glasse , so that it may successively be applyed to the point of inflammation . in like manner by this reflected light , one may reade farre off , provided that the letters be indifferent great , as an epitaph placed high , or in a place obscure ; or the letter of a friend which dares not approach without perill or suspicion . examination . this will be scarce sensible upon a wall remote from the glasse , and but indifferently seen upon a wall which is neare the glasse , and withall it must be in obscuritie or shadowed , or else it will not be seen . to cast light in the night to a place remote , with a candle placed in the point of concourse or inflammation , is one of the most notablest properties which can be shewne in a concave glasse : for if in the point of inflammation of a parabolicall section , a candle be placed , the light will be reflected by parallel lines , as a columne or cylinder ; but in the sphericall section it is defective in part , the beames being not united in one point , but somewhat scattering : notwithstanding it casteth a very great beautifull light . lastly , those which feare to hurt their sight by the approach of lampes or candles , may by this artifice place at some corher of a chamber , a lamp with a hollow glasse behinde it , which will commodiously reflect the light upon a table , or to a place assigned : so that the glasse be somewhat raised to make the light to streeke upon the table with sharp angles , as the sunne doth when it is but a little elevated above the horizon , for this light shall exceed the light of many candles placed in the roome , and be more pleasant to the sight of him that useth it . of other glasses of pleasure . first , the columnary and pyramidall glasses that are contained under right lines , do represent the images as plaine glasses do ; and if they be bowing , then they represent the image , as the concave and convex glasses do . secondly , those glasses which are plaine , but have ascents of angels in the middle , will shew one to have foure eyes , two mouthes , two noses , &c. examination . th●se experiments will be found different according to the diverse meeting of the glasses , which commonly are made scuing-wise at the end , 〈◊〉 which there will be two divers superficies in the glasse , making the exteriour angle somewhat raised , at the interiour onely one superficies , which may be covered according to ordinary glasses to c●use a reflexion , and so it will be but one glasse , which by refraction according to the different thicknesse of the glasse , and different angles of the scuing forme , do differently present the images to the eye , as foure eyes , two mouthes , two noses ; sometimes three eyes one mouth , and one nose , the one large and the other long , sometimes two eyes onely : with the mouth and the nose deformed , which the glasse ( impenetrable ) will not shew . and if there be an interiour solid angle , according to the difference of it ( as if it be more sharp ) there will be represented two distinct double images , that is , two entire visages and as the angle is open , by so much the more the double images will reunite and enter one within another , which will present sometimes a whole visage extended at large , to have foure eyes , two noses , and two mouthes : and by moving the glasse the angle will vanish , and so the two superficies will be turned into one , and the duplicity of images will also vanish and appeare but one onely : and this is easily experimented with two little glasses of steel , or such like so united , that they make divers angles and inclinations . thirdly , there are glasses which make men seeme pale , red , and coloured in diverse manners , which is caused by the dye of the glasse , or the diverse refraction of the species : and those which are made of silver , latine , steele , &c. do give the images a diverse colour also . in which one may see that the appearances by some are made fairer , younger or older than they are ; and contrarily others will make them foule and deformed : and give them a contrary visage : for if a glasse be cut as it may be , or if many pieces of glasse be placed together to make a conveniable reflexion : there might be made of a mole ( as it were ) a mountaine , of one haire a tree , a fly to be as an elephant , but i should be too long if i should say all that which might be said upon the property of glasses . i will therefore conclude this discourse of the properties of these glasses with these foure recreative problemes following . problem . lxxviii . 1 how to shew to one that is suspitious , what is done in another chamber or roome : notwithstanding the interposition of the wall . for the performance of this , there must be placed three glasses in the two chambers , of which one of them shall be tyed to the planching or seeling , that it may be common to communicate the species to each glasse by reflexion , there being left some hole at the top of the wall against the glasse to this end : the two other glasses must be placed against the two walls at right angles , as the figure here sheweth at b. and c. then the sight at e by the line of incidence fe , shall fall upon the glasse ba , and reflect upon the superficies of the glasse bc , in the point g ; so that if the eye be at g , it should see e , and e would reflect upon the third glass in the point h , and the eye that is at l , will see the image that is at e. in the point of the cath●r● : which image shall come to the eye of the suspicious , viz. at l. by help of the third glasse , upon which is made the second reflexion , and so brings unto the eye the object , though a wall be between it . corolarie . 1. by this invention of reflections the besiegers of a towne may be seene upon the rampart : notwithstanding the parapet , which the besieged may do by placing a glasse in the hollow of the ditch , and placing another upon the toppe of the wall , so that the line of incidence comming to the bottom of the ditch , make an angle equall to the angle of reflexion , then by this situation and reflexion , the image of the besiege● 〈◊〉 will be seen to him is upon the rampart corolarie 2. by which also may be inferred , that the same reflexions may be seen in a regular polygon , and placing as many glasses as there are sides , counting two for one ; for then the object being set to one of the glasses , and the eye in the other , the jmage will be seen easily . corolarie 3. farther , notwithstanding the interposition of many walls , chambers , or cabinets , one may see that which passeth through the most remotest of them , by placing of many glasses as there are openings in the walls , making them to receive the incident angles equall : that is , placing them in such sort by some geometricall assistant , that the incident points may meet in the middle of the glasses : but here all the defect will be , that the jmages passing by so many reflexions , will be very weak and scarce observable . problem . lxxix . how with a musket to strike a mark , not looking towards it , as exact as one aiming at it . as let the eye be at o ▪ and the mark c , place a plaine glasse perpendicular as ab . so the marke c shall be seen in catheti ca , viz. in d , and the line of reflexion is d , now let the musket fe , upon a rest ▪ be moved to and fro untill it be seen in the line od , which admit to be hg , so giving fire to the musket , it shall undoubtedly strike the mark . corolaries . from which may be gathered , that one may exactly shoot out of a musket to a place which is not seen , being hindered by some obstacle , or other interposition . as let the eye be at m , the mark c , and the wall which keeps it from being seene , admit to be qr , then set up a plaine glass as ab , and let the musket by gh , placed upon his rest po. now because the marke c is seen at d , move the musket to and fro , untill it doth agree with the line of reflection mb , which suppose at li , so shall it be truly placed , and giving fire to the musket , it shall not faile to strike the said mark at c. problem . lxxx . how to make an image to be seen hanging in the aire , having his head downeward . take two glasses , and place them at right angles one unto the other , as admit ab , and cb , of which admit cb , ho●izontall , and let the eye be at h , and the object or image to be de ; so d will be reflected at f , so to n , so to he : then at g , so to ● and then to h , and by a double reflection ed will seeme in qr , the highest point d in r , and the point l in q inversed as was said , taking d for the head , and e for the feet ; so it will be a man inversed , which will seem to be flying in the aire , if the jmage had wings unto it , and had secretly 〈◊〉 motion : and if the glasse were bigge enough to receive many reflexions , it would deceive the sight the more by admiring the changing of colours that would be seen by that motion . problem . lxxxi . how to make a company of representative souldiers seeme to be a regiment , or how few in number may be multiplyed to seem to be many in number . to make the experiment upon men , there must be prepared two great glasses ; but in stead of it we will suppose two lesser , as gh . and fi , one placed right against another perpendicular to the horizon , upon a plaine levell table : betvveene vvhich glasses let there be ranged in battalia-vvise upon the same table a number of small men according to the square g , h , i , f , or in any other forme or posture : hen may you evidently see hovv the said battel vvill be multiplyed and seem farre bigger in the appearance than it is in effect . corolarie . by this invention you may make a little cabinet of foure foot long , and tvvo foot large , ( more or lesse ) vvhich being filled vvith rockes or such like things , or there being put into it silver , gold , stones of luster , jewels , &c. and the walls of the said cabinet being all covered , or hung with plaine glasse ; these visibles will appeare manifoldly increased , by reason of the multiplicitie of reflexions , and at the opening of the said cabinet , having set something which might hide them from being seen , those that look into it will be astonished to see so few in number which before seemed to be so many . problem . lxxxii . of fine and pleasant dyal● . could you choose a more ridiculous one than the natural dyall written amongst the greek epigrams , upon which some sound poet made verses ; shewing that a man carrieth about him alwayes a dyall in his face by meanes of the nose and teeth ? and is not this a jolly dyall ? for he need not but open the mouth , the lines shall be all the teeth , and the nose shall serve for the style . of a dyall of hearbes . can you have a finer thing in a garden , or in the middle of a compartemeet , than to see the lines and the number of houres represented with little bushie hearbes , as of hysope or such which is proper to be cut in the borders ; and at the top of the style to have a fanne to shew which way the winde b●oweth ? this is very pleasant and useful . of the dyall upon the fingers and the hand . is it nor a commoditie very agreeable , when one is in the fie●d or in some vil●age vvithout any other dyall , to see onely by the hand what of the clock it is ? vvhich gives it very neare ; and may be practised by the left hand , in this manner . take a stravv or like thing of the length of the index or the second finger , hold this straw very right betvveen the thumb and the fore-finger , then stretch forth the hand ▪ and turne your back , and the palm of your hand tovvards the sunne ; so that the shadovv of the muscle vvhich is under the thumb , touch the line of life , vvhich is betvveen the middle of the tvvo other great lines , vvhich is seen in the palme of the hand , this done , the end of the shadovv vvill shevv vvhat of the clock it is : for at the end of the first finger it is 7 in the morning , or 5 in the evening , at the end of the ring-finger it is 8 in the morning , or 4 in the evening , at the end of the little finger or first joynt , it is 9 in the morning , or 3 in the after-noone , 10 & 2 at the second joynt , 11 and 1 at the third joynt , and midday in the line follovving , vvhich comes from the end of the index . of a dyall which was about an obeliske at rome . was not this a pretty fetch upon a pavement , to choose an obeliske for a dyall , having 106 foot in height , without removing the basis of it ? plinie assures us in his 26 book and 8 chap. that the emperour augustus having accom●odated in the field of mars an obeliske of this height , he made about it a pavement , and by the industry of man●lius the mathematician , there were enchaced markes of copper upon the pavement , and placed also an apple of gold upon the toppe of the said obeliske , to know the houre and the course of the sunne , with the increase and decrease of dayes by the same shadow : and in the same manner do some by the shadow of their head or other style , make the like experiments in astronomie . of dyals with glasses . pt●lomie w●ites , as cardanus reports , that long ago there were glasses which served for dyals , and presented the face of the beholder as many times as the houre ought to be , twice if it were 2 of the clock , 9 if it were 9 , &c. but this was thought to be done by the help of water , and not by glasses , which did leake by little and little out of the vessell , discovering anon one glasse , then anon two glasses , then 3 , 4 , 5 glasses , &c. to shew so many faces as there were houres , which was onely by leaking of water . of a dyall which hath a glasse in the place of the style . what will you say of the invention of mathematicians , which finde out daily so many fine and curious novelties ? they have now a way to make dyals upon the wainscot or seeling of a chamber , and there where the sunne can never shine , or the beames of the sunne cannot directly strike : and this is done in placing of a little glasse in the place of the style which reflecteth the light , with the same condition that the shadow of the style sheweth the houre : and it is easie to make experiment upon a common dyall , changing only the disposition of the dyall , and tying to the end of the style a piece of plaine glasse . the almaines use it much , who by this way have no greater trouble , but to put their noses out of their beds and see what a clock it is , which is reflected by a little hole in the window upon the wall or seeling of the chamber . examination . in this there are two experiments considerable , the first is with a very little glasse placed so that it may be open to the beames of the sunne , the other hath respect to a spacious or great glasse placed to a very little hole so that the sun may shine on it , for then the shadow which is cast upon the dyall is converted into beames of the sunne , and will reflect and becast upon a plain opposite : and in the other it is a hole in the window or such like , by which may passe the beames of the sun , which represent the extreamity of the style , & the glasse representeth the plaine of the dyall , upon which the beames being in manner of shadowes reflect cast upon a plaine opposite : and it is needfull that in this second way the glasse may be spacious , as before , to receive the delineaments of the dyall . otherwise you may draw the lineaments of a dyall upon any plaine looking-glasse which reflecteth the sunne-beames , for the applying a style or a pearle at the extreamitie of it : and placed to the sunne , the reflexion will be answerable to the delineaments on the glasse : but here note , that the glasse ought to be great , and so the delineaments thereon . but that which is most noble , is to draw houre-lines upon the outside of the glasse of a window , and placing a style thereto upon the outside , the shadow of the style will be seen within , and so you have the hour , more certaine without any difficulty . of dyals with water . svch kinde of dyals were made in ancient times , and also these of sand : before they had skill to make sun-dyals or dyals with wheeles ; for they used to fill a vessell with water , and having experience by tryall thar it would runne out all in a day , they did marke within the vessell the houres noted by the running of the water ; and some did set a piece of light board in the vessell to swimme upon the top of the water , carrying a little statue , which with a small stick did point out the houre upon a columne or wall , figured with houre-notes , as the vessell was figured within . novv it seemes a safer vvay that the vvater passe out by drop and drop , and drop into a cylindricall glasse by help of a pipe : for having marked the exterior part of the cylinder in the houre notes , the vvater it selfe vvhich falls vvithin it , vvill shevv vvhat of the clock it is , farre better than the running of sand , for by this may you have the parts of the houres most accurate , vvhich commonly by sand is not had : and to vvhich may be added the houres of other countreys vvith greater ease . and here note , that as soone as the vvater is out ▪ of one of the glasses , you may turne it over into the same againe out of the other , and so let it runne anevv . problem . lxxxiii . of cannons or great artillery . souldiers , and others would willingly see 〈◊〉 problems , which containe : three or foure subtile questions : the first is , how to charge a cannon without powder ? this may be done vvith aire and vvater , only having throvvn cold vvater into the cannon , vvhich might be squirted forceably in by the closure of the mouth of the piece , that so by this pressure the aire might more condense ; then having a round piece of vvood very just , and oiled vvell for the better to slide , and thrust the bullet vvhen it shall be time : this piece of vvood may be held fast vvith some pole , for feare it be not thrust out before his time : then let fire be made about the trunion or hinder part of the piece to heat the aire and vvater , and then vvhen one vvould shoot it , let the pole be quickly loosened , for then the aire searching a greater place , and having vvay novv offered , vvill thrust out the vvood and the bullet very quick : the experiment vvhich vve have in long trunkes shooting out pellats vvith aire only , shevveth the verity of this probleme . 2 in the second question it may be demanded , how much time doth the bull●● of a cannon spend in the aire before i● falls to the ground ? the resolution of this question depends upon the goodnesse of the piece & charge thereof , seeing in each there is great difference . it is reported , that tich● bra●e , and the landsgrave did make an experiment upon a cannon in germany , which being charged and shot off ; the bullet spent two minutes of time in the aire before it fell : and the distance was a germane mile , which distance proportionated to an hours time , makes 120 italian miles . 3. in the third question it may be asked , how it comes to passe , that a cannon shooting upwards , the bullet flies with more violence than being shot point-blanke , or shooting downeward ? if we regard the effect of a cannon when it is to batter a wall , the question is false , seeing it is most evident that the blowes which fall perpendicular upon a wall , are more violent than those which strike byas-wise or glaunsingly . but considering the strength of the blow only , the question is most true , and often experimented to be found true : a piece mounted at the best of the randon , which is neare halfe of the right , conveyes her bullet with a farre greater violence then that which is shot at point blanke , or mounted parallel to the horizon . the common reason is , that shooting high , the fire carries the bowle a longer time in the aire , and the aire moves more ●acill upwards , than dovvnevvards , because that the airy circles that the motion of the bullet makes , are soonest broken . hovvsoever this be the generall tenet , it is curious to finde out the inequality of moving of the aire ; vvhether the bullet fly upvvard , dovvnevvard , or right forvvard , to produce a sensible dfference of motion ; & some think that the cannon being mounted , the bullet pressing the povvder maketh a greater resistance , and so causeth all the povvder to be inflamed before the bullet is throvvne out , vvhich makes it to be more violent than othervvise it vvould be . when the cannon is othervvise disposed , the contrary arives , the fire leaves the bullet , and the bullet rolling from the povvder resists lesse : and it is usually seene , that shooting out of a musket charged onely vvith povvder , to shoot to a marke of paper placed point blanke , that there are seene many small holes in the paper , vvhich cannot be other than the graines of powder which did not take fire : but this latter accident may happen from the over-charging of the piece , or the length of it , or windy , or dampenesse of the powder . from which some may think , that a cannon pointed right to the zenith , should shoot with greater violence , then in any other mount or forme whatsoever : and by some it hath beene imagined , that a bullet shot in this fashion hath been consumed , melted , and lost in the aire , by reason of the violence of the blow , and the activity of the sire , and that sundry experiments have been made in this nature , and the bullet never found . but it is hard to believe this assertion : it may rather be supposed that the bullet falling farre from the piece cannot be discerned where it falls : and so comes to be lost . 4. in the fourth place it may be asked , whether the discharge of a cannon b● so much the greater , by how much it is longer ? it seemeth at the first to be most true , that the longer the piece is , the more violent it shoots : and to speak generally , that which is direction by a trunke , pipe , or other concavitie , is conveyed so much the more violent , or better , by how much it is longer , either in respect of the sight , hearing , water , fire , &c. & the reason seems to hold in cannons , because in those that are long , the fire is retained a longer time in the concavitie of the piece , and so throwes out the bullet with more violence ; and experience lets us see that taking cannons of the same boare , but of diversitie of length from 8 foot to 12 , that the cannon of 9 foot long hath more force than that of 8 foot long , and 10 more than that of 9 , and so unto 12 foote of length . now the usuall cannon carries 600 paces , some more , some lesse , yea some but 200 paces from the piece , and may shoot into soft earth 15 or 17 foot , into sand or earth which is loose , 22 or 24 foot , and in firme ground , about 10 or 12 foot , &c. it hath been seen lately in germany , where there were made pieces from 8 foot long to 17 foot of like boare , that shooting out of any piece which was longer than 12 foot ; the force was diminished , and the more in length the piece increaseth , the lesse his force was : therefore the length ought to be in a meane measure , and it is often seene , the greater the cannon is , by so much the service is greater : but to have it too long or too short , is not convenient , but a meane proportion of length to be taken , otherwise the flame of the fire will be over-pressed with aire : whic hinders the motion in respect of substance , and distance of getting out . problem . lxxxiiii . of predigious progression and multiplication , of creatures , plants , fruits , numbers , gold , silver , &c. when they are alwayes augmented by certaine proportion . here we shall shew things no lesse admirable , as recreative , and yet so certaine and easie to be demonstrated , that there needs not but multiplication only , to try each particular : and first , of graines of mustard-seed . first , therefore it is certaine that the increase of one graine of mustard-seed for 20 yeares space , cannot be contained within the visible world , nay if it were a hundred times greater than it is : and holding nothing besides from the centre of the earth even unto the firmament , but only small grains of mustard-seed : now because this seems but words , it must be proved by art , as may be done in this wise , as suppose one mustard-seed sowne to bring forth a tree or branch , in each extendure of which might be a thousand graines : but we will suppose onely a thousand in the whole tree , and let us proceed to ●0 yeares , every seed to bring forth yearely a thousand graines , now multiplying alwayes by a thousand , in lesse then 17 years you shall have to many graines which will surpasse the sands , which are able to fill the whole firmament : for following the supposition of archimedes , and the most probable opinion of the greatness of the firmament which ●i●ho brahe hath left us ; the number of graines of sand will be sufficiently expressed with 49 ciphers , but the number of graines of mustard-seed at the end of 17 yeares will have 52 ciphers : and moreover , graines of mustard-seed , are farre greater than these of the sands : it is therefore evident that at the seventeenth yeare , all the graines of mustard-seed which shall successively spring from one graine onely , cannot be contained within the limits of the whole firmament ; what should it be then , if it should be multiplied againe by a thousand for the ●8 yeare : and that againe by a thousand for every yeares increase untill you come to the 20 yeare , it 's a thing as cleare as the day , that such a heap of mustard-seed would be a hundred thousand times greater than the earth : and bring onely but the increase of one graine in 20 yeares . of pigges . secondly , is it not a strange proposition , to say that the great turke with all his revenues , is not able to maintaine for one yeares time , all the pigges that a sow may pigge with all her race , that is , the increase with the increase unto 12 years : this seemes impossible , yet it is most true , for let us suppose and put , the case , that a sow bring forth but 6 , two males , and 4 females , and that each female shall bring forth as many every yeare , during the space of 12 yeares , at the end of the time there will be found above 3● millions of pigges : now allowing a crowne for the maintenance of each pigge for a yeare , ( which is as little as may be , being but neare a halfe of a farthing allowance for each day ; ) there must be at the least so many crownes to maintaine them , one a year , viz. 33 millions , which exceeds the turkes revenue by much . of graines of corne. thirdly , it will make one astonished to think that a graine of corne , with his increase successively for the space of 12 yeares will produce in grains 24414062●000000000000 , which is able to load almost al the creatures in the world. to open which , let it be supposed that the first yeare one graine being sowed brings forth 50 , ( but sometimes there is seen 70 , sometimes 100 fold ) which graines sowen the next yeare , every one to produce 50 , and so consequently the whole and increase to be sowen every yeare , until 12 yeares be expired , there will be of increase the aforesaid prodigious summe of graines , viz. 244140625000000000000 , which will make a cubical heap of 6258522 graines every way , which is more than a cubicall body of 31 miles every way : for allowing 40 graines in length to each foot , the cube would be 156463 foot every way : from which it is evident that if there were two hundred thousand cities as great as london , allowing to each 3 miles square every way , and 100 foot in height , there would not be sufficient roome to containe the aforesaid quantitie of corne : and suppose a bushel of corne were equal unto two cubicke feet , which might containe twenty hundred thousand graines then would there be 122070462500000. bushells , and allowing 30 bushels to a tunne , it would be able to load 81380●0833 vessels , which is more than eight thousand one hundred and thirty eight millions , ship loadings of ●00 tunne to each ship a : quantity so great that the sea is scarce able to beare , or the universal world able to finde vessels to carry it . and if this corne should be valued at halfe a crown the bushel , it would amount unto 15258807812500 pounds sterling , which i think exceeds all the treasures of all the princes , and of other particular men in the whole world : and is not this good husbandry to sowe one grain of corne ; and to continue it in sowing , the increase only for 12 yeares to have so great a profit ? of the increase of sheep . fourthly , those that have great flocks of sheep may be quickly rich , if they would preserve their sheep without killing or selling of them : so that every sheep produce one each yeare , for at the end of 16 yeares , 100 sheepe will multiply and increase unto 6553600 , which is above 6 millions , 5 hundred 53 thousand sheep : now supposing them worth but a crown a piece , it would amount unto 1638400 pounds sterling , vvhich is above 1 million 6 hundred 38 thousand pounds , a faire increase of one sheep : and a large portion for a childe if it should be allotted . of the increase of cod-fish , carpes , &c. fifthly , if there be any creatures in the vvorld that do abound vvith increase or fertilitie , it may be rightly attributed to fish ; for they in their kindes produce such a great multitude of eggs , and brings forth so many little ones , that if a great part vvere not destroyed continually , vvithin a ●ittle vvhile they vvould fill all the sea , ponds , and rivers in the vvorld ; and it is easie to shevv hovv it vvould come so to passe , onely by supposing them to increase without taking or destroying them for the space of 10 or 12 yeares : having regard to the soliditie of the waters which are allotted for to lodge and containe these creatures , as their bounds and place of rest to live in . of the increase and multiplication of men . sixthly , there are some that cannot conceive how it can be that from eight persons ( which were saved after the deluge or noahs flood ) should spring such a world of people to begin a monarchie under nimrod , being but 200 yeares after the flood , and that amongst them should be raised an army of two hundred thousand fighting men : but it is easi●y proved if vve take but one of the children of noah , and suppose that a nevv generation of people begun at every 30 yeares , and that it be continued to the seventh generation vvhich is 200 yeares ; for then of one only family there vvould be produced one hundred and eleven thousand soules , three hundred and five to begin the vvorld : though in that time men lived longer , and vvere more capable of multiplication and increase : vvhich number springing onely from a simp●e production of one yearly , vvould be farre greater , if one man should have many vvives , vvhich in ancient times they had : from vvhich it is also that the children of israel , vvho came into egypt but onely 70 soules , yet after 210 yeares captivity , they came forth vvith their hostes , that there vvere told six hundred thousand fighting men , besides old people , women and children ; and he that shall separate but one of the families of joseph , it would be sufficient to make up that number : how much more should it be then if we should adjoyne many families together ? of the increase of numbers . seventhly , what summe of money shall the city of london be worth , if it should be sold , and the money be paid in a yeare after this manner : the first week to pay a pinne , the second week 2 pinnes , the third week 4 pinnes , the fourth week 8 pinnes , the fifth week 16 pinnes . and so doubling untill the 52 weeks , or the yeare be expired . here one would think that the value of the pinnes would amount but to a small matter , in comparison of the treasures , or riches of the whole city : yet it is most probable that the number of pinnes would amount unto the sum of 4519599628681215 , and if we should allow unto a quarter a hundred thousand pinnes , the whole would contain ninetie eight millions , foure hundred thousand tunne : which is able to load 45930 shippes of a thousand tunne apiece : and if we should allow a thousand pins for a penny , the summe of money would amount unto above eighteen thousand , eight hundred and thirty millions of pounds sterling , an high price to sell a citie at , yet certain , according to that first proposed . so if 40 townes were sold upon condition to give for the first a penny , for the second 2 pence , for the third 4 pence , &c. by doubling all the rest unto the last , it would amount unto this number of pence , 109951●62●●76 , which in pounds is 4581298444 , that is foure thousand five hundred and fourescore millions of pounds and more . of a man that gathered up apples , stones , or such like upon a condition . eightly , admit there were an hundred apples , stones , or such like things that were plac'd in a straight line or right forme , a pace one from another , and a basket being placed a pace from the first : how many paces would there be made to put all these stones into the basket , by fetching one by one ? this would require near halfe a day to do it , for there would be made ten thousand and ninety two paces before he should gather them all up . of changes in bells , in musicall instruments , transmutation of places , in numbers , letters , men or such like . ninethly , is it not an admirable thing to consider how the skill of numbers doth easily furnish us with the knowledge of mysterious and hidden things ? which simply looked into by others that are not versed in arithmetick , do present unto them a world of confusion and difficultie . as in the first place , it is often debated amongst our common ringers , what number of changes there might be made in 5 , 6 , 7 , 8 , or more bells : who spend much time to answer their owne doubts , entring often into a labyrinth in the search thereof : or if there were 10 voyces , how many severall notes might there be ? these are propositions of such facility , that a childe which can but multiply one number by another , may easily resolve it , which is but only to multiply every number from the unite successively in each others product , unto the terme assigned : so the 6 number that is against 6 in the table , is 720 , and so many ( hanges may be made upon 6 bells , upon 5 there are 120 , &c. in like manner against 10 in the table is 3618800 , that is , three millions , six hundred twenty eight thousand , eight hundred : which shews that 10 voices may have so many consorts , each man keeping his owne note , but only altering his place ; and so of stringed instruments , and the gamat may be varied according to which , answerable to the number against x , viz. 1124001075070399680000 notes , from which may be drawne this , or the like proposition . suppose that 7 schollers were taken out of a free schoole to be sent to an vniversitie , there to be entertained in some colledge at commons for a certaine summe of money , so that each of them have two meales daily , and no longer to continue there , then that sitting all together upon one bench or forme at every meale , there might be a divers transmutation of place , of account in some one of them , in comparison of another , and never the whole company to be twice alike in situation : how long may the steward entertaine them ? ( who being not skilled in this fetch may answere unadvisedly . ) it is most certaine that there will be five thousand and forty several 1 a 1 2 b 2 6 c 3 24 d 4 120 e 5 7●0 f 6 5040 g 7 403●0 h 8 362880 i 9 3628800 k 10 39916800 l 11 479001600 m 12 6227020800 n 13 87178291200 o 14 1307674368000 p 15 20922789888000 q 16 355687537996000 r 17 6402375683928000 s 18 121645137994632000 t 19 2432902759892640000 u 20 51090957957745440000 w 21 1124001075070399680000 x 22 25852024726619192640000 y 23 6●0448593438860623360000 z 24 positions or changings in the seatings , which maks 14 years time wanting 10 weeks and 3 dayes . hence from this mutability of transmutation , it is no marvell tha● by 24 letters there ariseth and is made such variety of languages in the world , & such infinite number of words in each language ; seeing the diversity of syllables produceth that effect , and also by the interchanging & placing of letters amongst the vowels , & amongst themselves maketh these syllables : vvhich alphabet of 24 letters may be varied so many times , viz. 620448593438860623360000 vvhich is six hundred tvventy thousand , foure hundred forty eight millions of millions of millions five hundred ninety three thousand , foure hundred thirty eight milions of milions , & more . novv allovving that a man may reade or speak one hundred thousand vvords in an houre vvhich is tvvice more vvords than there are conteined in the psalmes of david , ( a taske too great for any man to do in so short a time ) and if there were foure thousand six hundred and fifty thousand millions of men , they could not speak these words ( according to the hourely proportion aforesaid ) in threescore and ten thousand yeares ; which variation & transmutation of letters , if they should be written in bookes , allowing to each leaf 28000 words , ( which is as many as possibly could be inserted , ) and to each book a reame or 20 quire of the largest and thinnest printing paper , so that each book being about 15 inches long , 12 broad , and 6 thick : the books that would be made of the transmutation of the 24 letters aforesaid , would be at least 38778037089928788 : and if a library of a mile square every way , of 50 foot high , were made to containe 250 galleries of 20 foot broad apiece , it would containe foure hundred mill●ons of the said books : so there must be to containe the rest no lesse than 9●945092 such libraries ; and if the books were extended over the surface of the globe of the earth , it would be a decuple covering unto it : a thing seeming most incredible that 24 letters in their transmutation should produce such a prodigious number , yet most certaine and infallible in computation . of a servant hired upon certaine conditions . a servant said unto his master , that he would dvvell vvith him all his life-time , if he would but onely lend him land to sowe one graine of corne with all his increase for 8 years time ; how think you of this bargaine ? for if he had but a quarter of an inch of ground for each graine , and each graine to bring forth yearely of increase 40 graines , the whole sum would amount unto , at the terme aforesaid , 6553600000000 graines : and seeing that three thousand and six hundred millions of inches do but make one mile square in the superficies , it shall be able to receive foureteene thousand and foure hundred millions of graines , which is 14400000000. thus dividing the aforesaid 6553600000000 , the quotient will be 455 , and so many square miles of land must there be to sowe the increase of one graine of corne for 8 yeares , which makes at the least foure hundred and twenty thousand acres of land , which rated but at five shillings the acre per annum , amounts unto one hundred thousand pound ; which is twelve thousand and five hundred pound a yeare , to be continued for 8 yeares ; a pretty pay for a masters servant 8 yeares service . problem . lxxxv . of fountaines , hydriatiques , machinecke , and other experiments upon water , or other liquor . 1. first how to make water at the foot of a mountaine to ascend to the top of it , and so to descend on the other side ? to do this there must be a pipe of lead , which may come from the fountaine a , to the top of the mountaine b ; and so to descend on the other side a little lower then the fountaine , as at c. then make a hole in the pipe at the top of the mountaine , as at b , and stop the end of the pipe at a and c ; and fill this pipe at b with water : & close it very carefully againe at b , that no aire get in : then unstop the end at a , & at c ; then will the water perpetually runne up the hill , and descend on the other side , which is an invention of great consequence to furnish villages that want water . 2. secondly , how to know what wine or other liquor there is in a vessell without opening the bung-hole , and without making any other hole , than that by which it runnes out at the top ? in this problem there is nothing but to take a bowed pipe of glasse , and put it into the faucets hole , and stopping it close about : for then you shall see the wine or liquor to ascend in this pipe , untill it be just even with the liquor in the vessel ; by which a man may fill the vessel , or put more into it : and so if need were , one may empty one vessel into another without opening the bung-hole . 3. thirdly , how is it that it is said that a vessell holds more water being placed at the foot of a mountaine , than standing upon the top of it ? this is a thing most certaine , because that water and all other liquor disposeth it selfe sphericaliy about the centre of the earth ; and by how much the vessel is nearer the centre , by so much the more the surface of the water makes a lesser sphere , and therefore every part more gibbous or swelling , than the like part in a greater sphere : and therefore when the same vessell is farther from the centre of the earth , the surface of the water makes a greater sphere , and therefore lesse gibbous , or swelling over the vessell : from whence it is evident that a vessell near the centre of the earth holds more water than that which is farther remote from it ; and so consequently a vessel placed at the bottome of the mountaine holds more water , than being placed on the top of the mountaine . first , therefore one may conclude , that one and the same vessel will alwayes hold more : by how much it is nearer the centre of the earth . secondly , if a vessell be very neare the centre of the earth , there will be more water above the brims of it , than there is within the vessel . thirdly , a vessel full of water comming to the centre wil spherically increase , and by little and little leave the vessel ; and passing the centre , the vessel will be all emptied . fourthly , one cannot carry a paile of water from a low place to a higher , but it will more and more run out and over , because that in ascending it lies more levell , but descending it swels and becomes more gibbous . 4. fourthly , to conduct water from the top of one mountaine , to the top of another . as admit on the top of a mountaine there is a spring , and at the toppe of the other mountaine there are inhabitants which want water : now to make a bridge from one mountaine to another , were difficult and too great a charge ; by way of pipes it is easie and of no great price : for if at the spring on the top of the mountaine be placed a pipe , to descend into the valley , and ascend to the other mountlaine , the water will runne naturally , and continually , provided that the spring be somewhat higher than the passage of the water at the inhabitants . 5. fifthly , of a fine fountaine which spouts water very high , and with great violence by turning of a cock. let there be a vessell as ab , made close in all his parts , in the middle of which let cd be a pipe open at d neare the bottome , and then with a squirt squirt in the water at c , stopped above by the cock or faucet c , vvith as great violence as possible you can ; and turne the cock immediatly . novv there being an indifferent quantity of vvater and aire in the vessel , the vvater keeps it selfe in the bottome , and the aire vvhich vvas greatly pressed , seeks for more place , that turning the cock the water issueth forth at the pipe , and flyes very high , and that especially if the vessell be a little heated : some make use of this for an ewer to wash hands withall , and therefore putting a moveable pipe above c , such as the figure sheweth : which the water will cause to turne very quick , pleasurable to behold . 6. sixtly , of archimedes screw , which makes water ascend by descending . this is nothing else but a cylinder , about the which is a pipe in form of a screw , and when one turnes it , the water descends alwayes in respect of the pipe : for it passeth from one part which is higher to that which is lower , and at the end of the engine the water is found higher than it was at the spring . this great enginer admirable in all mathematicall arts invented this instrument to wash king hieroies great vessells , as some authors saye , also to water the fields of egypt , as diodorus witnesseth : and cardanus reporteth that a citizen of milan having made the like engine , thinking himselfe to be the first inventer , conceived such exceeding joy , that he be came mad , foll . 2. againe a thing may ascend by descending , if a spiral line be made having many circulations or revolutions ; the last being alwayes lesser than the first , yet higher than the plaine supposed it is most certaine that then putting a ball into it , and turning the spirall line so , that the first circulation may be perpendicular , or touch alwayes the supposed plain : the ball shall in descending continually ascend , untill at last it come to the highest part of the spirall line , & so fall out . and here especially may be noted , that a moving body as water , or a bullet , or such like , will never ascend if the helicall revolution of the screw be not inclining to the horizon : so that according to this inclination the ball or liquor , may descend alwayes by a continuall motion and revolution . and this experiment may be more usefull , naturally made with a thred of ●ron , or latine turned or bowed helically about a cylinder , with some distinction of distances between the heli●es , for then having drawn out the cylinder , or having hung or tyed some weight at it in such sort , that the water may easily drop if one lift up the said thred : these helices or revolutions , notwithstanding will remaine inclining to the horizon , and then turning it about forward , the said weight will ascend , but backward it will descend . now if the revolutions be alike , and of equallity amongst themselves , and the whirling or turning motion be quicke , the sight vvill be so deceived , that producing the action it vvill seeme to the ignorant no lesse than a miracle . 7. seventhly , of another fine fountaine of pleasure . this is an engine that hath two wheeles with cogges , or teeth as ab , which are placed within an ovall cd , in such sort , that the teeth of the one , may enter into the notches of the other ; but so just that neither aire nor water may enter into the ovall coffer , either by the middle or by the sides , for the wheele must joyne so neare to the sides of the coffer , that there be no vacuitie : to this there is an axeltree with a handle to each wheele , so that they may be turned , and a being turned , that turneth the other wheele that is opposite : by which motion the aire that is in e , & the water that is carried by the hollow of the wheeles of each side , by continuall motion , is constrained to mount and flie out by the funnell f : now to make the water runne what way one would have it , there may be applied upon the top of the pipe f , two other moveable pipes inserted one within another ; as the figure sheweth . but here note , that there may acrue some inconveniency in this machine seeing that by quick turning the cogges or teeth of the wheeles running one against another , may neare break them , and so give way to the aire to enter in , which being violently inclosed vvill escape to occupie the place of the vvater , vvhose vveight makes it so quick : hovvsoever , if this machine be curiously made as an able vvorkeman may easily do , it is a most sovereigne engine , to cast vvater high and farre off for to quench fires . and to have it to raine to a place assigned , accommodate a socket having a pipe at the middle , vvhich may point tovvards the place being set at the top thereof , and so having great discretion in turning the axis of the vvheele , it may vvork exceeding vvell , and continue long . 8. eightly , of a fine watering pot for gardens . this may be made in forme of a bottle according to the last figure or such like , having at the bottome many small holes , and at the neck of it another hole somevvhat greater than those at the bottome , vvhich hole at the top you must unstop vvhen you vvould fill this vvatering pot , for then it is nothing but putting the lovver end into a paile of vvater , for so it vvill fill it selfe by degrees : and being full , put your thumb on the hole at the neck to stop it , for then may you carry it from place to place , and it vvill not sensibly runne out , som●thing it vvill , and all in time ( if it vvere never so close stopped ) contrary to the ancient tenet in philosophy , that aire will not penetrate . 9. ninthly , how easily to take wine out of a vessell at the bu●g-hole , without piercing of a hole in the vessell ? in this there is no need but to have a cane or pipe of glasse or such like , one of the ends of which may be closed up almost , leaving some small hole at the end ; for then if that end be set into the vessell at the bung-hole , the whole cane or pipe will be filled by little and little ; and once being full , stop the other end which is without and then pull out the cane or pipe , so will it be ful of wine , then opening a little the top above , you may fill a glasse or other pot with it , for as the wine issueth out , the aire commeth into the cane or pipe to supply vacuity . 10. tenthly , how to measure irregular bodies by help of water ? some throw in the body or magnitude into a vessell , and keep that which floweth out over , saying it is alwayes equal to the thing cast into the water : let i● is more nea●er this way to poure into a vessell such a quantity of water , which may be thought sufficient to cover the body or magnitude , and make a marke how high the water is in the vessell , then poure out all this water into another vessell , and let the body or magnitude be placed into the first vessel ; then poure in water from the second vessell , until it ascend unto the former marke made in the first vessell , so the vvater vvhich remaines in the second vessel is equall to the body or magnitude put into the water : but here note that this is not exact or free from error , yet nearer the truth than any geometrician can otherwise possibly measure , and these bodies that are not so full of pores are more truly measured this way , than others are . 11. to finde the weight of water . seeing that 574 / 1000 part of an ounce weight , makes a cubicall inch of water : and every pound weight haverdepoize makes 27 cubicall inches , and 1 9 / ● ; fere , and that ● gallons and a halfe wine measure makes a foot cubicall , it is easie by inversion , that knowing the quantity of a vessel in gallons , to finde his content in cubicall feet or weight : and that late famous geometrician master brigs found a cubical foot of vvater to vveigh neare 62 pound vveight haverdepoize but the late learned simon stevin found a cubicall foot of vvater to vveigh 65 pound , vvhich difference may arise from the inequalitie of vvater ; for some vvaters are more ponderous than others , and some difference may be from the weight of a pound , and the measure of a foot : thus the weight and quantitie of a solid foot settled , it is easie for arithmeticians to give the contents of vessells or bodies which containe liquids . 12. to finde the charge that a vessell may carry as shippes , boates , or such like . this is generally conceived , that a vessell may carry as much weight as that water weigheth , which is equall unto the vessell in bignesse , in abating onely the weight of the vessell : we see that a barrel of wine or water cast into the water , will not sink to the bottome , but swim easily , and if a ship had not iron and other ponderosities in it , it might swim full of water without sinking : in the same manner if the vessell were loaden with lead , so much should the watter weigh : hence it is that marriners call shippes of 50 thousand tunnes , because they may containe one or two thousand tunne , and so consequently carry as much . 13. how comes it that a shippe having safely sayled in the vast ocean , and being come into the port or harbour , without any tempest will sink down right ? the cause of this is that a vessel may carry more upon some kinde of water than upon other ; now the water of the sea is thicker and heavier than that of rivers , wels , or fountains ; therefore the loading of a vessell which is accounted sufficient in the sea , becomes too great in the hurbour or sweet water . now some think that it is the depth of the water that makes vessells more easie to swimme , but it is an abuse ; for if the loading of a ship be no heavier than the water that would occupie that place , the ship should as easily swim upon that water , as if it did swim upon a thousand fathom deep of water , and if the vvater be no thicker than a leafe of paper , and weigheth but an ounce under a heavy body , it vvill support it , as vvell as if the vvater under it vveighed ten thousand pound vveight : hence it is if there be a vessell capable of a little more than a thousand pound vveight of vvater , you may put into this vessell a piece of vvood , vvhich shall vveigh a thousand pound vveight ; ( but lighter in his kinde than the like of magnitude of vvater : ) for then pouring in but a quart of vvater or a very little quantitie of vvater , the vvood vvill svvim on the top of it , ( provided that the vvood touch not the sides of the vessell : ) vvhich is a fine experiment , and seems admirable in the performance . 14. how a grosse body of mettle may swimme upon the water ? this is done by extending the mettle into a thin plate , to make it hollovv in forme of a vessel ; so that the greatnesse of the vessell which the aire vvith it containeth , be equal to the magnitude of the vvater , vvhich vveighes as much as it , for all bodies may svvim vvithout sinking , if they occupie the place of vvater equal in vveight unto them , as if it vveighed 12 pound it must have the place of 12 pound of vvater : hence it is that vve see floating upon the vvater great vessells of copper or brasse , vvhen they are hollovv in forme of a caldron . and how can it be otherwise conceived of islands in the sea that swim and float ? is it not that they are hollow and some part like unto a boat , or that their earth is very light and spongeous , or having many concavities in the body of it , or much wood within it ? and it would be a pretty proposition to shew how much every kinde of metall should be inlarged , to make it swim upon the water : which doth depend upon the proportion that is between the vveight of the vvater and each metall . novv the proportion that is betvveene metalls and water of equall magnitude , according to some authors , is as followeth . a magnitude of 10 pound weight of water will require for the like magnitude of gold. 187 ½ lead . 116 ½ silver . 104 copper . 91 iron . 81 tinne . 75 from which is inferred , that to make a piece of copper of ●0 pound weight to swimme , it must be so made hollow , that it may hold 9 times that weight of water and somewhat more , that is to say , 91 pound : seeing that copper and water of like magnitudes in their ponderosities , are as before , as ●0 to 91. 15. how to weigh the lightnesse of the aire ? place a ballance of wood turned upside downe into the water , that so it may swim , then let water be inclosed within some body , as within a bladder or such like , and suppose that such a quantitie of aire should weigh one pound , place it under one of the ballances , and place under the other as much weight of lightnesse as may counter-ballance and keep the other ballance that it rise not out of the water : by which you shall see how much the lightnesse is . but without any ballance do this ; take a cubicall hollow vessell , or that which is cylindricall , which may swimme on the water , and as it sinketh by placing of weights upon it , marke hovv much , for then if you vvould examine the vveight of any body , you have nothing to do but to put it into this vessell , and marke hovv deep it sinkes , for so many pound it vveighes as the vveights put in do make it so to sinke . 16. being given a body , to marke it about , and shew how much of it will sink in the water , or swim above the water . this is done by knovving the vveight of the body vvhich is given , and the quantity of vvater , vvhich vveighes as much as that body ; for then certainly it vvill sink so deep , untill it occupieth the place of that quantitie of vvater . 17. to finde how much severall mettle or other bodies doe weigh lesse in the water than in the aire : take a ballance , & vveigh ( as for example ) 9 pound of gold , silver , lead , or stone in the aire , so it hang in aequilibrio ; then comming to the vvater , take the same quantity of gold silver , lead , or stone , and let it softly dovvne into it , and you shall see that you shall need a lesse counterpoise in the other ballance to counter-ballance it : vvherefore all solids or bodies vveigh lesse in the vvater than in the aire , and so much the lesse it vvill be , by hovv much the vvater is grosse and thick , because the vveight findes a greater resistance , and therefore the vvater supports more than aire ; and further , because the vvater by the ponderositie is displeased , and so strives to be there againe , pressing to it , by reason of the other vvaters that are about it , according to the proportion of his weight . archimedes demonstrateth , that all bodies weigh lesse in the water ( or in like liquor ) by how much they occupie place : and if the water weigh a pound weight , the magnitude in the water shall weigh a pound lesse than in the aire . now by knowing the proportion of water and mettles , it is found that gold loseth in the water the 19 part of his weight , copper the 9 part , quicksilver the 15 part , lead the 12 part , silver the 10 part , iron the 8 part , tinne the 7 part and a little more : wherefore in materiall and absolute weight , gold in respect of the water that it occupieth weigheth 18 , and ¾ times heavier than the like quantitie of water , that is , as 18 ¾ to the quicksilver 15 times , lead 11 and ⅗ , silver 10 and ⅔ , copper 9 and 1 / 10 , iron 8 and ½ , and tinne 8 and 1 / ● . contrarily in respect of greatnesse , if the water be as heavy as the gold , then is the water almost 19 times greater than the magnitude of the gold , and so may you judge of the rest . 18. how is it that a ballance having like weight in each scale , and hanging in aequilibrio in the aire , being placed in another place , ( without removing any weight ) it shall cease to hang in aequilibrio sensibly : yea by a great difference of weight ? this is easie to be resolved by considering different mettles , which though they vveigh equall in the aire , yet in the vvater there vvill be an apparant difference ; as suppose so that in the scale of each ballance be placed 18 pound vveight of severall metalls , the one gold , and the other copper , vvhich being in aequilibrio in the aire , placed in the vvater , vvill not hang so , because that the gold los●eth neare the 18 part of his vveight , vvhich is about 1 pound , and the copper loseth but his 9 part , vvhich is 2 pound : vvherefore the gold in the vvater vveigheth but 17 pound , and the copper 16 pound , vvhich is a difference most sensible to confirme that point . 19. to shew what waters are heavier one than another , and how much . physicians have an especiall respect unto this , judging that vvater vvhich is lightest is most healthfull and medicinall for the body , & sea-men knovv that the heaviest vvaters do beare most , and it is knovvne vvhich water is heaviest thus . take a piece of wax , and fasten lead unto it , or some such like thing that it may but precisely swimme , for then it is equal to the like magnitude of water , then put it into another vessell which hath contrary water , and if it sinke , then is that water lighter than the other : but if it sinke not so deep , then it argueth the water to be heavier or more grosser than the first water , or one may take a piece of vvood , and marke the quantitie of sinking of it into severall waters , by vvhich you may judge which is lightest or heaviest , for in that which it sinkes most , that is infallibly the lightest , and so contrarily . 20. how to make a pound of water weigh as much as 10 , 2● , ●0 , or a hundred pound of lead ; nay as much as a thousand , or ten thousand and pound weight ? this proposition seems very impossible , yet water inclosed in a vessell , being constrained to dilate it selfe , doth weigh so much as though there were in the concavitie of it a solid body of water . there are many wayes to experiment this proposition , but to verifie it , it may be sufficient to produce two excellent ones onely : which had they not been really acted , little credit might have been given unto it . the first way is thus . take a magnitude which takes up as much place as a hundred or a thousand pound of water , and suppose that it were tied to some thing that it may hang in the aire ; then make a ballance that one of the scales may inviron it , yet so that it touch not the sides of it : but leave space enough for one pound of water : then having placed 100 pound weight in the other scale , throw in the water about the magnitude , so that one pound of water shall weigh downe the hundred pound in the other ballance . problem . lxxxvi . of sundry questions of arithmetick , and first of the number of sands . it may be said incontinent , that to undertake this were impossible , either to number the sands of lybia , or the sands of the sea ; and it vvas this that the poets sung , and that vvhich the vulgar beleeves ; nay , that vvhich long ago certaine philosophers to gelon king of sicily reported , that the graines of sand vvere innumerable : but i ansvvere vvith archimedes , that not only one may number those vvhich are at the border and about the sea ; but those vvhich are able to fill the vvhole vvorld , if there vvere nothing else but sand ; and the graines of sands admitted to be so small , that 10 may make but one graine of poppy : for at the end of the account there need not to expresse them , but this number 30840979456 , and 35 ciphers at the end of it . clavius and archimedes make it somevvhat more ; because they make a greater firmament than ticho brahe doth ; and if they augment the vniverse , it is easie for us to augment the number , and declare assuredly how many graines of sand there are requisite to fill another vvorld , in comparison that our visible vvorld vvere but as one graine of sand , an atome or a point ; for there is nothing to do but to multiply the number by it selfe , vvhich vvill amount to ninety places , vvhereof tvventie are these , 95143798134910955936 , and 70 ciphers at the end of it : vvhich amounts to a most prodigious number , and is easily supputated : for supposing that a graine of poppy doth containe 10 graines of sand , there is nothing but to compare that little bovvle of a graine of poppy , vvith a bovvle of an inch or of a foot , & that to be compared vvith that of the earth , and then that of the earth vvith that o the firmament ; and so of the rest . 2. divers metalls being melted together in one body , to finde the mixture of them . this wat a notable invention of archimedes , related by vitrivius in his architecture , where he reporteth that the gold-smith which king hiero imployed for the making of the golden crowne , which was to be dedicated to the gods , had stolen part of it , and mixed silver in the place of it : the king suspicious of the work proposed it to archimedes , if by art he could discover without breaking of the crowne , if there had been made mixture of any other metall with the gold. the way which he found out was by bathing himselfe ; for as he entred into the vessell of water , ( in which he bathed himselfe ) so the water ascended or flew out over it , and as he pulled out his body the water descended : from which he gathered that if a bowle of pure gold , silver , or other metall were cast into a vessell of water , the water proportionally according to the thing cast in would ascend ; and so by way of arithmetick the question lay open to be resolved : who being so intensively taken with the invention , leapes out of the bath all naked , crying as a man transported , i have found , i have found , and so discovered it . now some say that he took two masses , the one of pure gold , and the other of pure silver ; each equall to the weight of the crowne , and therefore unequall in magnitude or greatnesse ; and then knowing the severall quantities of water which was answerable to the crown , and the severall masses , he subtilly collected , that if the crowne occupied more place within the water than the masse of gold did : it appeared that there was silver or other metall melted with it . now by the rule of position , suppose that each of the three masses weighed 18 pound a piece , and that the masse of gold did occupie the place of one pound of water , that of silver a pound and a halfe ▪ and the crown one pound and a quarter only : then thus he might operate the masse of silver which weighed 18 pounds , cast into the water , did cast out halfe a pound of water more then the masse of gold , which weighed 18 pound , and the crowne which weighed also 18 pound , being put into a vessell full of water , threw out more water than the masse of gold by a quarter of a pound , ( because of mixt metall which was in it : ) therefore by the rule of proportion , if halfe a pound of water ( the excesse ) be answerable to 18 pound of silver , one quarter of a pound of excesse shall be answerable to 9 pound of silver , and so much was mixed in the crowne . some judge the way to be more facill by weighing the crowne first in the aire , then in the water ; in the aire it weighed 18 pound , and if it were pure gold , in the water it would weigh but 17 pound ; if it were copper it would weigh but 16 pound ; but because vve vvill suppose that gold and copper is mixed together , it vvill vveigh lesse then 17 pound , yet more than 16 pound , and that according to the proportion mixed : let it then be supposed that it vveighed in the vvater 16 pound and 3 quarters , then might one say by proportion , if the difference of one pound of losse , vvhich is betvveen 16 and 17 ) be ansvverable to 18 pound , to vvhat shall one quarter of difference be ansvverable to , vvhich is betvveen 17 and 16 ¾ , and it vvill be 4 pound and a halfe ; and so much copper vvas mixed vvith the gold. many men have delivered sundry vvayes to resolve this proposition since archimedes invention , and it vvere tedious to relate the diversities . baptista benedictus amongst his arithmeticall theoremes , delivers his vvay thus : if a masse of gold of equall bignesse to the crovvne did vveigh 20 pound , and another of silver at a capacity or bignesse at pleasure , as suppose did vveigh 12 pound , the crovvne or the mixt body would vveigh more than the silver , and lesser than the gold , suppose it vveighed 16 pound vvhich is 4 pound lesse than the gold by 8 pound , then may one say , if 8 pound of difference come from 12 pound of silver , from vvhence comes 4 pound vvhich vvill be 6 pound and so much silver vvas mixed in it , &c. 3. three men bought a quantitie of wine , each paid alike , and each was to have alike ; it happened at the last partition that there were 21 barrells , of which 7 were full , 7 halfe full , and 7 empty , how must they share the wine and vessells , that each have as many vessells one as another , & as much wine one as another ? this may be answered two wayes as followeth , and these numbers 2 , 2 , 3 , or 3 , 3 , 1 , may serve for direction , and signifies that the first person ought to have 3 barrells full , and as many empty ones , and one which is halfe full ; so he shall have 7 vessells and 3 barrels , and a halfe of liquor ; and one of the other shall in like manner have as much , so there will remaine for the third man 1 barrell full , 5 which are halfe full , and 1 empty , and so every one shall have alike both in vessells and wine . and generally to answer such questions , divide the number of vessells by the number of persons , and if the quotient be not an intire number , the question is impossible ; but when it is an intire number , there must be made as many parts as there are 3 persons , seeing that each part is lesse than the halfe of the said quotient : as dividing 21 by 3 there comes 7 for the quotient , which may be parted in these three parts , 2 , 2 , 3 , or 3 , 3 , 1 , each of which being lesse than ha●fe of 7. 4. there is a ladder which stands upright against a wall of 10 foot high , the foot of it is pulled out 6 foot from the wall upon the pavement : how much hath the top of the ladder descended ? the ansvver is , 2 foot : for by pythagoras rule the square of db , the hypothenusal is equall to the square of da 6 , & ab 10. novv if da be 6 foot , and ab 10 foot , the squares are 36 and 100 , vvhich 36 taken from 100 rests 64 , vvhose roote-quadrate is 8 so the foot of the ladder being novv at d , the toppe vvill be at c , 2 foot lovver than it vvas vvhen it vvas at b. problem . lxxxvii . witty suits or debates between caius and sempronius , upon the forme of f●gures , which geometricians call isoperimeter , or equall in circuit or compasse . marvell ●ot at it if i make the mathematicks take place at the ba●●e , and if i set forth here b●rtoleus , who witnesseth of himselfe , that being then an ancient doctor in the law , he himselfe took upon him to learne the elements and principles of geometry , by which he might set forth certaine lawes touching the divisions of fields , waters , islands , and other incident places : now this shall be to shew in passing by , that these sciences are profitable and behovefull for judges , counsellors , or such , to explaine many things which fall out in lawes , to avoid ambiguities , contentions , and suits often . 1. incident . caius had a field which was directly square , having 24 measures in circuit , that was 6 on each side : sempronius desiring to fit himselfe , prayed caius to change with him for a field which should be equivalent unto his , and the bargaine being concluded , he gave him for counterchange a piece of ground which had just as much in circuit as his had , but it was not square , yet quadrangular and rectangled , having 9 measures in length for each of the two longest sides , and 3 in breadth for each shorter side : now caius which was not the most subtillest nor wisest in the world accepted his bargaine at the first , but afterward● having conferred with a land-measures and mathematician , found that he was over-reached in his bargaine , and that his field contained 36 square measures , and the other field had but 27 measures , ( a thing easie to be knowne by multiplying the length by the breadth : ) sempronius contested with him in suite of law , and argued that figures which have equall perimeter or circuit , are equall amongst themselves : my field , saith he , hath equall circuit with yours , therefore it is equall unto it in quantitie . now this was sufficient to delude a judge which was ignorant in geometricall proportions , but a mathematician will easily declare the deceit , being assured that figures which are isoperemiter , or equall in circuit , have not alwayes equall capacitie or quantitie : seeing that with the same circuit , there may be infinite figures made which shall be more and more capable , by how much they have more angles , equall sides , and approach nearer unto a circle , ( which is the most capablest figure of all , ) because that all his parts are extended one from anothes , and from the middle or centre as much as may be : so we see by an infa●lible rule of experience , that a square is more capable of quantitie than a triangle of the same circuit , and a pentagone more than a square , and so of others , so that they be regular figures that have their sides equall , otherwise there might be that a regular triangle , having 24 measures in circuit might have more capacitie than a rectangled parallelogram , which had also 24 measures of circuit , as if it were 11 in length , and 1 inbreadth , the circuit is still 24 , yet the quantitie is but 11. and if it had 6 every way , it gives the same perimeter , viz. 24. but a quantitie of 36 as before . 2. incident . sempronius having borrowed of caius a sack of corne , which was 6 foot high and 2 foot broad , and when there was question made to repay it , sempronius gave caius back two sacks full of corne , which had each of them 6 foot high & 1 foot broad : who beleeved that if the sackes were full he was repaid , and it seems to have an appearance of truth barely looked on . but it is most evident in demonstration , that the 2 sacks of corn paid by sempronius to caius , is but halfe of that one sack which he lent him : for a cylinder or sack having one foot of diameter , and 6 foot of length , is but the 4 part of another cylinder , whose length is 6 foot , and his diameter is 2 foot : therefore two of the lesser cylinders or sackes , is but halfe of the greater ; and so caius was deceived in halfe his corne. 3. incident . some one from a common fountaine of a city hath a pipe of water of an inch diameter ; to have it more commodious , he hath leave to take as much more water , whereupon he gives order that a pipe be made of two inches diameter . now you will say presently that it is reason to be so bigge , to have just twice as 〈…〉 before : but if the magistrate of the citie understood geometricall proportions , he would soon cause it to be amended , & shew that he hath not only taken twice as much water as he had before , but foure times as much : for a circular hole which is two inches diameter is foure times greater than that of one inch , and therefore vvill cast out four times as much vvater as that of one inch , and so the deceit is double also in this . moreover , if there vvere a heap of corne of 20 foot every vvay , vvhich vvas borrovved to be paid next yeare ▪ the party having his corne in heapes of 12 foot every vvay , and of 10 foot every vvay , proffers him 4 heapes of the greater or 7 heaps of the lesser , for his ovvne heap of 20 every vvay , vvhich vvas lent : here it seems that the proffer is faire , nay vvith advantage , yet the losse vvould be neare 1000 foot . infinite of such causes do arise from geometricall figures , vvhich are able to deceive a judge or magistrate , vvhich is not somevvhat seene in mathematicall documents . problem . lxxxviii . containing sundry questions in matter of cosmography . first , it may be demanded , vvhere is the middle of the vvorld ? i speak not here mathematically , but as the vulgar people , vvho ask , vvhere is the middle of the vvorld ? in this sence to speak absolutely there is no point vvhich may be said to be the middle of the surface , for the middle of a globe is every vvhere : notvvithstanding the holy scriptures speake respectively , and make mention of the middle of the earth , and the interpreters apply it to the citie of jerusalem placed in the middle of palestina , and the habitable vvorld , that in effect taking a mappe of the vvorld , and placing one foot of the compasses upon jerusalem , and extending the other foot to the extremity of europe , asia , and afric● , you shall see that the citie of jerusalem is as a centre to that circle . 2. secondly , how much is the depth of the earth , the height of the heavens , and the compasse of the world ? from the surface of the earth unto the centre according to ancient traditions , is 3436. miles , so the vvhole thicknesse is 6872 miles , of which the whole compasse or circuit of the earth is 21600 miles . from the centre of the earth to the moone there is neare 56 semidiameters of the earth , which is about 192416 miles . unto the sunne there is 1142 semidiameters of the earth , that is in miles 3924912 ; from the starry firmament to the centre of the earth there is 14000 semidiameters , that is , 48184000 miles , according to the opinion and observation of that learned ticho brahe . from these measures one may collect by arithmeticall supputations , many pleasant propositions in this manner . first , if you imagine there were a hole through the earth , and that a milstone should be let fall down into this hole , and to move a mile in each minute of time , it would be more than two dayes and a halfe before it would come to the centre , and being there it would hang in the aire . secondly , if a man should go every day 20 miles , it would be three yeares wanting but a fortnight , before he could go once about the earth ; and if a bird should fly round about it in two dayes , then must the motion be 450 miles in an houre . thirdly , the moone runnes a greater compasse each houre , than if in the same time she should runne twice rhe circumference of the whole earth . fourthly , admit it be supposed that one should go 20 miles in ascending towards the heavens every day , he should be above 15 years before he could attaine to the orbe of the moone . fifthly , the sunne makes a greater way in one day than the moone doth in 20 dayes , because that the orbe of the sunnes circumference is at the least 20 times greater than the orbe of the moone . sixthly , if a milstone should descend from the p●ace of the sunne a thousand miles every houre , ( which is above 15 miles in a minute , farre beyond the proportion of motion ) it would be above 163 dayes before it would fall dovvne to the earth . seventhly , the sunne in his proper sphere moves more than seven thousand five hundred and seventy miles in one minute of time : novv there is no bullet of a cannon , arrovv , thunderbolt , or tempest of vvinde that moves vvith such quicknesse . eightly , it is of a farre higher nature to consider the exceeding and unmoveable quicknesse of the starry firmament , for a starre being in the aequator , ( which is just between the poles of the world ) makes 12598666 miles in one houre which is two hundred nine thousand nine hundred and seventy foure miles in one minute of time : & if a horseman should ride every day 40 miles , he could not ride such a compasse in a thousand yeares as the starry firmament moves in one houre , which is more than if one should move about the earth a thousand times in one houre , and quicker than possible thought can be imagined : and if a starre should flye in the aire about the earth with such a prodigious quicknesse , it would burne and consume all the world here below . behold therefore how time passeth , and death hasteth on : this made copernicus , not unadvisedly to attribute this motion of primum mobile to the earth , and not to the starry firmament ; for it is beyond humane sense to apprehend or conceive the rapture and violence of that motion being quicker than thought ; and the word of god testifieth that the lord made all things in number , measure , weight , and time . problem . xcii . to finde the bissextile yeare , the dominicall letter , and the letters of the moneth . let 123 , or 124 , or 125 , or 26 , or 27 , ( which is the remainder of 1500 , or 1600 ) be divided by 4 , which is the number of the leape-yeare , and that which remaines of the division shewes the leap-yeare , as if one remaine , it shewes that it is the first yeare since the bissextile or leap-year , if two , it is the second year &c. and if nothing remaine , then it is the bissextile or leap-yeare , and the quotient shews you how many bissextiles or leap-yeares there are conteined in so many yeares . to finde the circle of the sun by the fingers . let 123 , 24 , 25 , 26 , or 27 , be divided by 28 , ( which is the circle of the sunne or whole revolution of the dominicall letters ) and that which remaines is the number of joynts , which is to be accounted upon the fingers by filius esto dei , coelum bonus accipe gratis : and where the number ends , that finger it sheweth the yeare which is present , and the words of the verse shew the dominicall letter . example . divide 123 by 28 for the yeare ( and so of other yeares ) and the quotient is 4 , and there remaineth 11 , for which you must account 11 words : filius esto dei , &c. upon the joynts beginning from the first joynt of the index , and you shall have the answer . for the present to know the dominicall letter for each moneth , account from january unto the moneth required , including january , and if there be 8 , 9 , 7 , or 5 , you must begin upon the end of the finger from the thumbe and account , adam degebat , &c. as many words as there are moneths , for then one shall have the letter which begins the moneth ; then to know what day of the moneth it is , see how many times 7 is comprehended in the number of dayes , and take the rest , suppose 4 , account upon the first finger within & without by the joynts , unto the number of 4 , which ends at the end of the finger : from whence it may be inferred that the day required was wednesday , sunday being attributed to the first joynt of the first finger or index : and so you have the present yeare , the dominicall letter , the letter which begins the moneth , and all the dayes of the moneth . problem . xciii . to finde the new and full moone in each moneth . adde to t●e epact for the yeare , the moneth from march , then subtract that surplus from 30 , and the rest is the day of the moneth that it vvill be new moone , and adding unto it 14 , you shall have that full moone . note that the epact is made alwayes by adding 11 unto 30 , and if it passe 30 , subtract 30 , and adde 11 to the remainder , and so ad infinitum : as if the epact were 12 , adde 11 to it makes 23 for the epact next year , to vvhich adde 11 makes 34 , subtract 30 , rests 4 the epact for the yeare after , and 15 for the yeare follovving that , and 26 for the next , and 7 for the next , &c. problem . xciv . to finde the latitude of ● countrey . those that dwell between the north-pole and the tropicke of cancer , have their spring and summer between the 10 of march , and the 13 of september : and therefore in any day between that time , get the sunnes distance by instrumentall observation from the zenith at noone , and adde the declination of the sun for that day to it : so the aggragate sheweth such is the latitude , or poles height of that countrey . now the declination of the sunne for any day is found out by tables calculated to that end : or mechanically by the globe , or by instrument it may be indifferently had : and here note that if the day be between the 13 of september and the 10 of march , then the sunnes declination for that day must be taken out of the distance of the sunne from the zenith at noone : so shall you have the latitude , as before . prbolem xcv . of the climates of countreys , and to finde in what c●imate any countrey is under . climates as they are taken geographically signifie nothing else but when the l●ngt● of the longest day of any place , is half an houre longer , or shorter than it is in another place ( and so of the sh●rtest day ) and this account to begin from the equinoctia●l circle , seeing all countreys under it have the shortest and longest day that can be but 12 houres ; but all other countreys that are from the equinoctiall circle either towards the north or south of it unto the poles themselves , are said to be in some one climate or other , from the equinoctiall to either of the poles circles , ( which are in the latitude of 66 degr . 30 m. ) between each of which polar circles and the equinoctial circle there is accounted 24 climates , which differ one from another by halfe an hours time : then from each polar circle , to each pole there are reckoned 6. other climates which differ one from another by a moneths time : so the whole earth is divided into 60 climates , 30 being allotted to the northerne hemisphere , and 30● to the southerne hemispheare . and here note , that though these climats which are betweene the equinoctiall and the polar circles are equall one unto the other in respect of time , to wit , by halfe an houre ; yet the latitude , breadth , or internall , conteined between climate and climate , is not equall : and by how much any climate is farther from the equinoctiall than another climate , by so much the lesser is the intervall between that climate and the next : so those that are nearest the equinoctial are largest , and those which are farthest off most contracted : and to finde what climate any countrey is under : subtract the length of an equinoctiall day , to wit , 12 houres from the length of the longest day of that countrey ; the remainder being doubled shews the climate : so at london the longest day is neare 16 houres and a halfe ; 12 taken from it there remaines 4 houres and a halfe , which doubled makes 9 halfe houres , that is , 9 climates ; so london is in the 9 climate . problem . xcvi . of longitude and latitude of the earth and of the starres . longitude of a countrey , or place , is an arcke of the aequator conteined between the meridian of the azores , and the meridian of the place , and the greatest longitude that can be is 360 degrees . note . that the first meridian may be taken at pleasure upon the terrestriall globe or mappe , for that some of the ancient astronomers would have it at hercules pillars , which is at the straights at gibraltar : ptolomy placed it at the canary isl●nds , but now in these latter times it is held to be neare the azores . but why it was first placed by ptolomy at the canary islands , were because that in his time these islands were the farthest westerne parts of the world that vvas then discovered . and vvhy it reteines his place novv at saint michaels neare the azores , is that because of many accurate observations made of late by many expert navigators and mathematicians , they have found the needle there to have no variation , but to point north and south : that , is to each pole of the world : and why the longitude from thence is accounted eastwards , is from the motion of the sunne eastward , or that ptolomy and others did hold it more convenient to begin from the westerne part of the world and so account the longitude eastward from countrey to countrey that was then knowne ; till they came to the easterne part of asia , rather than to make a beginning upon that which was unknowne : and having made up their account of reckoning the longitude from the westerne part to the eastern part of the world knowne , they supposed the rest to be all sea , which since their deaths hath been found almost to be another habitable world . to finde the longitude of a countrey . if it be upon the globe , bring the countrey to the brasen meridian , and whatsoever degree that meridian cuts in the equinoctiall , that degree is the longitude of that place : if it be in a mappe , then mark what meridian passeth over it , so have you the longitude thereof , if no meridian passe over it , then take a paire of compasses , and measure the distance betweene the place and the next meridian , and apply it to the divided parallel or aequator , so have you the longitude required . of the latitude of countreys . latitude of a countrey is the distance of a countrey from the equinoctiall , or it is an arke of the meridian conteined between the zenith of the place and the aequator ; which is two-fold , viz. either north-latitude or south-latitude , either of which extendeth from the equinoctiall to either pole , so the greatest latitude that can be is but 90 degrees : if any northern countrey have the artick circle verticall , which is in the latitude of 66. gr . 30. m. the sun will touch the horizon in the north part thereof , and the longest day will be there then 24 houres , if the countrey have lesse latitude than 66. degrees 30. m. the sun will rise and set , but if it have more latitude than 66. gr . 30 m. it will be visible for many dayes , and if the countrey be under the pole , the sun will make a circular motion above the earth , and be visible for a half yeare : so under the pole there will be but one day , and one night in the whole yeare . to finde the latitude of countreys . if it be upon a globe , bring the place to the brasen meridian , and the number of degrees which it meeteth therewith , is the latitude of the place . or with a paire of compasses take the distance between the countrey and the equinoctiall , which applied unto the equinoctiall will shew the latitude of that countrey ; which is equall to the poles height ; if it be upon a mappe . then mark what parallel passeth over the countrey and where it crosseth the meridian , that shall be the latitude : but if ●o parallel passeth over it , then take the distance betweene the place and the next parallel , which applied to the divided meridian from that parallel will shew the latitude of that place . to finde the distance of places . if it be upon a globe : then with a paire of compasses take the distance betweene the two places , and apply it to the divided meridian or aequator , and the number of degrees shall shew ●e distance ; each degree being 60. miles . ●f it be in a mappe ( according to wrights pro●ection ) take the distance with a paire of com●asses between the two places , and apply this distance to the divided meridian on the mappe right against the two places ; so as many degrees as is conteined between the feet of the compasses so much is the distance between the two places . if the distance of two places be required in a particular map then with the compasses take the distance between the two places , and apply it to the scale of miles , so have you the distance , if the scale be too short , take the scale between the compasses , and apply that to the two places as often as you can , so have you the distance required . of the longitude , latitude , declination , and distance of the starres . the declination of a starre is the nearest distance of a star from the aequator ; the latitude of a starre is the nearest distance of a sarre from the ecliptick : the longitude of a starre is an ark of the ecliptick conteined between the beginning of aries , and the circle of the starres latitude , which is a circle drawne from the pole of the ecliptick unto the starre , and so to the ecliptick . the distance between two sarres in heaven is taken by a crosse-staffe or other instrument , and upon a globe it is done by taking between the feet of the compasses the two starres , and applying it to the aequator , so have you the distance betweene those two starre● . how is it that two horses or other creatures being foaled or brought forth into the world at one and the same time , that after certaine dayes travell the one lived more dayes than the other , notwithstanding they dyed together in one and the sam● moment also ? this is easie to be answered : let one of them travell toward the west and the other towards the east : then that which goes towards the west followeth the sunne : and therefore shall have the day somewhat longer than if there had been no travell made , and that which goes east by going against the sunne , shall have the day shorter , and so in respect of travell though they dye at one and the selfe same houre and moment of time , the one shall be older than the other . from which consideration may be inferred that a christian , a jew , and a saracen , may have their sabbaths all upon one and the same day though notwithstanding the saracen holds his sabath upon the friday , the jew upon the saturday , and the christian upon the sunday : for being all three resident in one place , if the saracen and the christian begin their travell upon the saturday , the christian going west , and the saracen eastwards , shall compasse the globe of the earth , thus the christian at the conclusion shall gaine a day , and the saracen shall lose a day , and so meet with the jew every one upon his owne sabbath . certaine fine observations . 1 under the equinoctiall the needle hangs in equilibrio , but in these parts it inclines under the horizon , and being under the pole it is thought it will hang verticall . 2 in these countreys which are without the tropicall circles , the sunne comes east and west every day for a halfe yeare , but being under the equinoctiall the sun is never east , nor west ▪ but twice in the yeare , to wit , the 10. of march and the 13 of september . 3 if a ship be in the latitude of 23 gr . 30 m. that is , if it have either of the tropicks verticall : then at what time the sunnes altitude is equall to his distan●e from any of the equinoctiall points , then t●e sunne is due east or west . 4 if a ship be betweene the equinoctiall and either of the tropicks , the sunne will come twice to one point of the compasse in the forenoone , that is , in one and the same position . 5 vnder the equinoctiall neare guinea there is but two sorts of windes all the year , 6 moneths a northerly winde , and 6 moneths a southerly winde , and the flux of the sea is accordingly . 6 if two ships under the equinoctiall be 100. leagues asunder , and should sayle northerly untill they were come under the articke circle , they should then be but 50 leagues asunder . 7 those which have the artick circle , verticall : when the sunne is in the tropick of cancer , the sun setteth not , but toucheth the western part of the horizon . 8 if the complement of the sunnes height at noon be found equall to the sunnes declination for that day , then the ●quinoctiall is verticall : or a shippe making such an observation , the equinoctiall is in the zenith , or direct over them , by which navigators know when they crosse the line , in their travels to the indies , or other parts . 9 the sunne being in the equinoctiall , the extremity of the stile in any sunne-dyall upon a plaine , maketh a right line , otherwise it is eclipticall , hyperbolicall , &c. 10 when the shadow of a man , or other thing upon a horizontall 〈◊〉 is equall unto it in length , then is the sunne in the middle point between the horizon and the zenith , that is , 45 degrees high . problem . xcvii . to make a triangle that shall have three right angles . open the c●passes at p●easure : and upon a , describe an arke bc. then at the same opening , place one of the feet in b , and describe the ark ac . lastly , place one of the feet of the compasses in c. and describe the arke ab· so shall you have the sphericall aequilaterall triangle abc , right angled at a , at b , and at c. that is , each angle comprehended 9● . degrees : which can never be in any plaine triangle , whether it be equilaterall , isocelse , scaleve , orthogonall , or opigonall . problem . xcviii . to divide a line in as many equall parts as one will , without compasses , or without seeing of it . this proposition hath a fallacie in it , & cannot be practised but upon a maincordion : for the mathematicall line which proceeds from the flux of a point , cannot be divided in that wise : one may have therefore an instrument which is called maincordion , because there is but one cord : and if you desire to divide your line into 3 parts , run your finger upon the frets untill you sound a third in musick : if you would have the fourth part of the line , then finde the fourth sound , a fifth , &c. so shall you have the answer . problem . xcix . to draw a line which shall incline to another line , yet never meet : against the axiome of parallels . this is done by help of a conoeide line , produced by a right line upon one & the same plaine , held in great account amongst the ancients , and it is drawne after this manner . draw a right line infinitely , and upon some end of it , as at i , draw a perpendicular line i a. augment it to h. then from a. draw lines at pleasure to intersect the line i. m. in each of which lines from the right line , im . transferre ih . viz. kb . lc.od.pe.qf.mg . then from those points draw the line h.b.c.d.e.f.g. which will not meet with the line im . and yet incline nearer and nearer unto it . problem . c. to observe the variation of the compasses , or needle in any places . first describe a circle upon a plaine , so that the sun may shine on it both before noone and afternoone : in the centre of which circle place a gn●●on or wire perpendicular as ab , and an houre before noone marke the extremitie of the shadow of ab , which suppose it be at c. describe a circle at that semidiamiter cdf . then after noone mark when the top of the shadow of ab . toucheth the circle , which admit in d ; divide the distance cd into two equall parts , which suppose at e. draw the line eaf . which is the meridian line , or line of north & south : now if the arke of the circle cd . be divided into degrees . place a needle gh , upon a plaine set up in the centre , and marke how many degrees the point of the needle g , is from e. so much doth the needle vary from the north in that place . problem . ci. how to finde at any time which way the wind is in ones chamber , without going abroad ? vpon the plancking or floore of a chamber , parlor , or hall , that you intend to have this device , let there come downe from the top of the house a hollow post , in which place an iron rod that it ascend above the house 10 , or 6 foot with a vane or a scouchen at it to shew the winds without : and at the lower end of this rod of iron , place a dart which may by the moving of the vane with the wind without , turne this dart which is within : about which upon the plaister must be described a circle divided into the 32 points of the mariners compasse pointed and distinguished to that end , then may it be marked by placi● to compasse by it ; for having noted the north point , the east , &c ▪ it is easie to note all the rest of the points : and so at any time comming into this roome , you have nothing to do but to look up to the dart , which will point you out what way the winde bloweth at that instant . problem . cii . how to draw a parallel sphericall line with great ease ? first draw an obscure line gf . in the middle of it make two points ab , ( which serves for centres then place one foot of the compasses in b , and extend the other foot to a , and describe the semicircle ac . then place one foot of the compasses in a , and extend the other foot to c , and describe the semicircle cd . now place the compasses in b , and extend the other foot unto d , and describe the semicircle df , and so ad infinitum ; which being done neatly , that there be no right line seene nor where the compasses were placed , will seeme very strange how possibly it could be drawne with such exactnes , to such which are ignorant of that way . problem . ciii . to measure an in accessible distance , as the breadth of a river with the help of ones hat onely . the way of this is easie : for having ones hat upon his head , come neare to the bank of the river , and holding your head upright ( which may be by putting a small stick to some one of your buttons to prop up the chin ) pluck downe the brim or edge of your hat untill you may but see the other side of the water , then turne about the body in the same posture that it was before towards some plaine , and marke where the sight by the brimme of the hat glaunceth on the ground ▪ for the distance from that place to your standing , is the breadth of the river required . problem . ciiii. how to measure a height with two strawes or two small stickes . take two strawes or two stickes which are one as long as another , and place them at right angles one to the other , as ab . and ac . then holding ab . parallel to the ground , place the end a to the eye at a. and looking to the other top bc. at c. by going backward or forward untill you may see the top of the tower or tree , which suppose at e. so the distance from your standing to the tower or tree , is equall to the height thereof above the levell of the eye : to which if you adde your ovvne height you have the whole height . otherwise . take an ordinary square which carpenters or other workemen use , as hkl . and placing h. to the eye so that hk . be levell , go back or come nearer untill that by it you may see the top m. for then the distance from you to the height is equall to the height . problem . cv . how to make statues , letters , bowles , or other things which are placed in the side of a high building , to be seen below of an equall bignesse . let bc. be a pillar 7 yards high , and let it be required that three yards above the levell of the eye a , viz. at b. be placed a globe , and 9 yards above b. be placed another , & 22. yards above that be placed another globe : how much shall the diameter of these globes be , that at the eye , at a , they may all appeare to be of one and the same magnitude : it is thus done , first draw a line as ak . and upon k. erect a perpendicular kx . divide this line into 27 parts ▪ and according to ak . describe an arke ky . then from k ▪ in the perpendicular kx , account● ▪ par●s , viz at l. which shall represent the former three yardes , and draw the line la. from l , in the said perpendicular reckon the diameter of the lesser globe of what magnitude it is intended to be : suppose sl , and draw the line sa . cutting the arke vk . in n. then from k. in the perpendicular account 9 yards , which admit at t. draw ta , cutting yk. in o transferre the arke mn , from a to p. and draw ap. which will cut the perpendicular in v. so a line drawne from the middle of vf . unto the visuall lines ai , and av , shall be the diameter of the next globe : lastly , account from k. in the perpendicular xk . 22 parts , and draw the line wa . cutting yk in q. then take the arke mn , and transferre it from q to r and draw ar ▪ which will cut the perpendicular in x so the line which passeth by the meddle of xw . perpendicular to the visuall line aw , and ax. be the diameter of the third globe , to wit 5 , 6. which measures transferred in the pillar bc. which sheweth the true magnitude of the globes 1 , 2 , 3. from this an architect or doth proportion his images , & the foulding of the robes which are most deformed at the eye below in the making , yet most perfect when it is set in his true height above the eye . problem . cvi. how to disg●is● or disfigure an image , as a head , an arme , a whole body , &c. so that it hath no proportion the eares to become long : the nose as that of a swan , the mouth as a coaches entrance , &c yet the eye placed at a certaine point will be seen in a direct & exact proportion . i will not strive to set a geometricall figure here , for feare it may seeme too difficult to understand , but i will indeavour by discourse how mechanically with a candle you may perceive it sensible : first there must be made a figure upon paper , such as you please , according to his just proportion , and paint it as a picture ( which painters know well enough to do ) afterwards put a candle upon the table , and interpose this figure obliquely , between the said candle and the bookes of paper , where you desire to have the figure disguised in such sort that the height passe athwart the hole of the picture : then will it carry all the forme of the picture upon the paper , but with deformity ; follow these tracts and marke out the light with a coles black head or ink : and you have your desire . to finde now the point where the eye must see it in his naturall forme : it is accustomed according to the order of perspective , to place this point in the line drawne in height , equall to the largenesse of the narrowest side of the deformed square , and it is by this way that it is performed . problem . cvii . how a cannon after that it hath shot , may be covered from the battery of the enemy . let the mouth of a cannon be i , the cannon m. his charge no , the wheele l , the axletree pb . upon which the cannon is placed , at which end towards b , is placed a pillar ae· supported with props d , c , e , f , g ▪ about which the axeltree turneth : now the cannon being to shoot , it retires to h , which cannot be directly because of the axletree , but it make a segment of a circle ▪ and hides himselfe behind the wal qr , and so preserves it selfe from the enemies battery , by which meanes one may avoid many inconveniences which might arise : and moreover , one man may more easily replace it againe for another shot by help of poles tyed to the wall , or other help which may multiply the strength . problem . cviii . how to make a lever , by which one man may alone place a cannon upon his carriage , or raise what other weight he would . first place two thick boards upright , as the figure sheweth , pierced with holes , alike opposite one unto another as cd , and ef : & let l , and m , be the two barres of iron which passeth through the holes gh , and f , k , the two supports , or props , ab . the cannon , op , the lever , rs , the two notches in the lever , and q , the hooke where the burthen or cannon is tyed to . the rest of the operation is ●cill , that the youngest schollers or learners cannot faile to performe it : to teach minerva were in vaine , and it were to mathematicians injury in the succeeding ages . problem . cix . how to make a clock with one onely wheele . make the body of an ordinary dyall , and divide the houre in the circle into 12. parts : make a great wheele in height above the axletree , to the which you shall place the cord of your counterpoize ▪ so that it may descend , that in 1● houres of time your index or needle may make one revolution , which may be knowne by a watch which you may have by you : then put a balance which may stop the course of the wheele , and give it a regular motion , and you shall see an effect as just from this as from a clock with many wheeles . problem . cx . how by help of two wheeles to make a childe to draw up alone a hogshead of water at a time : and being drawne up shall cast out it selfe into another vessell as one would have it . let r be the pit from whence water is to be drawne , p the hook to throw out the water when it is brought up ( this hook must be moveable ) let ab be the axis of the wheele sf , which wheele hath divers forkes of iron made at g , equally fastened at the wheele ; let i , be a card , which is drawne by k , to make the wheele s , to turne , vvhich vvheele s , beares proportion to the vvheele t , as 8 to ● . let n be a chaine of iron to vvhich is tyed the vessel o , and the other vvhich is in the pit : e● is a piece of vvood vvhich hath a mortes in 1 , and ● , by vvhich the cord i , passeth , tyed at the vvall , as kh , and the other piece of timber of the little vvheele as m , mortified in likevvise for the chaine to passe through : draw the cord i , by k , and the wheele will turne , & so consequently the wheele t , which will cause the vessell o to raise ; which being empty , draw the cord againe by y , and the other vessell which is in the pit ●ill come out by the same reason . this is an invention which will save labour if practised ; but here is to be noted that the pit must be large enough , to the end that it conteine two great vessels to passe up and downe one by another ▪ problem . cxi . to make a ladder of cords , which may be carryed in ones pocket : by which one may easily mount up a wall , or tree alone . take two pullies a , & d , unto that of a , let there be fastened a cramp of iron as b ; and at d , let there be fastened a staffe of a foot and a halfe long as f , then the pully a : place a hand of iron , as e , to vvhich tie a cord of an halfe inch thick ( vvhich may be of silk because it is for the pocket : ) then strive to make fast the pully a , by the help of the crampe of iron b , to the place that you intend to scale ; and the staffe f , being tyed at the pully d , put it betvveen your legges as though you vvould sit upon it : then holding the cord c in your hand , you may guide your selfe to the place required ▪ vvhich may be made more facill by the multiplying of pullies . this secret is most excellent in warre , and for lovers , its supportablenesse avoids suspition . problem . cxii . how to make a pumpe whose strength is marvelous by reason of the great weight of water that it is able to bring up at once , and so by continuance . let 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , be the height of the case about two or three foot high , and broader according to discretion : the rest of the case or concavity let be o : let the sucker of the pumpe vvhich is made , be just for the case or pumpes head 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , & may be made of vvood or brasse of 4 inches thick , having a hole at e , vvhich descending raiseth up the cover p , by which issueth forth the water , & ascending or raising up it shuts it or makes it close : rs , is the handle of the sucker tyed to the handle tx , which works in the post vz . let a , b , c , d , be a piece of brasse , g the piece which enters into the hole to f , to keep out the aire . h , i , k , l , the piece tyed at the funnell or pipe : in which playes the iron rod or axis g , so that it passe through the other piece mn , which is tyed with the end of the pipe of brasse . note , that the lower end of the cisterne ought to be rested upon a gridiron or iron grate ▪ which may be tyed in the pit , by which means lifting up and putting downe the handle , you may draw ten times more water than otherwise you could . problem . cxiii . how by meanes of a cisterne , to make water of a pit continually to ascend without strength , or the assistance of any other pumpe . let il , be the pit where one would cause water to ascend continually to ●●ach office of a house or the places which are separated from it : let there be made a receive● as a , well closed up with lead or other matter that aire enter not in , to which fasten a pipe of lead as at e , which may have vent at pleasure , then let there be made a cisterne as b , which may be communicative to a , by helpe of the pipe g , from vvhich cistern b , may issue the vvater of pipe d , vvhich may descend to h , vvhich is a little belovv the levell of the vvater of the pit as much as is gh . to the end of vvhich shall be soldered close a cock vvhich shall cast out the vvater by kh . novv to make use of it , let b be filled full of vvater , and vvhen you vvould have it run turne the cock , for then the vvater in b , vvill descend by k. and for feare that there should be vacuity , nature vvhich abhors it , vvill labour to furnish and supply that emptinesse out of the spring f , and that the pit dry not , the pipe ought to be small of an indifferent capacity according to the greatnesse or smalnesse of the spring . problem . cxiiii . how out of a fountaine to cast the water very high : different from a probleme formerly delivered . let the fountaine be bd , of a round forme ( seeing it is the most capable and most perfect figure ) place into it two pipes conjoyned as ea , and hc , so that no aire may enter in at the place of joyning : let each of the pipes have a cock g , & l : the cocke at g , being closed , open that at i ▪ & so with a squirt force the water through the hole at h , then close the cocke at a , & draw out the squirt , and open the cock at g. the aire being before rarified will extend his dimensions , and force the water with such violence , that it will amount above the height of one or two pipes : and so much the more by how much the machine is great : this violence will last but a little while if the pipe have too great an opening , for as the aire approacheth to his naturall place , so the force will diminish . problem . cxv . how to empty the water of a cisterne by a pipe which shall have a motion of it selfe . let ab , be the vessell ; cde , the pipe : hg , a little vessell under the greater , in which one end of the pipe is , viz. c , and let the other end of the pipe e. passing through the bottome of the vessell at f , then as the vessell filleth so will the pipe , and when the vessell , shall be full as farre as po , the pipe will begin to runne at e , of his owne accord , and never cease untill the vessell be wholly empty . problem cxvi . how to squirt or spout out a great height , so that one pot of water shall last a long time . let there be prepared two vessels of brasse , lead , or of other matter of equal substance as are the two vessels ab , and bd , & let them be joyned together by the two pillars mn , & ef : then let there be a pipe hg . which may passe through the cover of the vessell cd , and passe through ab , into g , making a little bunch or rising in the cover of the vessell ab , so that the pipe touch it not at the bottome : then let there be soldered fast another pipe il , which may be separated from the bottome of the vessell , and may have his bunchie swelling as the former without touching the bottome : as is represented in l , and passing through the bottome of ab , may be continued unto i , that is to say , to make an opening to the cover of the vessell ab , & let it have a little mouth as a trumpet : to that end to receive the water . then there must further be added a very smal pipe which may passe through the bottome of the vessell ab , as let it be op , and let there be a bunch ; or swelling over it as at p , so that it touch not also the bottome : let there be further made to this lesser vessell an edge in forme of a basin to receive the water , which being done poure water into the pipe il , untill the vessell cd , be full , then turne the whole machine upside downe that the vessell cd , may be uppermost , and ab , undermost ; so by helpe of the pipe gh , the water of the vessell cd , will runne into the vessel ab , to have passage by the pipe po. this motion is pleasant at a feast in filling the said vessel with wine , which will spout it out as though it were from a boyling fountaine , in the forme of a threed very pleasant to behold . problem . cxviii . how to practise excellently the reanimation of simples , in case the plants may not be transported to be replanted by reason of distance of places . take what simple you please , burne it and take the ashes of it , and let it be calcinated two houres between two creusets wel luted , and extract the salt : that is , to put water into it in moving of it ; then let it settle : and do it two or three times , afterwards evaporate it , that is , let the water be boyled in some vessel , untill it be all consumed : then there will remaine a salt at the bottome , which you shall afterwards sowe in good ground wel prepared : such as the theatre of husbandry sheweth , and you shall have your desire . problem . cviii . how to make an infalliable perpetuall motion . m●xe 5. or 6. ounces of ☿ with is equall weight of ♃ , grinde it together with 10. or 12 ounces of sublimate dissolved in a celler upon a marble the space of foure dayes , and it will become like oile , olive , which distill with fire of chaffe or driving fire , and it will sublime dry substance , then put water upon the earth ( in forme of lye ) which will be at the bottom of the limbeck , and dissolve that which you can ; filter it , then distill it , and there will be produced very subtill antomes , which put into a bottle close stopped , and keep it dry , and you shall have your desire , with astonishment to all the world , and especially to those which have travelled herein without fruit . problem . cxix . of the admirable invention of making the philosophers tree , which one may see with his eye to grow by little and little . take two ounces of aqua fortis , and dissolve in it halfe an ounce of fine silver refined in a cappell : then take an ounce of aqua fortis , and two drams of quick-silver : which put in it , and mixe these two dissolved things together , then cast it into a viall of halfe a pound of water , which may be well stopped ; for then every day you may see it grow both in the tree and in the branch . this liquid serves to black haire which is red , or white , without fading untill they fall , but here is to be noted that great care ought to be had in anointing the haire , for feare of touching the flesh : for this composition is very corrosive or searching , that as soone as it toucheth the flesh it raiseth blisters , and bladders very painfull . problem . cxx . how to make the representation of the great world ? draw salt niter out of salt earth ▪ which is found along the rivers side , and at the foot of mountaines , where especially are minerals of gold and silver : mix that niter well cleansed with ♃ , then calcinate it hermetically ▪ then put it in a limbeck and let the receiver be of glasse , well luted , and alwayes in which let there be placed leaves of gold at the bottome , then put fire under the limbeck untill vapours arise which will cleave unto the gold ; augment your fire untill there ascend no more , then take away your receiver , and close it hermetically , and make a lampe fire under it untill you may see presented in it that which nature affords us : as flowers , trees , fruits , fountaines , sunne , moone , starres , &c. behold here the forme of the limbeck , and the receiver : a represents the limbeck , b stands for the receiver . problem . cxxi . how to make a cone , or a pyramidall body move upon a table without springs or other artificiall meanes : so that it shall move by the edge of the table without falling ? this proposition is not so thornie and subtile as it seemes to be , for putting under a cone of paper a beetle or such like creature , you shall have pleasure with astonishment & admiration to those which are ignorant in the cause : for this animall will strive alwayes to free herself from the captivity in which she is in by the imprisonment of the cone : for comming neere the edge of the table she will returne to the other side for feare of falling . problem cxxii . to cleave an anvill with the blow of a pistoll . this is proper to a warrier , and to performe it , let the anvill be heated red hot as one can possible , in such sort that all the solidity of the body be softned by the fire : then charge the pistoll with a bullet of silver , and so have you infallibly the experiment . problem . cxxiii . how to r●st a capon carried in a budget at a saddle-bowe , in the space of riding 5 or 6 miles ? having made it ready and larded it , stuffe ●t with butter ; then heat a piece of steele which may be formed round according to the length of the capon , and big enough to fill the belly of it , and then stop it with butter ; then wrap it up well and inclose it in a box in the budget , and you shall have your desire : it is said that count mansfield served himse●fe with no others , but such as were made ready in this kinde , for that it loseth none of its substance , and it is dressed very equally . problem . cxxiv . how to make a candle burne and continue three times as long as otherwise it would ? vnto the end of a candle half●burned stick a farthing lesse or more , to make it hang perpendicular in a vessel of water , so that it swimme above the water ; then light it , and it will susteine it self & float in this manner ; and being placed into a fountaine , pond , or lake that runnes slowly , where many people assemble , it will cause an extreme feare to those which come therein in the night , knowing not what it is . problem . cxxv . how out of a quantitie of wine to extract that which is most windy , and evill , that it hurt not a sick person ? take two vials in such sort that they be of like greatnesse both in th● belly and the neck ; fill one of them of wine , and the other of water : let the mouth of that which hath the water be placed into the mouth of that which hath the wine , so the water shall be uppermost , now because the water is heavier than the wine , it will descend into the other viall , and the wine which is lowest , because it is highest will ascend above to supply the place of the water , and so there will be a mutuall interchange of liquids , and by this penetration the wine wil lose her vapors in passing through the water . problem cxxvi . how to make two marmouzets , one of which shall light a candle , and the other put it out ? upon the side of a wall make the figure of a marmouzet or other animall or forme , and right against it on the other wall make another ; in the mouth of each put a pipe or quill so artificially that it be not perceived ; in one of which place salt peter very fine , and dry and pulverised ; and at the end set a little match of paper , in the other place sulphur beaten smal , then holding a candle lighted in your hand , say to one of these images by way of command , blow out the candle ; then lighting the paper with the candle , the salt-peter wil blow out the candle immediatly , and going to the other image ( before the match of the candle be out ) touch the sulphur with it and say , light the candle , & it will immediatly be lighted , which will cause an admiration to those which see the action , if it be wel done vvith a secret dexterity . problem . xxvii . how to keepe wine fresh as if it were in a celler though it were in the heat of summer , and without ice or snow , yea though it were carried at a saddles bow , and exposed to the sun all the day ? set your wine in a viall of glasse ; and place it in a box made of wood , leather , or such like : about which vial place salt-peeter , and it will preserve it and keep it very fresh : this experiment is not a little commodious for those which are not neare fresh waters , and whose dwellings are much exposed to the sunne . puoblem . cxxviii . to make a cement which indureth or lasteth as marble , which resisteth aire and water without ever disjoyning or uncementing ? take a quantity of strong and gluing morter vvell beaten , mixe vvith this as much nevv slaked lime , and upon it cast oile of olive or linseed-oile , and it vvill become hard as marble being applyed in time . problem . cxxix . how to melt metall very quickly , yea in a shell upon a little fire . make a bed upon a bed of metall with pouder of sulphur , of salt-peeter , and saw-dust alike ; then put fire to the said pouder with a burning charcole , and you shall see that the metall will dissolve incontinent and be in a masse . this secret is most excellent , and hath been practised by the reverend father mercen●● of the order of the minims . problem . cxxx . how to make iron or steele exceeding hard ? qvench your blade or other instrument seven times in the blood of a male hog mixt with goose-grease , and at each time dry it at the fire before you wet it : and it will become exceeding hard , and not brittle , which is not ordinary according to other temperings and quenchings of iron : an experiment of small cost , often proved , and of great consequence for armorie in warlike negotiations . prbolem cxxxi . to preserve fire as long as you will , imitating the inextinguible fire of vestales . after that you have extracted the burning spirit of the salt of ♃ , by the degrees of fire , as is required according to the art of chymistrie , the fire being kindled of it selfe , break the limbeck , and the irons which are found at the bottome will flame and appeare as burning coles as soone as they feele the aire ; which if you promptly inclose in a viall of glasse , and that you stop it exactly with some good lute : or to be more assured it may be closed up with hermes wax for feare that the aire get not in . then will it keep more than a thousand yeares ( as a man may say ) yea at the bottome of the sea ; and opening it at the end of the time , as soone as it feeles the aire 〈◊〉 takes fi●e ▪ with which you may light a match . this secret merits to be travelled after and put in practice , for that it is not common , and full of astonishment , seeing that all kinde of fire lasteth but as long as his matter lasteth , and that there is no matter to be found that will so long in●●●e . artificiall fire-workes : or the manner of making of rockets and balls of fire , as well for the water , as for the aire ; with the composition of starres , golden-rain , serpen●s , lances , whee●s of fire and such like , pleasant and recreative . of the composition for rockets . in the making of rockets , the chiefest thing to be regarded is the composition that they ought to be filled with ; forasmuch as that which is proper to rockets which are of a lesse sort is very improper to those which are of a more greater forme ; for the fire being lighted in a great concave , which is filled with a quick composition , burnes with great violence ; contrarily , a weak composition being in a small concave , makes no effect : therefore we shall here deliver in the first place rules and directions , which may serve for the true composition , or matter with which you may charge any rocket , from rockets which are charged but with one ounce of powder unto great rockets which requireth for their charge 10 pound of powder , as followeth . for rockets of one ounce . vnto each pound of good musket powder smal beaten , put two ounces of smal cole dust , and with this composition charge the rocket . for rockets of 2 or 3 ounces . vnto every foure ounces and a halfe of powder dust , adde an ounce of salt-peter , or to every 4 ounces of powder dust , adde an ounce of cole dust . for rockets of 4 ounces . vnto every pound of powder dust adde 4 ounces of salt peter & one ounce of cole dust : but to have it more slow , unto every 10. ounces of good dust powder adde 3 ounces of salt-peter , and 3 ounces of cole dust . for rockets of 5 or 6 ounces . vnto every pound of powder dust , adde 3 ounces and a halfe of salt peter , and 2 ounces and a halfe of coledust , as also an ounce of sulphur , and an ounce of fyle dust . for rockets of 7 or 8 ounces . vnto every pound of powder dust adde 4 ounces of salt peter , and 3 ounces of sulphur . of rockets of 10 or 12 ounces . vnto the precedent composition adde halfe an ounce of sulphur , and it will be sufficient . for rockets of 14 or 15 ounces . vnto every pound of powder dust adde 4 ounces of salt peter , or cole dust 2 ¼ ounces of sulphur and file dust of 1 ¼ ounce . for rockets of 1 , pound . vnto every pound of powder dust adde 3 ounces of cole dust , and one ounce of sulphur . of rockets of 2 , pound . vnto every pound of powder dust adde 9 ½ ounces of salt peter , of cole dust 2 1 / ● ounces , filedust 1 ● / 2 ounce , and of sulphur ¾ of ounce . for rockets of 3 , pound . vnto every pound of salt peter adde 6 ounces of cole dust , and of sulpher 4 , ounces . for rockets of 4 , 5 , 6 , or 7 , pound . vnto every pound of salt peter adde 5 ounces of cole dust , and 2 ½ ounces of sulphur . for rockets of 8 , 9 , or 10 pound . vnto every pound of salt peter , adde 5 ½ ounces of cole dust , and of sulphur 2 ½ ounces . here note that in all great rockets , there is no powder put , because of the greatnesse of the fire which is lighted at once , which causeth too great a violence , therefore ought to be filled with a more weaker composition . of the making of rockets and other fireworkes . for the making of rockets of sundry kindes , divers moulds are to be made , with their rolling pins , breaths , chargers , &c. as may be seen here in the figure . and having rolled a case of paper upon the rolling pin for your mould , fill it with the composition belonging to that mould as before is delivered : now may you load it on the top , with serpents , reports , stars , or golden raine : the serpents are made about the bignesse of ones little finger , by rolling a little paper upon a small stick , and then tying one end of it , and filling it with the mixt composition somewhat close , and then tying the other end . the reports are made in their paper-cases as the serpents , but the paper somewhat thicker to give the greater report . these are filled with graine-powder or halfe powder and halfe composition , and tying both ends close , they are finished . the best kinde of starres are made with this mixture following ; unto every 4 ounces of salt-peter , adde 2 ounces of sulphur , and to it put 1. ounce of powder-dust , and of this composition make your starres , by putting a little of it within a small quantity of towe ; and then tying it up in the form of a ball as great as an hasel-nut or a little wal-nut , through which there must be drawne a little primer to make it take fire . touching the making of the golden raine , that is nothing but filling of quilles with the composition of your rockets somewhat hard . now if the head of a rocket be loaded with a thousand of those quilles , it s a goodly sight to see how pleasantly they ●pread themselves in the aire , and come downe like streames of gold much like the falling downe of snow being agitated by some turbulent winde . of recreative fires . 1 phil●strates saith , that if wine in a platter be placed upon a receiver of burning coles , to exhale the spirit of it , and be inclosed within a cupboard or such like place , so that the aire may not go in , nor out , and so being shut up for 30 yeares , he that shall open it , having a wax candle lighted , and shall put it into the cubboard there will appeare unto him the figure of many cleare starres . 2 if aquavitae have camphire dissolved in it ; and be evaporated in a close chamber , where there is but a charcole fire , the first that enters into the chamber with a candle lighted , will be extremely astonished , for all the chamber will seeme to be full of fire very subtile , but it will be of little continuance . 3 candles which are deceitful are made of halfe powder , covered over with tallow , and the other halfe is made of cleane tallow , or waxe , with an ordinary week ; this candle being lighted , and the upper halfe consumed , the powder will take fire , not without great noise and astonishment to those which are ignorant of the cause . 4 a dozen or twenty smal serpents placed secretly under a candlestick that is indifferent big , which may have a hole passe through the socket of it to the candle , through which a piece of primer may be placed , and setting a smal c●ndle in the socket to burne according to a time limited : which candlestick may be set on a side table without suspition to any ; then when the candle is burned , that it fires the primer , that immediately will fire all the serpents , which overthrowing the candlestick will flye here and there , intermixing themselves , sometimes in the aire , sometimes in the planching , one amongst another , like the crawling of serpents , continuing for a pretty while in this posture , and in extinguishing every one will give his report like a pistoll ; this will not a little astonish some , thinking the house will be fired , though the whole powder together makes not an ounce , and hath no strength to do such an effect . how to make fire run up and downe , forward and backward take small rockets , and place the taile of one to the head of the other upon a cord according to your fancie , as admit the cord to be abcdefg . give fire to the rocket at a , which will flye to b , which will come back againe to a , and fire another at c , that will flie at d , which will fire another there , and fl●e to e , and that to f , and so from f , to g , and at g , may be placed a pot of fire , viz. gh . which fired will make good sport ▪ bec●u●e the serpents which are in it will variously ●ntermix themselves in the aire , and upon the ground , and every one will extinguish with a report : and here may you note that upon the rockets may be placed fierie dragons , combatants , or such like to meet one another , having lights placed in the concavity of their bodies which will give great grace to the action . how to make wheels of fire . take a hoop , and place two lath● acrosse one the other ; upon the crossing of which make a hole , so that it may be placed upon a pin to turne easily , as the figure q. sheweth upon the sides of which hoope or round circle place your rockets , to which you may place lances of fire between each rocket : let this wheele be placed upon a standard as here is represented , and place a piece of primer from one lance to another , then give fire at g , which will fire f , that b , that will fire d , that c , and that will fire the rocket at a ▪ then immediatly the wheel will begin to move , and represent unto the spectators a circle of changeable fire , and if pots of fire be tied to it , you will have fine sport in the turning of the wheele and casting out of the serpents . of night-combatants . clubbes , targets , faulchons , and maces charged with severall fires , do make your night-combatants , or are used to make place amongst a throng of people . the clubbes at the ends are made like a round panier with small sticks , filled with little rockets in a spirall forme glu●d and so placed that they fire but one after another ; the ma●es are of divers fashions , some made oblong at the end , some made of a sp●rall forme , but all made hollow to put in several composition , and are boared in divers places , which are for sundry rockets , and lances of weak composition to be fired at pleasure : the faulchons are made of wood in a bowing forme like the figure a , having their backes large to receive many rockets , the head of one neare the neck of another , glued and fastned well together , so that one being spent another may be fired . 〈◊〉 targets are made of wooden thinne boards , which are channeled in spiral lines to containe primer to fire the rockets one after another , which is all covered with thinne covering of wood , or pastboard , boared with holes spirally also ; which rockets must be glued and made fast to the place of the channels : now if two men , the one having a target in his hand , and the other a falchon , or mace of fire , shall begin to fight , it will appeare very pleasant to the spectators : for by the motion of fighting , the place will seem to be ful of streames of fire : and there may be adjoyned to each target a sunne or a burning comet with lances of fire , which will make them more beautifull and resplendent in that acti●n . of standing fires . svch as are used for recreation , are collossus , statues , arches , pyramides , chariots , chaires of triumph and such like , which may be accommodated with rockets of fire , and beautified with sundry other artificiall fires , as pots of fire for the aire which may cast forth several figures , scutchions , rockets of divers sorts , starres , crownes , leaters , and such like , the borders of which may be armed with sundry lances of fire , of small flying rockets with reports , flames , of small birds of cypres , lan●hornes of fire , candles of divers uses , and colours in burning : and whatsoever the fancie of an ingenious head may allude unto . of pots of fire for the aire , which are throwne out of one case one after another of a long continuance . make a long trunk as ag , and by the side ah , let there be a channel which may be fiered with slow primer or composition ; then having charged the trunk ag , with the pots of fire for the aire at igec , and make the trunk ag , very fast unto a post as ik , give fire at the top as at a , which burning downewards will give fire to c , and so throw out that pot in the aire , vvhich being spent , in the meane time the fire vvil-burne from b to d , and so fire e , and throvv it out also into the ayre , and so all the rest one after another vvill be throvvne out : and if the pots of fire for the aire vvhich are cast out , be filled vvith diverse fire-vvorkes , they vvill be so much the more pleasant to the beholders . these trunks of fire doe greatly adorne a firevvorke , and may conveniently be placed at each angle of the vvhole vvorke . of pots of fire for the ground . many pots of fire being fired together do give a fine representation , and recreation to the spectators , and cause a vvonderfull shout amongst the common people vv ch are standers by ; for those pots being filled vvith balles of fire and flying serpents for the aire , they vvill so intermix one vvithin another , in flying here and there a little above the ground , and giving such a volley of reports that the aire vvill rebound vvith their noise , and the vvhole place be filled vvith sundry streames of pleasant fire ; which serpents will much occupie these about the place to defend themselves in their upper parts , when they will no lesse be busied by the balls of fire , which seeme to annoy their feet . of balles of f●re . these are very various according to a mans fancy ; some of which are made with very small rockets , the head of one tyed to the neck of another : the ball being made may be covered over with pitch except the hole to give fire to it ; this ball will make fine sport amongst the standers by , which will take all a fire , and rolle sometimes this way , sometimes that way , between the legs of those that are standers by ▪ if they take not heed , for the motion will be very irregular , and in the motion will cast forth severall fires with reports . in the second kind there may be a channell of iron placed in divers places in spirall manner , against which may be placed as many small petards of paper as possible may be , the channell must be full of slow comp●sition , and may be covered a● the former , and made fit with his rockets in the middle : this ball may be shot out of a morter peece , or charged on the top of a roc●et : for in its motion it will flye here and there , and give many reports in the aire : because of the discharge of the petards . of fire upon the water . places which are 〈◊〉 upon rivers or great ponds , are proper to make recreative fres on : and if it be required to make some of consequence , such may conveniently be made upon two bo●ts , upon which may be built two beasts , turrets , pagins , castles , or such like , to receive or hold the diversity of fire workes that may be made within it , in which may play 〈◊〉 fires , petards , &c. and cast out many simple granadoes , balls of fire to burne in the water-serpents and other things , and often times these boates in their incounters may hang one in another , that so the combatants with the targets , and maces may fight ; which will give great ▪ content to the eyes of those which are lookers on , and in the conclusion fire one another , ( for which end they were made : ) by which the dexterity of the one may be knowne in respect of the other , and the triumph and victory of the fight gotten . of balles of fire which move upon the water . these may be made in forme of a ball stuffed with other little balls , glued round about and filled with composition for the water , which fiered , will produce marvellous and admirable effects , for which there must be had little cannons of white iron , as the ends of small funnels ; these iron cannons may be pierced in sundry places , to which holes , may be set small balles ful of composition for the water which small balls must be peirced deep and large , and covered with pitch , except the hole : in which hole must be first placed a little quantitie of grain-powder ; and the rest of the hole filled up with composition ; and note further that these iron cannons , must be filled with a slow composition ; but such which is proper to burne in the water : then must these cannons with their small balls be put so together that it may make a globe , and the holes in the cannons be answerable to the hollow balls , and all covered over with pitch and tallow ; afterwards pierce this ball against the greatest cannon ( to which all the lesser should answer ) unto the composition , then fire it , and when it begins to blow , throw it into the water , so the fire comming to the holes will fire the graine powder , the which will cause the balls to separate and fly here and there , sometimes two at a time , sometimes three , sometimes more , which will burne within the water with great astonishment and content to those which see it . of lances of fire . standing lances of fire , are made commonly with hollow wood , to containe sundry petards , or rockets , as the figure here sheweth , by which is easie to invent others occording to ones fancy . these lances have wooden handles , that so they may be fastned at some post , so that they be not overthrowne in the flying out of the rockets or petards : there are lesser sorts of lances whose cases are of three or foure fouldings of paper of a foote long , and about the bignesse of ones finger , which are filled with a composition for lances . but if these lances be filled with a composition , then ( unto every 4 ouncs of powder add● 2 ounces of salt-peter , and unto that adde 1 ounce of sulphur ) it will make a brick fire red before it be halfe spent , if the lance be fiered and held to it : and if 20 such lances were placed about a great rocket and shot to a house or ship , it would produce a mischievous effect . how to shoot a rocket horizontall , or otherwise . vnto the end of the rocket place an arrow which may not be too heavy , but in stead of the feathers let that be of thinne white tinne plate , and place it upon a rest , as here you may see by the figure , then give fire unto it , and you may see how serviceable it may be . to the head of such rockets , may be placed petards , balls of fire , granadoes , &c. and so may be applyed to warlike affaires . how a rocket burning in the water for a certaine time , at last shall fly up in the aire with an exceeding quickness . to do this , take two rockets , the one equall to the other , and joyne them one unto another in the middle at c. in such sort that the fire may easily passe from one to another : it being thus done , tye the two rockets at a stick in d , and let it be so long and great that it may make the rockets in the water hang , or lye upright : then take a pack-thread and tye it at g. and let it come double about the stick dm . at 〈◊〉 and at that point hang a bullet of some weight as k. for then giving fire at a. it will burne to b. by a small serpent filled there and tyed at the end , and covered so that the water injure it hot , which will fire the rocket bd , and so mounting quick out of the water by the loose tying at c. and the bullet at the pack-thread , will leave the other rocket in the vvater : and so ascend like a rocket in the aire , to the admiration of such as knovv not the secrecie . of the framing of the parts of a fire-worke , together , that the severall workes may fire one after another . cause a frame to be made as abcd. of tvvo foot square every vvay , or thereabouts ( according to the quantity of your severall vvorkes ) then may you at each angle have a great lance of fire to stand , vvhich may cast out pots of fire as they consume : upon the ledges ab.bc. and cd . may be placed small lances of fire about the number of 30 or 60 , some sidevvise , and others upright , betvveen these lances may be placed pots of fire sloping outvvards , but made very fast , and covered very close , that they chance not to fire before they should ; then upon the ledges re. fg.hi . and ad may be placed your soucisons , and behinde all the vvork may be set your boxes of rockets , in each of vvhich you may place 6 , 9 , ●2 . or 20 small rockets : novv give fire at a. ( by help of a piece of primer going from one lance to another ) all the lances vvill instantly at once be lighted , and as soone as the lance at a is consumed , it vvill fire the channell vvhich is made in the ledge of the frame vvhich runnes under the pots of fire , and as the fire goes along burning , the pots vvill be cast forth , and so the rank of pots upon the sides of the frame ab.bc. and cd . being spent , the soucisons vvill begin to play being fiered also by a channel vvhich runnes under them , upon the ledges ad , hi●g , and re. then when the soucisons are spent upon the last ledge re. there may be a secret channel in the ledge cd which may fire the box of rockets at k. and may fire all the rest one after another , which boxes may be all charged with severall fire-workes : for the rockets of the first box may be loaden with serpents , the second with stars , the third with reports , the fourth with golden raine , and the fifth with small flying serpents ; these mounting one after another and flying to and fro will much inlighten the aire in their ascending , but when these rockets discharge themselves above , then will there be a most pleasant representation , for these fires will dilate themselves in divers beautifull formes , some like the branching of trees , others like fountaines of water gliding in the aire , others like flashes of lightning , others like the glittering of starres , giving great contentment , and delight to those which behold them ; but if the worke be furnished also with balons ( which is the chiefest in recreative fire-works ) then shall you see ascending in the aire but as it were onely a quill of fire , but once the balon taking fire , the aire will seeme more than 100. foot square full of crawling , and flying serpents , which will extinguish with a volley of more than 500 reports : and so fill the aire and firmament with their rebounding clamour . the making of which with many other rare and excellent fire-workes , and other practises , not onely for recreation , but also for service : you may finde in a book intituled artificiall fire-workes , made by mr. malthas ( a master of his knowledge ) and are to be sold by vvilliam leake , at the crowne in fleet-street , between the two temple-gates . conclusion . in this booke we have nothing omitted what was materiall in the originall , but have abundantly augmented it in sundry experiments : and though the examinations are not so full , and manifold ; yet ( by way of brevitie ) we have expressed fully their substance , to avoid prolixitie , and so past by things reiterated . finis . printed or sold by william leak , at the crovvne in fleetstreet neere the temple , these books following . york's heraldry , folio a bible of a very fair large roman letter , 4● orlando f●rios● folio . callu learned readings on the scat. 21. hen. 80. cap 5 of sewer● perkins on the laws of england . wi●kinsons office of she●●●fs . vade mecum , of a justice of peace . the book of fees. peasons law. mirrour of just●ce . topicks in the laws of england . sken de significatione verborum . delaman's use of the horizontal quadrant . wilby's 2d set of musique , 345 and 6 parts . corderius in english. d●ctor fulk's meteors . malthus fire-workes . nyes gunnery & fire-workes c●to ma●or with annotations , by wil. austin esquire . mel helliconium , by alex. ross● nosce teipsum , by sr john davis animadversions on lil●i●s grammer . the history of vienna , & paris lazarillo de tormes . hero and l●ander , by g. chapman and christoph. marlow . al●ilia or philotas loving folly . bishop andrews sermons . adams on ●eter . posing of the accidence . am●dis de gaule . guillieliam's heraldry . herberts travels . bacc●s tales . man become guilty , by john francis sen●●t , and englished by henry earl of monmouth . the ideot in 4 books ; the first and second of wisdom ; the third of the mind , the fourth of s●●tick experiments of the ballance . the life and reign of hen. the eighth , written by the l. herbet cornwallis essays , & paradoxes . clenards greek g●ammar 80 a●laluci● , or the house of light : a discourse written in the year 1651 , by sn . a modern speculator . a tragedy written by the most learned hugo grotius called , christus patience , and translated into engl. by george sand ▪ the mount of olives : or sollitary devotions , by henry vaughan silurist vvith an excellent discourse of man in glory , written by the reverend anselm arch bishop of canterbury . the fort royall of holy scriptures by i. h. playes . hen. the fourth . philaster . the wedding . the hollander . maids tragedie . king & no k. the gratefull servant . the strange discovery . othello ; the moor of venice . the merchant of venice . the description and use of the dovble horizontall dyall . whereby not onely the houre of the day is shewn ; but also the meridian line is found : and most astronomicall questions , which may be done by the globe : are resolved . invented and written by w. o. whereunto is added , the description of the generall horologicall ring . london , printed for william leake , and are to be sold at his shop at the signe of the crown in fleetstreet , between the two temple gates . 1652. the description , and use of the double horizontall diall . there are upon the plate two severall dyals . that which is outermost , is an ordinary diall , divided into houres and quarters , and every quarter into three parts which are five minutes a piece : so that the whole houre is understood to contein 60 minutes . and for this dyall the shadow of the upper oblique , or slanting edge of the style , or cocke , doth serve . the other diall , which is within , is the projection of the upper hemisphaere , upon the plain of the horizon : the horizon it self is understood to be the innermost circle of the limbe : and is divided on both sides from the points of east and west into degrees , noted with 10.20.30 , &c. as far as need requireth : and the center of the instrument is the zenith , or verticall point . within the horizon the middle straight line pointing north and south upon which the style standeth , is the meridian or twelve a clock line : and the other short arching lines on both sides of it , are the houre lines , distinguished accordingly by their figures : and are divided into quarters by the smaller lines drawn between them : every quarter conteining 15 minutes . the two arches which crosse the houre lines , meeting on both sides in the points of intersection of the sixe a clocke lines with the horizon , are the two semicircles of the ecliptick or annuall circle of the sun : the upper of which arches serveth for the summer halfe yeere ; and the lower for the winter half yeer : and therefore divided into 365 dayes : which are also distinguished into twelve moneths with longer lines , having their names set down : and into tenths and fifts with shorter lines : and the rest of the dayes with pricks as may plainly be seene in the diall . and this is for the ready finding out of the place of the sun every day : and also for the shewing of the suns yeerely motion , because by this motion the sun goeth round about the heavens in the compasse of a yeer , making the four parts , or seasons thereof ▪ namely , the spring in that quarter of the ecliptick which begins at the intersection on the east side of the diall ▪ and is therefore called the vernall intersection . then the summer in that quarter of the ecliptick which begin at the intersection with the meridian in the highest point next the zenith . after that , autumne in that quarter of the ecliptick which beginneth at the intersection on the west side of the diall , and is therefore called the au●umna●l intersection and lastly , the winter in that quarter of the ecliptic● , which beginneth at the intersection , with the meridian i● the lowest point next the horizon . but desides this yeerely motte● , the sun hath a diurnall , or daily motion , whereby it maketh day and night , with all the diversities and inaequalities thereof : which is expressed by those other circles drawn crosse the houre lines ; the middlemost whereof , being grosser then the rest , meeting with the ec●iptick in the points of the vernall , and autumnall intersections ▪ is the equinoctiall : and the rest on both sides of it are called the parallels , or diurnall arch of the sun , the two outermost whereof are the tropicks , because in them the sun hath his furthe●t digression or declination from the aequinoctiall , which is degrees 23 1 / ● ▪ and thence beginneth againe to return towards the equinoctiall . the upper of the two tropicks in this nor northerne hemisphere is the trop●ck of cancer , and the sun being in it , is highest into the north , making the longest day of summer : and the lower next the horizon is the tropick of capricorne ; and the sun being in it , is lowest into the south , making the shortest day of winter . between the two tropicks and the aequinoctiall , infinite such parallel circles are understood to be conteined : for the sun , in what point soever of the ecliptick it is carried ▪ describeth by his lation a circle parallel to the aequinoctiall : yet those parallels which are in the instrument , though drawn but to every second degree of declination , may be sufficient to direct the eye in imagining and tracing out through every day of the whole yeere in the ecliptick , a proper circle which may be the diurnall arch of the sun for that day . for upon the right estimation of that imaginary parallel doth the manifold use of this instument especially rely : because the true place of the sun all that day is in some part or point of that circle . wherefore for the bet●er conceiving and bearing in minde thereof , every fift parallel is herein made a little g●osser then the rest . for this inner diall serveth the shadow of the upright edge of the style ; which i therefore call the upright shadow . and thus by the eye and view onely to behold and comprehend the course of the sun ▪ throughout the whole yeere both for his annuall and diurnall motion , may be the first use of this instrument . ii use. to finde the declination of the sun every day . looke the day of the moneth proposed in the ecliptick , and mark how many degrees the prick shewing that day , is distant from the equinoctiall , either on the summer or winter side , viz. north or south . example 1. what will the declination of the sun be upon the eleven●h day of august ? look the eleventh day of august and you shall finde it in the sixth circle above the ●quinoctiall : now because each parallel standeth ( as hath been said before ) for two degrees , the sun shall that day decline northwards 12. degrees . example 2. what declination hath the sun upon the 24 day of march ? look the 24 day of march , and you shall finde it betweene the second and third northern parallels , as it were an half and one fift part of that di●tance from the second : reckon therefore four degrees for the two circles , and one de●ree for the halfe space : so shall the suns declination be five degrees , and about one fift part of a degree northward that same day . example 3. what declination hath the sun upon the 13 day of november ? look the 13 day of november , and you shall finde it below the equinoctiall ten parallels , and about one quarter which is 20 degrees and an halfe southward . so much is the declination . and according to these examples judge of all the rest . iii. use. to finde the diurnall arch , or circle of the suns course every day . the sun every day by his motion ( as hath been said ) describeth a circle parallel to the ●quinoctiall , which is either one of the circles in the diall , or some-where ●etween two of them . first , theref●re se●k the day of the moneth ; and if it fall upon one of those parallels ; that is the circle of the suns course that same day : but if it fall betweene any two of the parallels , imagine in your mind● , and estimate with your eye , another parallel th●ough that point betweene those two parallels keeping still the same distance from each of them . as in the first of the three former examples , the circle of the suns course upon 11 of august ▪ shal be the very sixt circle above the equinoctiall toward the cente● . in ●xample 2. the circle of the suns cou●se upon the 24 of march shall be an imaginary circle between the second and third parallels still keeping an half of that space , and one fifth part more of the rest , from the second . in example 3. the circle of the suns course upon the 13 of november : shall be an imaginary circle between the tenth and eleventh parallels below the equinoctiall , still keeping one quarter of that space from the tenth . iiii use. to finde the r●sing and setting of the sun eve●yday . 〈…〉 ( as was last shewed ) the imaginary circle or parallel of the suns course for that day , and marke the point where it meeteth with the horizon , both on the east and w●st sides , for that is the very point of the suns r●sing , and setting that same day , and the houre lines which are on both sides of it , by proportioning the distance reasonably , according to 15 minutes for the quarter of the houre , will shew the houre of the suns rising on the east side , and the suns setting on the west side . v use. to know the reason and manner of the increasing and decreasing of the nights●hroughout ●hroughout the whole yeere . when the sun is in the equinoctiall , it riseth and setteth at 6 a clock , for in the instrument the intersection of the equinoctiall , and the ecliptick with the horizon is in the six a clocke circle on both sides . but if the sun be out of the equinoctial , declining toward the north , the intersections of the parallel of the sun with the horizon is before 6 in the morning , and after 6 in the evening : and the diurnall arch greater then 12 houres ; and so much more great , the greater the northerne declination is . againe , if the sun be declining toward the south , the intersections of the parallel of the sun , with the horizon is after 6 in the morning , and before 6 in the evening : and the diurnall arch lesser then 12 houres ; and by so much lesser , the greater the southerne declination is . and in those places of the ecliptick in which the sun most speedily changeth his declination , the length also of the day is most a●tered : and where the ecliptick goeth most parallel to the equinoctiall changing the declination , but little altered . as for example , when the sun is neer unto the equinoctiall on both sides , the dayes increase and also decrease suddenly and apace ; because in those places the ecliptick inclineth to the equinoctiall in a manner like a streight line , making sensible declination . again , when the sun is neere his greatest declination , as in the height of summer , and the depth of winter , the dayes keep for a good time , as it were , at one stay , because in these places the ecliptick is in a manner parallel to the equinoctiall , the length o● the day also is but little , scarce altering the declination : and because in those two times of the yeer , the sun standeth as it were still at one declination , they are called the summer solstice , and winter solstice . and in the mean space the neerer every place is to the equinoctiall , the greater is the diversity of dayes . wherefore , we may hereby plainly see that the common received opinion , that in every moneth the dayes doe equally increase , is erroneous . also we may see that in parallels equally distant from the equinoctiall , the day on the one side is equall to the night on the other side . vi. vse . to finde how far the sun riseth , and setteth from the true east and west points , which is called the suns amp●itude ortive , and occasive . seek out ( as was shewed in iii vse ) the imaginary circle , or parallel of the suns course , and the points of that circle in the horizon , on the east and west sides cutteth the degree of the amplitude ortive , and occasive . vii use. to finde the length of every day and night . double the houre of the sunnes setting , and you shal have the length of the day ; & double the hour of the sunnes rising , and you shal have the length of the right . viii vse . to finde the true place of the sun upon the dyall , that is , the point of the instrument which answereth to the place of the sun in the heavens at any time , which is the very ground of all the questions following . if the dyall be fixed upon a post : look what a clock it is by the outward dyall , that is , look what houre and part of houre the shadow of the slanting edge of the style sheweth in the outward limbe . then behold the shadow of the upright edge , and marke what point thereof is upon that very houre and part in the inner dyall among the parallels , that point is the true place of the sunne at the same instant . if the dyal be not fixed , and you have a meridian line no●ed in any window where the sunne shineth : place the meridian of your dyal upon the meridian line given , so that the top of the stile may point into the north : and so the dyal is as it were fixed , wherefore by the former rule you may finde the place of the sunne upon it . if the dyal be not fixed , neither you have a meridian line , but you know the true houre of the day exactly : hold the dyal even and parallel to the horizon , moving it till the slanting edge of the stile cast his shadow justly upon the time or houre given ; for then the dyal is truly placed , as upon a post . seek therefore what point of the upright shadow falleth upon that very houre , and there is the place of the sun. but if your dyal be loose , and you know neither the meridian nor the time of the day . first , by the day of the moneth in the ecliptique , finde the su●s parallel , or d●urnall arch for that day ▪ then holding the dyal level to the horizon , move it every way untill the slanting shadow of the style in the outward limbe , and the upright shadow in the sunnes diurnal arch , both shew the very same houre and minute , for that very point of the sunnes parallel , which the upright shadow cutteth , is the true place of the sun on the dyal at that present . but note that by reason of the thicknes of the style , and the bluntnesse of the angle of the upright edge , the sun cannot come unto that edge for some space before and after noone . and so during the time that the sunne shineth not on that upright edge , the place of the sunne in the dyal cannot be found . wherefore they that make this kinde of double dyal , are to be careful to file the upright edge of the style as thinne and sharpe as possible may be . that which hath here bin taught concerning the finding out the suns true place in the dyal , ought perfectly to be understood , that it may be readily , and dexteriously practised , for upon the true performance thereof dependeth all that followeth . ix vse . to finde the houre of the day . if the dyal be fastned upon a post , the houre by the outward dyal , or limbe , is known of every one , and the upri●ht shadow in the suns parallel , or diurnal arch will also shew the very same houre . but if the dyall be loose , either hold it or set it parallel to the horizon , with the style pointing into the north and move it gently every way untill the houre shewed in both dialls exactly agreeth , or which is all one , finde out the true place of the sun upon the dyall , as was taught in the former question , for that point among the houre lines sheweth the houre of the day . x vse . to finde out the meridian , and other points of the compasse . first , you must seek the tru● houre of the day ( by the last question ) for in that situation the meridian of the dyall standeth direct●y north and south : and the east pointeth into the east , and the west into the west , and the rest of the points may be given by allowing degrees 11. 1 / ● unto every point of the compasse . xi vse . to finde out the azumith of the sun , that is , the distance of the verticall circle , in which the sun is at that present , from the meridian . set your diall upon any plain or flat which is parallel to the horizon , with the meridian pointing directly north or south , as was last shewed : then follow with your eye the upright shadow in a streight line , till it cutteth the horizon : for the degree in which the point of intersection is , shal shew how far the suns azumith is distant from the east and west points , and the complement thereof unto 90 ; shal give the distance thereof from the meridian . xii vse . to finde out the declination of any wall upon which the sun shineth , that is , how far that wall swerveth from the north or south , either eastward or westward . take aboard having one streight edg ▪ & a line stricken perpendicular upon it ; apply the streight edg unto the wall at what time the sun shineth upon it , holding the board parallel to the horizon : set the dyal thereon , and move it gently every way , untill the same hour and minute be shewed in both dyals : and so let it stand : then if the dyal have one of the sides parallel to the meridian strike a line along that side upon the board , crossing the perpendicular , or else with a bodkin make a point upon the board , at each end of the meridian , and taking away the instrument from the board , and the board from the wall , lay a ruler to those two points , and draw a line crossing the perpendicular : for the angle which that line maketh with the perpendicular , is the angle of the decli●nation of the wall . and if it be a right angle , the wall is exactly east or west : but if that line be parallel to the perpendicular , the wall is direct north or south without any declination at all . you may also finde out the declination of a wall , if the dial be fixed on a post not very far from that wall ; in this manner . your board being applyed to the wall , as was shewed , hang up a thred with a plummet , so that the shadow of the thred may upon the board crosse the perpendicular line : make two pricks in the shadow and run instantly to the dyal and look the horizontal distance of the suns azumith , or upright shadow from the meridian . then through the two pricks draw a line crossing the perpendicular : and upon the point of the intersection , make a circle equal to the horizon of your instrument , in which circle you shal from the line through the two pricks measure the horizontal distance of the upright shadow , or azumith from the meridian , that way toward which the meridian is : draw a line out of the center , to the end of that arch measured : and the angle which this last line maketh with the perpendicular , shall be equall to the declination of the wall . xiii vse . how to place the dyall upon a post without any other direction but it selfe . set the diall upon the post , with the stile into the north , as neere as you can guesse : then move it this way and that way , till the same houre and minute be shewed , both in the outward and inward dials by the severall shadowes , as hath been already taught , for then the diall standeth in its truest situation ; wherefore let it be nailed down in that very place . xiiii vse . to finde the height of the sun at high noon everyday . seeke out the diurnall arch or parallel of the suns course for that day , ( by vse iii. ) and with a paire of compasses , setting one foot in the center , and the other in the point of intersection of that parallel with the meridian , apply that same distance unto the semidiameter divided : for that measure shal therein shew the degree of of the suns altitude above the the horizon that day at high noon . xv vse . to finde the height of the sun at any houre or time of the day . seeke out the diurnal arch , or parallel of the suns course for that day : and marke what point of it is in the very houre and minute proposed . and with a paire of compasses , setting one foot in the center , and the other in that point of the parallel , apply the same distance upon the semidiameter divided : for that measure shall shew the degree of the suns altitude above the horizon at that time . and by this meanes you may finde the height of the sun above the horizon at every houre throughout the whole yeere , for the making of rings and cylinders and other instruments which are used to shew the houre of the day . xvi vse . the height of the sun being given , to finde out the houre , or what it is a clocke . this is the converse of the former : seeke therefore in the semidiameter divided , the height of the sun given . and with a paire of compasses , setting one foot in the center , and the other at that height , apply the same distance unto the diurnall arch , or parallel of the sun for that day : for that point of the diurnall arch , upon which that same distance lights , is the true place of the sun upon the dial ; and sheweth among the houre lines , the true time of the day . xvii use. considerations for the use of the instrument in the night . in such questions as concerne the night ▪ or the time before sun rising , and after sun setting , the instrument representeth the lower hemisphaere wherein the southerne pole is elevated . and therefore the parallels which are above the aequinoctiall toward the center shall be for the southerne , or winter parallels : and those beneath the aequinoctiall , for the northerne or summer paral●els ; and the east shall be accounted for west , and the west for east ; altogether contrary to that which was before , when the instrument represented the upper hemisphaere . xviii use. to finde how many degrees the sun is under the horizon at any time of the night . seeke the declination of the sun for the day proposed ( by vse ii. ) and at the same declination the contrary side imagine a parallel for the sun that night ▪ and mark what point of it is in the very houre and minute proposed : and with a pair of compasses , setting one foot in the center , and the other in that point of the parallel , apply that same distance unto the semidiameter divided : for that measure shall shew the degree of the suns depression below the horizon at that time . xix use. to finde out the length of the c●epusculum , or twylight , every day . seek the declination of the sun for the day proposed ( by vse ii. ) and at the same declination on the contrary side imagine a parallel for the sun that night . and with a paire of compasses setting one foot in the center , and the other at 72 degrees upon the semidiameter divided , apply that same distance , unto the suns nocturnall parallel : for that point of the parallel , upon which that same distance shall light , sheweth among the houre lines , the beginning of the twilight in the morning , or the end of the twilight in the evening . xx use. if the day of the moneth be not known , to finde it out by the dyall . for the working of this question , either the diall must be fixed rightly on a post , or else you must have a true meridian line drawn in some window where the sun shineth , wherefore supposing the diall to be justly set either upon the post , or upon the meridian . look what a clock it is by the outward diall , and observe what point of the upright shadow falleth upon the very same minute in the inner diall , and through that same point imagine a parallel circle for the suns course ; that imaginary circle in the ecliptick shall cut the day of the moneth . i the description of it . this instrument serveth as a diall to finde the houre of the day , not in one place onely ( as the most part of dials do ) but generally in all countreys lying north of the aequinoctiall : and therefore i call it the generall h●rologicall ●ing . it consisteth of two br●zen circles : a diameter , and a little ring to hang it by . the two circles are so made , that though they are to be set at right angles , when you use the instrument : yet for more convenient carrying , they may be one folded into the other . the lesser of the two circles is for the aequinoctiall , having in the midst of the inner side or thicknesse , a line round it , which is the true aequinoctiall circle , divided into twice twelue hours , from the two opposite points in which it is fastened within the greater . the greater and outer of the two circles is the meridian : one quarter whereof , beginning at one of the points in which the aequin●cti●ll is hung , is divided into ninety degrees . the diameter is fastened to the meridian in two opposite points or poles , o●e of them being the very end of the quadrant , and is the north pole. wherefore it is perpendicular to the ●quinoctiall , having his due position . the diameter is broad , and slit in the middle : and about the slit on both sides are the moneths and dayes of the yeer . and within this slit is a litt●e sliding plate pierced through with a small hole : which hole in the motion of it , while it is applied to the dayes of the yeer , representeth the axis of the world . the little ring whereby the instrument hangeth , is made to slip up and down along the quadrant : that so by help of a little tooth annexed , the instrument may be rectified to any elevation of the pole. ii. the use of it . in using this instrument , first , the tooth of the little ring must carefully be set to the height of the pole in the quadrant , for the place wherein you are . secondly , the hole of the sliding plate within the slit , must be brought exactly unto the day of the moneth . thirdly , the aeqinoctiall is to be drawn out , and by means of the two studs in the meridian staying it , it is to be set perpendicular thereto . fourthly , guesse as neer as you can at the houre , and turn the hole of the little plate toward it . lastly , hold the instrument up by the little ring , that it may hang freely with the north pole thereof toward the north : and move it gently this way and that way , till the beams of the sun-shining thorow that hole , fall upon that middle line within the aequinoctiall : for there shall be the houre of the day : and the meridan of the instrument shall hang directly north and south . these instrument all dials are made in brasse by elias allen dwelling over against st. clements church without temple barre , at the signe of the horse-shooe neere essex gate . finis