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 .

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 .