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
.
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
.