Of
Numeration
.
NVmeration
containeth
the
maner
how
to
expresse
the
valewe
of
anie
somme
or
number
.
Whiche
occasion
may
present
,
beeyng
small
or
great
,
and
is
furthered
by
tenne
Carecters
or
Figures
followyng
,
to
say
.
|
1.
|
2.
|
3.
|
4.
|
5.
|
6.
|
7.
|
8.
|
9.
|
10.
|
|
one
|
two
|
thrée
|
fower
|
fiue
|
sixe
|
seuen
|
eight
|
nine
|
tenne
|
|
j
.
|
ij
.
|
iij
.
|
iiij
.
|
v.
|
vj
.
|
vij
.
|
viij
.
|
ix
.
|
x
|
The
whiche
nine
Figures
in
proper
signification
of
value
equall
to
the
Woordes
and
Letters
vnder
theym
sette
,
beyng
separate
with
pricke
or
lyne
.
Howbeit
,
beeyng
sette
together
and
mixed
without
pricke
or
line
of
separation
:
than
an
encrease
of
value
they
receiue
,
by
vertue
and
propertie
of
the
place
:
wherein
they
stande
,
which
places
being
of
number
infinite
,
doe
yelde
vnto
euerie
vnity
of
any
Figure
:
ten
tymes
so
much
in
any
place
towarde
the
lefte
hande
,
as
that
same
vnitie
is
worthe
in
place
next
to
it
towardes
the
right
hande
,
the
effect
wherof
more
plainly
may
appeare
by
the
Table
folowyng
,
for
the
same
purpose
furthered
.
The
Table
of
Numeration
.
|
100000000
|
10000000
|
1000000
|
100000
|
10000
|
1000
|
100
|
10
|
1
|
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
|
9
|
8
|
7
|
6
|
5
|
4
|
3
|
2
|
1
|
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
|
9
|
9
|
9
|
9
|
9
|
9
|
9
|
9
|
9
|
|
Hundreth
Millions
.
|
Tenne
Millions
.
|
Millions
.
|
Hundreth
thousands
.
|
Tenne
thousands
.
|
Thousands
.
|
Hundrethes
.
|
Tennes
.
|
Vnities
.
|
THE
nine
vnities
set
aboue
the
vpper
lyne
of
the
Table
,
doe
signifie
the
value
of
euery
vnitie
in
the
Figures
against
any
of
the
same
vnder
the
lyne
,
and
that
by
helpe
of
Ciphers
made
like
the
Letter
.
0.
The
whiche
being
of
no
value
in
proper
signification
,
the
same
notwithstandyng
,
they
are
of
necessarie
vse
in
practise
of
Arithmetique
,
only
to
kepe
the
places
,
wherby
is
expressed
infinite
nombers
,
which
without
helpe
of
theim
,
the
other
Figures
could
not
performe
,
as
by
the
forenamed
vnities
,
with
Ciphers
before
them
,
the
effect
may
appeare
for
the
figure
of
one
,
in
the
first
place
is
there
but
one
:
But
in
the
second
place
is
tenne
,
by
helpe
of
the
Cipher
set
thus
.
10.
So
in
the
thirde
place
a
hundreth
thus
100.
And
so
vnderstand
of
all
the
rest
infinitely
.
The
titles
written
vnder
the
Table
,
serue
also
to
shewe
the
value
of
euery
vnitie
found
in
the
figures
standyng
in
the
places
aboue
the
titles
,
as
9
in
the
first
place
is
but
nine
,
in
the
second
place
it
is
nine
tymes
ten
,
in
the
thirde
place
nine
hundreth
,
and
so
forthe
infinitely
.
And
thus
muche
may
seeme
sufficient
for
an
introduction
for
the
vnderstandyng
of
Numeration
,
which
is
to
shewe
the
value
of
any
nomber
,
which
occasion
may
procure
to
be
knowen
.
Howbeit
,
it
may
séeme
necessarie
heare
to
make
distinction
of
certaine
Termes
,
belongyng
to
Nomber
.
Not
for
vse
of
any
thereof
in
this
parte
,
but
for
helpe
in
other
partes
,
by
the
saide
termes
furthered
,
as
in
place
of
their
neede
hereafter
will
appeare
,
whiche
termes
are
to
say
,
Nombers
Diget
,
Article
,
and
compound
,
or
Mixed
.
The
Diget
nombers
are
not
onely
euery
one
of
the
nine
Caracters
or
Figures
standyng
alone
:
but
also
sometyme
are
founde
amongst
mixed
or
compound
nombers
remaining
in
workes
vnder
ten
.
Betwéene
10
and
20.
Betweene
30
and
40.
&
so
forth
100.
&c.
Article
nobers
are
suche
as
are
furthered
by
Ciphers
,
&
no
mixed
figures
with
theim
,
as
10.
20.
30.
40.
and
so
for
the
infinitely
.
The
mixed
nombers
are
set
together
thus
123.
542.
3045.
and
euery
suche
like
,
either
sondrie
figures
together
,
or
figure
together
and
Ciphers
betweene
.
But
if
a
Cipher
bee
founde
in
the
firste
place
towarde
the
right
hande
of
any
nomber
,
then
euery
suche
nomber
is
an
Article
nomber
.
&c.
Of
Addition
.
ADdition
containeth
the
maner
how
to
assemble
,
and
ioyne
sondrie
perticular
sommes
or
numbers
,
into
one
totall
.
As
if
three
sondrie
menne
should
owe
vnto
a
Marchaunte
,
three
seuerall
sommes
.
The
firste
548.
li.
the
seconde
1346.
li.
and
the
third
15.
li.
The
which
to
bryng
into
one
totall
,
ye
shall
set
the
said
three
seuerall
perticulers
together
,
one
right
vnder
an
other
,
to
saie
:
vnitie
vnder
vnitie
,
tenne
vnder
tenne
,
hundreth
vnder
hundreth
,
and
in
like
maner
infinitely
in
this
order
hereafter
apperyng
.
|
|
li.
|
|
Particulars
.
|
548
|
|
15
|
|
1346
|
|
Totall
.
|
1909
|
The
whiche
Perticulars
set
in
order
accordynglie
,
you
shal
drawe
a
line
vnder
them
,
and
then
resorte
vnto
the
vnities
,
placed
euer
in
the
first
place
towardes
the
right
hande
,
all
those
vnities
added
together
as
5.
and
6.
make
11.
and
therto
8.
make
19.
the
whiche
founde
,
sette
the
digette
number
,
whiche
is
all
aboue
10.
beyng
9.
vnder
the
line
,
as
you
see
,
and
for
10.
the
Article
,
you
shall
retaine
one
in
memorie
,
to
bee
borne
to
the
seconde
place
,
for
10.
in
the
firste
place
,
is
but
one
in
the
seconde
place
,
and
tenne
in
the
seconde
place
,
is
but
one
in
the
thirde
,
and
so
from
place
to
place
infinitely
.
Thus
hauyng
ended
the
worke
of
the
first
place
,
findyng
5.
6.
and
8.
to
make
19.
whereof
the
9.
sette
vnder
the
line
in
the
firste
place
,
and
for
the
article
10.
one
kepte
in
memorie
,
then
saie
one
in
memorie
,
and
one
founde
in
the
seconde
place
make
2.
the
whiche
added
to
4.
standing
ouer
1.
make
6.
wherewith
4.
standyng
ouer
1.
make
together
10.
the
whiche
beyng
an
Article
,
set
a
Cipher
vnder
the
line
in
the
seconde
place
,
and
for
10.
there
founde
,
beare
one
to
the
thirde
place
,
the
whiche
put
to
3.
and
fiue
there
standyng
,
makyng
together
9.
to
bee
sette
vnder
the
line
in
the
third
place
,
then
commyng
to
the
fowerth
and
last
place
findyng
one
,
set
for
the
same
1.
vnder
the
line
in
the
fowerth
place
,
and
so
the
worke
is
ended
,
and
the
totall
is
found
1909.
li.
of
equal
value
to
the
perticulars
.
In
the
practice
whereof
is
to
bée
seen
the
order
of
Addition
,
in
euery
occasion
thereof
furthered
to
bée
performed
.
And
for
to
amplifie
the
effecte
,
take
here
a
fewe
lines
in
verse
.
¶
Of
sondrie
sommes
perticulars
,
one
totall
for
to
frame
,
Set
them
doune
right
orderly
,
as
worke
doeth
best
require
:
What
place
ye
giue
to
any
one
,
the
rest
let
haue
the
same
,
So
maie
you
well
performe
the'ffecte
,
of
that
you
doe
desire
.
¶
To
the
figures
in
first
place
set
,
firste
sée
ye
doe
resorte
,
And
of
the
somme
whiche
thei
doe
make
,
sette
diget
vnder
line
:
And
for
eche
tenne
in
article
founde
,
one
shall
ye
thence
transporte
,
Vnto
the
nexte
and
seconde
place
,
by
memorie
right
fine
.
¶
And
so
all
vnities
ioynde
in
one
,
by
right
of
euery
place
,
And
for
more
order
duely
kepte
,
from
firste
vnto
the
ende
:
So
is
the
worke
at
full
performde
,
required
in
this
case
,
What
so
euer
circumstaunce
,
some
other
maie
pretende
.
Hereafter
is
sette
sunderie
examples
of
whole
numbers
in
practise
,
whereof
maie
bée
seen
the
effecte
before
taught
,
with
the
order
of
proofe
of
the
same
.
These
fower
examples
maie
giue
the
learner
occasion
,
to
examine
his
vnderstandyng
in
the
preceptes
before
giuen
of
Addition
.
And
also
to
note
the
order
of
proofe
,
of
the
same
in
workes
of
the
whole
numbers
,
wherof
the
effecte
(
I
meane
of
proofe
)
consisteth
in
castyng
awaie
euery
9.
founde
in
the
simple
figures
of
any
example
,
without
respecte
of
place
:
first
the
perticulars
aboue
the
line
,
and
the
remaine
aboue
euery
9.
caste
awaie
,
set
at
the
vpper
ende
of
a
Burgunion
crosse
,
in
maner
before
apperyng
.
Then
so
many
times
as
9.
is
to
bée
founde
in
the
totall
of
the
same
example
,
caste
theim
awaie
also
,
and
the
remaine
sette
at
the
lower
ende
of
the
saied
Crosse
.
Then
if
the
2.
remaines
,
the
one
at
the
heade
,
and
the
other
at
the
foote
of
the
crosse
bée
equall
,
then
the
worke
is
true
,
and
els
not
,
as
practise
of
the
firste
example
maie
more
at
large
manifest
.
To
proue
the
first
of
the
foure
former
examples
,
repaire
to
the
first
place
,
where
standeth
the
figures
of
4.
2.
and
9
,
in
the
perticulers
,
whereof
9.
cast
awaie
,
there
is
6.
to
be
ioyned
with
8.
4.
8.
in
the
second
place
,
which
makyng
26.
and
18
thereof
cast
away
,
the
remaine
is
.8
.
to
be
ioyned
with
5.
8.
and
4.
in
the
thirde
place
,
which
makyng
25
and
therof
twise
9
caste
away
,
the
reste
is
7
to
be
ioyned
with
6.
5.
&
6
in
the
fourth
place
,
which
makyng
24.
and
thereof
twise
9
caste
of
,
the
remaine
is
6.
to
be
ioyned
with
3.
6
and
5.
in
the
fift
and
last
place
which
makyng
20.
and
thereof
twise
9.
cast
awaie
,
the
remaine
is
2.
to
be
set
at
the
toppe
of
the
Crosse
as
remain
for
the
perticulars
.
Then
resort
to
the
totall
,
where
is
founde
519851
and
make
together
29.
whereof
thrise
9
cast
away
,
which
is
27.
the
remaine
is
2.
to
set
at
the
foote
of
the
Crosse
for
remaine
of
the
totall
,
and
for
that
the
figures
in
the
toppe
and
bothom
of
the
Crosse
are
like
and
equall
,
therefore
the
Addition
is
well
and
truely
made
,
and
so
for
all
other
examples
wrought
in
whole
Nombers
.
Thus
muche
may
seeme
to
suffice
for
the
woorke
of
whole
nombers
,
howbeit
there
is
some
varietie
of
worke
in
the
diminute
partes
,
of
many
and
innumerable
thyngs
of
sondry
Denominations
.
But
for
that
it
is
not
possible
to
write
of
all
matters
,
I
haue
furthered
some
examples
of
Moneys
,
waights
and
Measures
,
as
moste
apte
for
the
purpose
in
commune
:
referryng
all
men
to
th'
appliyng
the
same
order
to
matters
in
priuate
vocation
,
seruyng
their
occasions
.
Firste
is
to
be
noted
,
that
in
sommyng
of
many
perticuler
sommes
of
Money
,
contaynyng
Poundes
,
Shillings
,
Pence
,
Farthinges
and
Mytes
,
firste
giue
heede
howe
many
Mites
make
one
Farthyng
,
and
that
beeyng
6.
you
shall
for
euery
6
Mytes
eary
one
Farthyng
to
the
place
of
farthynges
,
and
the
remain
in
Mytes
vnder
6.
you
shall
set
vnder
the
lyne
againste
the
Mytes
,
whiche
stande
next
the
right
hand
.
Also
when
you
come
to
the
place
of
Farthinges
,
consider
that
as
4
Farthinges
make
one
penie
:
so
for
euerie
4
Farthinges
cary
one
penie
to
the
place
of
pence
,
and
set
the
remaine
vnder
4.
vnder
the
line
against
the
Farthinges
likewise
.
As
12.
Pence
make
one
shillyng
:
so
in
the
place
of
Pence
cary
for
euery
12.
one
shillyng
to
the
place
of
shillynges
,
and
the
remaine
vnder
12.
set
vnder
the
lyne
in
the
place
of
pence
.
Also
for
euery
20
shillinges
,
carry
one
pounde
vnto
the
place
of
poundes
,
and
the
remaine
of
shillinges
vnder
20
set
vnder
the
line
against
the
Shillynges
,
and
so
with
pounds
beeyng
whole
nombers
,
carry
for
euery
10
one
from
place
to
place
,
as
before
is
taught
,
&c.
and
for
the
further
vnderstandyng
of
the
effect
,
hereafter
is
set
doune
sondry
examples
of
Moneis
.
|
li
|
s
|
d
|
q
|
mi.
|
|
li
|
s
|
d
|
q
|
mi.
|
|
12.
|
15.
|
7.
|
1.
|
4.
|
25.
|
11.
|
10.
|
3.
|
4
|
|
23.
|
16.
|
7.
|
2.
|
5
|
48.
|
9.
|
11.
|
2.
|
3.
|
|
34.
|
17.
|
9.
|
3.
|
3
|
59.
|
13.
|
9.
|
3.
|
2
|
|
71.
|
10.
|
1.
|
0.
|
0
|
133.
|
15.
|
8.
|
1.
|
3
|
Other
examples
wherein
Farthings
are
omitted
,
and
the
mytes
are
borne
for
euery
24.
one
peny
.
|
li
|
s
|
d
|
mits
|
|
|
|
|
|
|
54.
|
12.
|
3.
|
17
|
24.
|
16.
|
3.
|
23
|
|
36.
|
15.
|
7.
|
11
|
32.
|
13.
|
4.
|
18
|
|
42.
|
10.
|
11.
|
9
|
53.
|
15.
|
9.
|
13
|
|
65.
|
17.
|
8.
|
22
|
41.
|
18.
|
2.
|
16
|
|
199.
|
16.
|
07.
|
11
|
153.
|
03.
|
8.
|
22
|
Here
may
bee
seene
in
the
formar
of
the
2
last
examples
,
that
the
myts
being
22.
9.
11.
and
17.
make
together
.
59.
whereof
48.
for
2
pence
taken
away
,
the
remaine
is
11.
to
set
vnder
the
line
,
then
the
2
pence
ioyned
with
8.
11.
7.
and
3.
d
.
make
together
31.
d
.
wherof
24
for
2
s
.
taken
away
,
the
rest
is
7
to
set
vnder
the
Lyne
.
Then
the
2
still
borne
to
the
place
of
shillinges
,
with
the
other
there
standyng
,
make
56.
shilligns
,
from
the
which
40
for
2
poundes
taken
away
,
reste
16.
s
.
to
set
vnder
the
lyne
,
and
the
2
li.
borne
to
the
first
place
of
the
poundes
,
and
ioyned
with
the
other
Figures
make
19.
li.
wherof
the
Diget
9.
is
set
vnder
the
line
,
and
for
the
Article
.
10.
one
is
caried
to
the
seconde
place
,
and
with
the
Figures
there
standyng
make
19.
wherof
the
Diget
9
is
set
vnder
the
lyne
in
the
second
place
,
and
for
the
Article
10.
one
is
caried
to
the
thirde
place
,
and
so
the
woorke
is
ended
,
wherein
appeareth
the
varietie
of
worke
betweene
whole
nombers
and
broken
in
the
practise
of
Addition
.
For
proofe
of
adding
the
Diminute
parts
there
is
no
better
,
then
double
perusing
the
examples
or
Additions
made
.
Howbeit
whan
you
come
to
the
whole
nombers
,
you
haue
to
consider
what
vnities
are
borne
from
the
place
next
before
the
whole
,
and
with
theim
ioyned
,
for
those
borne
vnities
make
a
parte
of
the
totall
,
of
the
said
whole
Numbers
,
and
therefore
in
making
the
proofe
,
must
be
parcell
of
the
perticulars
,
when
the
nienes
are
cast
awaie
,
for
otherwise
the
remaine
of
the
perticulars
,
after
the
nienes
cast
awaie
wilbe
so
muche
lesse
than
the
remaine
of
the
totall
,
as
by
profe
of
the
former
and
last
practized
example
the
effect
may
appeare
.
The
totall
of
the
foresayd
example
being
199.
the
Figures
make
together
19.
wherof
twise
9
cast
away
,
rest
one
to
put
vnder
the
crosse
of
proofe
,
as
doth
appeare
.
Then
adde
all
the
Figures
of
the
perticulers
together
,
and
they
make
35.
wherof
thrise
9
cast
away
,
rest
.
8.
and
agreeth
not
with
the
remayne
of
the
totall
Wherefore
to
that
8
put
2
whiche
in
the
Addition
was
brought
from
the
place
of
shillinges
,
and
that
maketh
10.
whereof
9
cast
away
rest
one
,
equall
to
the
rest
of
the
totall
.
And
so
the
worke
found
true
.
Hereafter
is
set
sondrie
examples
of
Addition
of
weightes
and
measures
,
referryng
the
learner
to
the
maner
heretofore
shewed
,
giuyng
good
heede
to
the
nomber
of
vnities
in
a
smaller
denomination
contained
in
an
vnitie
of
a
greater
,
and
accordyngly
to
beare
from
place
to
place
in
former
order
.
¶
Examples
of
Additions
of
Weightes
.
|
C.
|
q
.
|
li.
|
onz
.
|
|
C.
|
q
.
|
li.
|
onz
.
|
|
34.
|
3.
|
16.
|
13
|
25.
|
3.
|
22.
|
15
|
|
52.
|
2.
|
18.
|
11
|
28.
|
1.
|
17.
|
9
|
|
24.
|
3.
|
12.
|
9
|
84.
|
3.
|
25.
|
14
|
|
112.
|
1.
|
20.
|
1
|
139.
|
1.
|
10.
|
6
|
|
C.
|
q
.
|
li.
|
onz
.
|
|
C.
|
q
.
|
li.
|
onz
.
|
|
53.
|
1.
|
21.
|
6
|
35.
|
2.
|
18.
|
11
|
|
62.
|
3.
|
25.
|
11
|
46.
|
3.
|
20.
|
13
|
|
58.
|
3.
|
23.
|
14
|
57.
|
2.
|
12.
|
10
|
|
44.
|
1.
|
17.
|
8
|
68.
|
3.
|
22.
|
14
|
|
219.
|
3.
|
4.
|
7
|
209.
|
0.
|
19.
|
00
|
To
make
these
formar
Additions
of
weightes
and
suche
like
.
Firste
it
behoueth
the
learner
to
vnderstande
,
that
the
hundreth
waight
at
the
Common
Beame
in
London
containeth
112.
lib
.
haberdepoiz
,
the
halfe
hundreth
56.
lib
.
the
q.
28.
lib
.
&
the
pound
16.
onz
.
The
whiche
knowen
,
carry
in
Addition
for
euery
16.
onz
one
pound
to
the
place
of
lib
.
for
euery
28.
lib
j
.
q
.
to
the
place
of
quarters
,
for
euery
4.
quarters
one
hundreth
to
the
place
of
hundrethes
,
and
so
the
worke
is
well
performed
.
Examples
of
Addition
of
Measures
.
|
yards
|
q
.
|
nayles
.
|
|
yards
|
q
.
|
nayles
|
|
31247.
|
3.
|
2
|
7568.
|
1.
|
2
|
|
57689.
|
2.
|
3
|
6756.
|
2.
|
3
|
|
68754.
|
3.
|
3
|
8573.
|
3.
|
2
|
|
157692.
|
2.
|
0
|
22898.
|
3.
|
3
|
|
Yards
|
foote
|
Inch.
|
|
yards
|
foote
|
Inch.
|
|
656
|
2.
|
7
|
7869.
|
1.
|
5
|
|
645
|
1.
|
9
|
6543.
|
2.
|
8
|
|
784
|
2.
|
8
|
9586.
|
2.
|
10
|
|
978
|
1.
|
3
|
8594.
|
1.
|
11
|
|
3065
|
2.
|
3
|
32594
|
2.
|
10
|
To
make
the
formar
Additions
of
measures
and
suche
like
,
it
behoueth
the
learner
to
vnderstande
that
the
yarde
is
diuided
into
sondry
Diminute
partes
,
that
is
to
say
.
For
the
measuryng
of
Veluet
.
Silkes
.
Clothe
,
Lace
,
and
sondrie
other
thinges
.
The
yarde
is
diuided
into
4
quarters
,
and
euery
quarter
into
4
nayles
,
and
accordingly
the
additions
of
suche
partes
furthered
,
as
before
appeareth
.
And
for
the
measuryng
,
of
Timber
,
Wainscottes
,
Séelings
,
Pauements
,
Land
,
and
suche
like
thinges
,
the
yarde
is
diuided
into
3.
foot
,
the
foote
into
12
Inches
,
and
the
Inche
into
3
Barly
cornes
ordained
by
Statute
for
Standard
measure
of
England
,
and
according
to
such
Diminute
partes
,
the
Additions
of
those
denominations
are
furthered
,
as
before
likewise
may
appeare
.
¶
Substraction
.
SVbstraction
containeth
the
maner
how
to
deduct
or
take
away
a
smallar
somme
or
Nomber
from
a
greater
,
by
practise
wherof
is
found
and
brought
forth
a
remain
sought
for
&
desired
,
as
if
one
man
owe
vnto
an
other
356
li.
wherof
he
hath
paid
234
li.
and
would
knowe
what
rested
vnpaid
.
Then
when
the
paiment
is
rebated
from
the
debte
,
the
remaine
will
appeare
as
practise
by
the
same
sommes
the
effect
will
manifest
.
|
|
l.
|
|
Debte
|
356
|
|
Payde
|
234
|
|
Reste
|
122
|
Here
is
to
bee
perceaued
the
debt
beyng
the
greatest
somme
is
placed
vppermost
,
and
the
paiments
vnder
the
same
.
Vnity
vnder
vnitie
,
cen
vnder
ten
,
and
hundreth
vnder
hundreth
,
and
a
line
drawen
vnder
all
and
so
made
apt
for
the
worke
.
Then
to
performe
the
Substraction
,
resort
to
the
first
place
,
which
is
of
vnities
and
say
.
4
payde
taken
out
of
6.
of
debt
,
the
remayne
is
2.
to
set
vnder
the
lyne
in
the
firste
place
,
then
say
3
payd
out
of
5
of
debt
in
the
second
place
rest
.
2.
to
be
set
vnder
the
line
in
the
second
place
also
,
2
out
of
3
in
the
place
of
hundrethes
rest
.
1.
set
vnder
the
line
in
the
third
place
,
and
so
the
worke
ended
,
wherein
appeareth
that
234
li.
taken
out
of
356.
the
remaine
appeareth
122
li.
&c.
When
you
haue
made
a
substraction
,
and
would
proue
,
whether
you
haue
made
a
true
reste
or
not
,
then
adde
together
the
reste
,
and
the
paimente
,
and
if
the
totall
agree
with
the
firste
debte
,
then
the
Substraction
is
true
,
or
els
not
.
Whereof
the
practise
hereafter
sheweth
the
effecte
by
the
same
numbers
,
wherof
the
former
substraction
was
made
.
|
Debte
.
|
356
|
|
Paied
.
|
234
|
|
Reste
.
|
122
|
|
Proofe
.
|
356
|
Here
doeth
appere
that
2.
of
rest
,
added
to
4.
of
paiment
,
maketh
6
vnder
the
line
in
the
firste
place
:
also
2.
reste
with
3.
paied
,
maketh
5.
vnder
the
line
in
the
seconde
place
,
and
so
1.
reste
with
2.
paied
,
is
3.
to
sette
vnder
the
line
in
the
thirde
and
laste
place
:
and
so
the
totall
beyng
356.
li.
equall
to
the
debte
,
proue
the
worke
true
,
whiche
otherwise
would
not
bée
.
Thus
muche
maie
seem
sufficiente
for
the
woorke
of
substraction
,
where
the
figures
of
the
lesser
number
,
are
smaller
then
the
figures
standyng
right
ouer
them
in
the
greater
noumber
,
but
when
the
contrary
is
founde
,
then
the
woorke
is
of
more
difficultie
,
as
by
example
.
|
Debte
.
|
3576.
li.
|
|
Paied
.
|
2989.
|
|
Reste
.
|
0587.
|
|
Proofe
.
|
3576.
|
Here
resortyng
to
9.
in
the
firste
place
of
paiment
,
to
be
taken
out
of
6.
ouer
it
,
whiche
can
not
bee
doen
,
therefore
borowe
an
vnitie
of
7.
in
the
seconde
place
of
the
debt
to
ioyne
with
6.
in
the
first
place
,
and
so
haue
you
16.
from
the
whiche
9.
paied
,
rebated
,
reste
7.
vnder
the
line
in
the
first
place
.
Then
not
forgettyng
the
vnitie
,
borrowed
of
7.
in
the
seconde
place
,
to
make
the
woorke
of
the
first
,
saie
one
that
was
borowed
with
8.
in
the
seconde
place
of
paiment
,
maketh
9.
to
be
taken
out
of
7.
aboue
,
whiche
can
not
be
,
wherfore
in
former
order
,
borrowe
an
vnitie
of
5.
in
the
third
place
of
debte
,
to
make
17.
in
the
seconde
,
from
the
whiche
9.
aforesaied
rebated
,
the
remaine
is
8.
vnder
line
in
the
seconde
place
.
Then
saie
as
before
,
1.
borrowed
of
5.
in
the
thirde
place
ioyned
with
9.
vnder
5.
maketh
the
10.
to
bée
rebated
from
5.
ouer
9.
whiche
can
not
be
,
but
by
the
helpe
of
an
vnitie
,
borrowed
of
3.
in
the
fowerth
place
,
and
so
10.
from
15.
reste
5.
vnder
the
line
in
the
third
place
.
Lastlie
saie
one
borowed
of
3.
with
2.
paied
in
the
fowerth
place
,
make
thrée
to
bée
taken
out
of
thrée
of
debte
in
the
same
place
,
and
so
remaineth
nothyng
,
wherefore
a
Cipher
is
sette
vnder
the
line
,
in
the
fowerth
and
laste
place
,
and
so
the
woorke
ended
.
Wherein
doeth
appeare
that
2989.
li.
Substracted
from
3576.
li.
the
rest
vnpaied
is
587.
li.
The
proofe
whereof
is
by
addyng
the
paimentes
and
remaine
together
,
and
the
totall
thereof
agréeyng
with
the
debte
,
proueth
the
woorke
true
,
as
before
is
taught
.
A
like
or
more
difficultie
is
founde
in
woorke
of
Substraction
,
when
the
places
in
the
debte
haue
fewe
or
no
figures
,
but
Supplied
with
Ciphers
,
for
that
the
woorke
requireth
a
borrowyng
of
an
vnitie
in
euery
place
of
wante
,
from
one
place
to
an
other
,
vnto
the
ende
,
as
by
example
the
effecte
maie
appeare
.
|
Debt
.
|
302003.
l.
|
|
Paied
.
|
135976
|
|
Reste
.
|
166027
|
|
Proofe
.
|
302003
|
Here
6.
out
of
13
made
by
helpe
of
one
borrowed
in
the
seconde
place
of
the
debt
rest
7.
vnder
the
line
for
the
firste
woorke
.
Then
to
paie
that
was
borrowed
saie
,
one
and
7.
make
8.
to
bée
taken
out
of
10.
in
the
seconde
place
,
by
the
helpe
of
one
borrowed
in
the
third
place
,
and
so
remaineth
2.
vnder
line
in
the
seconde
place
.
Againe
,
one
with
9
in
the
thirde
place
,
make
10.
to
bée
taken
out
of
10
aboue
made
by
one
borrowed
in
the
4.
place
,
and
the
reste
is
nothyng
,
and
therefore
a
Cipher
vnder
line
in
the
thirde
place
.
Also
in
the
same
maner
,
one
and
5.
maketh
6.
to
be
taken
out
of
12.
made
by
one
borrowed
in
the
fifte
place
,
and
so
resteth
6.
vnder
line
in
the
fourth
place
.
So
again
one
and
3.
make
4.
out
of
10.
and
so
reste
6.
in
the
fifte
place
.
Lastlie
one
borowed
with
one
in
the
sixt
and
laste
place
,
make
2.
to
bée
taken
out
of
three
ouer
,
and
so
reste
1.
in
the
same
place
,
and
the
worke
finished
,
and
as
aforesaid
,
the
paimentes
and
restes
together
,
makyng
againe
the
debte
,
proue
the
worke
true
.
Thus
muche
maie
séem
sufficiente
for
the
practise
of
Substraction
in
whole
numbers
:
howbeit
to
further
the
vnderstandyng
of
the
learner
,
take
these
fewe
lines
in
verse
.
¶
When
diget
of
debt
,
is
not
so
greate
,
as
that
in
paiment
made
,
Then
nexte
place
lende
,
to
wantyng
frende
,
to
helpe
this
pleasaunt
trade
.
And
in
repaire
,
one
with
thee
beare
,
to
paiyng
seconde
place
:
So
with
his
feare
,
whiche
standeth
theare
,
paie
thou
that
borrowed
was
.
Thus
to
procede
,
in
worke
with
spede
,
from
place
to
place
I
saie
:
The
restes
in
fine
,
set
vnder
line
,
agréeyng
to
thy
paie
.
When
restyng
due
,
with
paiments
true
,
the
debte
againe
doe
make
.
Then
is
well
doen
,
whiche
was
begon
,
that
dare
I
vndertake
.
When
occasion
presenteth
workes
of
Substraction
,
of
diminute
partes
,
of
what
denomination
so
euer
.
Then
like
consideration
is
to
bée
had
(
as
was
noted
in
Addition
)
what
quantitie
of
vnities
in
one
denomination
,
is
conteined
in
an
vnitie
of
an
other
denomination
:
and
accordynglie
make
the
Substraction
,
whereof
the
effecte
in
sondrie
examples
followyng
maie
appeare
.
Of
Money
.
|
|
li.
|
s
.
|
d
.
|
mites
.
|
|
Debte
.
|
65.
|
17.
|
16.
|
19.
|
|
Paied
.
|
52.
|
12.
|
9.
|
15.
|
|
Reste
.
|
13.
|
05.
|
7.
|
4.
|
|
Proofe
.
|
65.
|
17.
|
16.
|
19.
|
|
|
li.
|
s
.
|
d
.
|
mites
.
|
|
Debte
.
|
8764.
|
12.
|
7.
|
11.
|
|
Paied
.
|
5897.
|
17.
|
9.
|
18.
|
|
Reste
.
|
2866.
|
14.
|
9.
|
17.
|
|
Proofe
.
|
8764.
|
12.
|
7.
|
11.
|
In
the
former
of
these
twoo
examples
,
the
woorke
is
performed
with
greate
facilitie
,
howbéeit
in
the
seconde
there
is
founde
more
difficultie
,
for
that
the
figures
in
the
paimentes
are
for
the
moste
parte
,
greater
then
in
the
debt
:
wherfore
in
the
place
of
mites
wantyng
,
borrowe
one
penie
,
whiche
is
24.
mites
,
and
then
performe
the
woorke
,
so
borrowe
one
shillyng
,
whiche
is
12.
d
.
to
supplie
the
wante
of
pence
.
Likewise
borrowe
1.
li.
whiche
is
20.
s
.
to
supplie
the
wante
of
shillynges
,
and
then
your
restes
sette
doune
,
and
the
vnities
borrowed
,
borne
in
memorie
truely
,
to
aunswere
euery
one
in
his
place
,
then
you
can
not
faile
to
make
good
worke
.
¶
Other
examples
where
in
the
debt
is
no
figures
,
but
one
in
the
laste
place
.
|
|
li.
|
s
.
|
d
.
|
mites
.
|
|
Debte
.
|
500.
|
0.
|
0.
|
0.
|
|
Paied
.
|
368.
|
11.
|
9.
|
16.
|
|
Reste
.
|
131.
|
8.
|
2.
|
8.
|
|
Proofe
.
|
500.
|
0.
|
0.
|
0.
|
|
|
li.
|
s
.
|
d
.
|
mites
.
|
|
Debte
.
|
4032.
|
0.
|
0.
|
0.
|
|
Paied
.
|
2978.
|
15.
|
10.
|
17.
|
|
Reste
.
|
1053.
|
4.
|
1.
|
7.
|
|
Proofe
.
|
4032.
|
0.
|
0.
|
0.
|
Examples
of
waightes
.
|
|
C.
|
q
.
|
li.
|
onz
.
|
|
Bought
.
|
52.
|
3.
|
16.
|
11.
|
|
Receiued
|
37.
|
2.
|
12.
|
8.
|
|
Reste
.
|
15.
|
1.
|
04.
|
3.
|
|
Proofe
.
|
52.
|
3.
|
16.
|
11.
|
|
C.
|
quar
.
|
li.
|
onz
.
|
|
40.
|
0.
|
0.
|
0.
|
|
25.
|
3.
|
16.
|
14.
|
|
14.
|
0.
|
11.
|
2.
|
|
40.
|
0.
|
0.
|
0.
|
Examples
of
Measures
.
|
|
yardes
.
|
quar
.
|
nailes
.
|
|
Solde
.
|
5684.
|
3.
|
2.
|
|
Deliuered
.
|
3879.
|
2.
|
1.
|
|
Reste
,
|
1805.
|
1.
|
1
|
|
Proofe
.
|
5684.
|
3.
|
2.
|
|
yardes
.
|
quart
.
|
nailes
.
|
|
3000.
|
0.
|
0.
|
|
1978.
|
3.
|
2.
|
|
1021.
|
0.
|
2.
|
|
3000.
|
0.
|
0.
|
|
|
yardes
.
|
foote
.
|
inches
.
|
|
Bought
.
|
6523.
|
2.
|
7.
|
|
Receites
|
4879.
|
2.
|
5.
|
|
Reste
.
|
1644.
|
0.
|
2.
|
|
Proofe
.
|
6523.
|
2.
|
7.
|
|
yardes
.
|
foote
.
|
ynches
.
|
|
8000.
|
0.
|
0.
|
|
5684.
|
1.
|
10.
|
|
2315.
|
1.
|
2.
|
|
8000.
|
0.
|
0.
|
Multiplication
.
MVltiplication
conteineth
the
maner
how
to
finde
the
number
of
vnities
,
of
a
smaller
denomination
,
in
an
other
number
of
vnities
,
in
a
greater
denomination
conteined
.
The
effect
whereof
is
better
to
vnderstande
with
fewe
examples
,
then
with
many
wordes
.
And
for
that
it
is
necessarie
for
euery
learner
,
to
vnderstande
the
contente
or
somme
,
produced
by
multiplication
of
one
diget
by
an
other
,
before
he
can
muche
profite
without
the
same
,
therefore
is
prepared
a
Table
for
the
effecte
thereof
:
and
notes
giuen
for
vnderstanding
,
and
vse
of
the
same
,
as
hereafter
appeareth
.
¶
The
Table
of
Multiplication
of
digettes
,
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
|
2
|
4
|
6
|
8
|
10
|
12
|
14
|
16
|
18
|
|
3
|
6
|
9
|
12
|
15
|
18
|
21
|
24
|
27
|
|
4
|
8
|
12
|
16
|
20
|
24
|
28
|
32
|
36
|
|
5
|
10
|
15
|
20
|
25
|
30
|
35
|
40
|
45
|
|
6
|
12
|
18
|
24
|
30
|
36
|
42
|
48
|
54
|
|
7
|
14
|
21
|
28
|
35
|
42
|
49
|
56
|
63
|
|
8
|
16
|
24
|
32
|
40
|
48
|
56
|
64
|
72
|
|
9
|
18
|
27
|
36
|
45
|
54
|
63
|
72
|
81
|
To
vnderstand
the
vse
of
this
Table
,
note
that
the
Digettes
Multiplicatours
are
set
in
2
Collombes
,
to
saye
,
in
the
highest
side
of
the
table
,
in
places
distinct
from
one
vnto
.
9.
and
likewise
in
the
left
ende
of
the
Table
,
also
from
1
vnto
9.
And
all
the
rest
of
the
table
,
except
those
17.
places
,
wherein
the
Digets
do
stand
,
are
places
for
the
seuerall
products
of
Multiplication
of
one
of
the
sayd
Digets
by
an
other
.
And
when
you
would
know
the
somme
or
product
of
any
such
multiplication
,
as
for
example
,
of
5
and
7.
take
the
one
in
the
one
collumne
,
and
the
other
in
the
other
,
and
in
the
place
where
the
2
Collomnes
méete
,
wherein
the
saide
figures
doe
stande
:
the
one
proceedyng
from
one
ende
to
the
other
,
and
the
other
descendyng
from
the
higher
side
to
the
lougher
,
there
shall
you
finde
35.
for
product
or
somme
sought
for
,
and
in
like
order
may
you
finde
any
other
desired
.
The
effect
furthered
in
the
former
Table
,
Let
euery
desirous
learner
haue
perfectly
in
memory
:
for
that
the
same
had
the
workes
of
multiplication
are
performed
with
more
facilitie
,
then
by
wante
thereof
is
possible
.
And
for
aide
of
memorie
note
,
when
2
digets
are
to
be
multiplied
together
,
consider
if
any
of
the
same
may
bee
parted
in
halfes
,
and
so
found
multiply
the
contrary
diget
by
the
one
halfe
,
and
the
double
of
that
product
is
the
somme
ye
would
haue
.
For
example
when
7.
is
to
be
multiplied
by
6.
you
see
6.
may
be
parted
into
twise
3.
wherfore
say
3
tymes
7.
the
contrary
Diget
maketh
21.
then
by
former
note
the
double
thereof
beyng
42.
is
the
product
of
6.
and
7.
multiplied
together
,
and
so
of
all
other
.
When
9.
is
to
be
multiplied
by
9.
7.
or
5.
then
shal
you
put
9
in
3
partes
,
as
into
thrise
3.
and
whith
one
of
the
sayd
partes
multiply
the
contrarie
diget
as
5
beyng
admitted
for
example
,
saiyng
3
tymeg
5
is
15.
the
whiche
taken
3
tymes
,
maketh
45.
which
is
the
product
of
9
and
5
multiplied
together
.
Likewise
for
7
by
9
say
3
tymes
7.
is
21.
the
whiche
trebled
,
maketh
63.
the
product
desired
.
Also
for
9
by
9.
saye
3
tymes
9
is
27.
the
which
trebled
maketh
81.
the
product
sought
for
.
Note
that
when
9
is
to
bee
multiplied
by
8.
6.
or
4.
it
is
better
to
mediate
or
halfe
any
of
the
same
,
then
to
tripertate
or
put
9
into
three
partes
.
Wherefore
when
9
is
to
be
multiplied
by
8.
say
4
beeyng
the
halfe
of
8
and
multiplied
with
9
maketh
36.
The
double
whereof
beyng
72.
is
the
product
of
8
and
9
beyng
multiplied
together
.
So
for
9
by
6.
say
3
the
halfe
of
6
multiplied
in
9.
maketh
27.
the
double
whereof
beyng
54.
is
the
product
of
6.
tymes
9.
&c.
More
to
be
sayd
for
the
vnderstandyng
of
the
former
Table
,
or
maner
to
finde
the
product
of
any
2
Digetts
,
multiplied
the
one
by
the
other
,
might
seeme
superfluous
,
wherefore
now
I
will
shewe
the
order
of
Multiplication
of
one
number
of
figures
by
an
other
.
First
there
is
to
bee
noted
in
Multiplication
three
Nombers
by
seuerall
names
.
Distinct
,
that
is
to
say
,
the
Multiplicande
,
which
is
the
nomber
to
bee
multiplied
,
the
Multiplicatour
,
whiche
is
the
multiplier
,
and
the
Product
whiche
is
brought
foorthe
by
the
worke
,
the
effect
whereof
to
be
shewed
by
example
,
may
be
performed
in
sondry
and
infinite
matters
,
whereof
take
this
that
followeth
,
to
mee
seemyng
very
apte
for
the
purpose
,
for
an
entraunce
thereunto
.
If
you
bye
5678.
Yardes
of
Clothe
,
costyng
86.
pence
euery
yarde
,
&
would
know
how
many
pence
the
whole
amounteth
,
then
the
nomber
of
yardes
shal
be
Multiplicande
,
and
stande
vppermost
in
worke
,
and
the
nomber
pence
shal
be
set
vnder
the
same
for
Multiplicatour
.
Vnitie
of
pence
vnder
vnitie
of
yardes
,
tenne
vnder
tenne
,
and
so
forth
,
when
both
partes
haue
the
places
supplied
,
with
Figures
.
Hundreth
vnder
hundreth
,
thousandes
vnder
thousandes
,
and
so
infinitely
in
maner
,
as
in
examples
heare
may
appeare
.
|
5678
|
|
86
|
|
34068
|
|
45424
|
|
488308
|
The
whiche
2
Nombers
sette
downe
as
you
see
,
and
a
Lyne
drawen
vnder
theim
,
then
the
Product
of
the
worke
wil
be
so
many
Pence
,
as
will
paye
for
5678
yardes
of
clothe
,
at
86
Pence
the
Yarde
,
whiche
is
488308
pence
,
as
appeareth
in
the
totall
of
the
perticuler
Productes
added
together
,
as
the
order
of
woorke
requireth
,
whereof
the
manner
followeth
.
Firste
you
shall
resorte
to
the
place
of
Vnities
,
and
saie
,
6
tymes
8.
is
48.
whereof
the
Diget
8
put
vnder
the
lyne
in
the
place
of
vnities
,
and
for
the
article
40.
you
shall
retaine
in
memory
4
vnities
to
bee
borne
to
worke
of
the
second
place
.
Then
say
6
tymes
7
is
42.
and
4
retained
in
memory
,
maketh
46
in
the
seconde
place
,
whereof
the
Diget
6.
is
set
vnder
lyne
,
and
for
40
retain
4
in
memory
to
bee
borne
to
the
worke
of
the
thirde
place
.
Then
saie
,
6
tymes
6
is
36.
and
4
in
memory
maketh
40
an
Article
nomber
,
and
therefore
put
a
Cipher
vnder
the
line
in
the
third
place
,
and
retain
4
in
memory
(
that
is
)
for
euery
10.
of
the
Article
one
,
to
bee
borne
to
the
worke
of
the
fourth
place
.
Then
say
,
6
times
5
is
30.
and
4
in
memory
is
34.
wherof
the
Diget
4
is
put
vnder
line
in
the
fourth
place
,
and
for
the
Article
30.
beare
three
to
the
fift
place
,
and
because
the
Multiplicand
hath
no
Figure
in
that
place
,
therfore
put
3.
retained
in
memorie
vnder
the
line
in
the
same
place
,
and
so
the
woorke
is
ended
,
for
.
6.
the
firste
Figure
in
the
Multiplitour
,
whereof
the
Product
perticuler
,
is
34068.
as
doth
appeare
.
Then
resorte
to
8.
in
the
second
place
of
the
Multiplicatour
,
and
therewith
multiply
euery
Figure
of
the
multiplicande
in
former
order
saiyng
.
8
tymes
8.
is
64.
wherof
put
the
Diget
4
vnder
the
line
right
vnder
8.
the
multiplicatour
,
and
beare
6.
for
the
Article
60.
in
minde
for
the
seconde
worke
,
and
say
,
8
tymes
7.
is
56.
and
6
in
memory
maketh
62.
whereof
put
2.
vnder
line
in
the
second
place
of
that
seconde
ranke
,
&
beare
6
for
the
next
worke
,
saiyng
,
8
tymes
.
6.
is
48.
and
6.
in
minde
maketh
54.
whereof
put
4
vnder
lyne
and
beare
.
5.
for
the
Article
to
the
next
woorke
saiyng
,
8
tymes
5
is
40.
and
5
in
memory
maketh
45.
whereof
put
5
vnder
line
,
and
for
the
Article
carry
4
to
the
next
place
where
no
Figures
founde
to
make
further
woorke
,
set
it
vnder
the
line
,
and
so
the
multiplication
is
ended
.
Then
adde
together
the
2
perticuler
Productes
,
and
the
totoll
thereof
will
containe
so
many
Pence
as
dooeth
amounte
of
5678.
yardes
of
clothe
at
68
d
.
euerie
yarde
,
which
is
the
effect
desired
in
the
example
furthered
,
and
so
of
other
woorkes
.
Here
is
to
be
noted
,
that
for
euery
Figure
in
the
multiplicatour
of
any
example
,
there
is
a
perticuler
Product
,
and
euery
Diget
made
in
the
firste
woorke
of
any
of
the
same
shal
be
set
vnder
the
Figure
Multiplicatour
,
in
what
place
soeuer
it
stande
,
and
the
Article
nombers
to
bee
transpozed
for
euery
10.
in
any
place
founde
one
to
be
carried
by
memory
to
the
next
place
toward
the
left
hand
,
to
bee
ioyned
with
the
vnities
made
by
the
woorke
in
the
sayde
place
.
All
and
euery
the
whiche
preceptes
well
vnderstanded
,
are
sufficient
for
the
practise
of
Multiplication
,
howbeit
hereafter
is
set
doune
sondry
examples
,
wherein
the
effect
aforesaide
doth
appeare
,
and
for
a
further
ayde
to
the
learner
hereafter
are
furthered
a
few
lynes
in
Verse
.
By
Multiplicator
,
and
Multiplicand
,
a
Product
out
to
finde
:
Giue
eche
his
place
,
as
taught
thee
was
,
that
beare
thou
well
in
minde
:
What
doth
amount
,
in
multiplied
accompt
,
set
Diget
vnder
line
:
Of
Figure
together
.
2.
one
by
the
other
,
in
first
place
doe
assigne
:
The
Articles
conuey
,
by
memory
I
say
,
to
next
and
second
place
:
To
worke
there
made
thou
shalt
them
adde
,
and
so
holde
on
thy
race
.
Thus
maist
thou
haue
a
Product
braue
,
pretended
by
thy
paine
:
If
thou
proceed
as
worke
doth
neede
,
the
ende
till
thou
attaine
:
Of
Figures
iust
,
thou
maist
mée
trust
,
in
multiplier
to
be
seen
:
So
many
will
there
productes
appeare
,
in
order
as
I
wene
:
The
whiche
found
out
,
then
go
about
,
in
one
theim
all
to
frame
:
So
hast
thou
ended
that
was
pretended
,
without
suspect
of
blame
.
Hereafter
are
set
doune
sondrie
examples
for
the
practise
of
multiplication
,
by
3.
4.
and
5.
Figures
in
the
Multiplicatours
.
|
|
6547382
|
|
345
|
|
32736910
|
|
26189528
|
|
|
19642146
|
|
|
2258846790
|
|
47869524
|
|
|
132
|
|
|
95739048
|
|
143608572
|
|
47869524
|
|
|
6318777168
|
|
|
|
7654321
|
|
5462
|
|
15308642
|
|
45925926
|
|
|
30617284
|
|
|
38271605
|
|
|
41807901302
|
|
12435264
|
|
|
8643
|
|
|
37305792
|
|
|
49741056
|
|
74611584
|
|
99482112
|
|
|
107477986752
|
|
|
|
987654
|
|
|
51423
|
|
2962962
|
|
1975308
|
|
|
3950616
|
|
|
987654
|
|
|
4938270
|
|
|
50788131642
|
|
92837451
|
|
|
15263
|
|
|
278512353
|
|
|
557024706
|
|
185674902
|
|
464187255
|
|
|
92837451
|
|
|
1416978014613
|
|
The
proofe
of
Multiplication
is
made
by
casting
away
all
the
Neines
first
in
the
multiplicand
&
the
remaine
set
at
the
one
side
of
a
crosse
,
than
the
remaine
of
the
multiplicator
set
at
the
other
side
therof
.
The
whiche
2
remaines
multiplie
together
and
from
the
result
thereof
caste
away
all
the
nyenes
and
set
the
remaine
at
the
vpper
ende
of
the
crosse
.
Lastly
caste
away
all
the
nienes
in
the
product
,
&
set
the
remain
at
the
foote
of
the
same
crosse
,
the
whiche
performed
,
if
the
remaines
at
the
toppe
and
foote
of
the
crosse
be
equall
,
the
worke
of
that
multiplication
is
true
,
and
else
not
,
as
by
an
example
may
appeore
.
|
345627
|
|
|
4532
|
|
|
691254
|
|
|
1036881
|
|
1728135
|
|
1382508
|
|
1566381564
|
|
In
the
multiplicande
of
this
example
,
the
Figures
make
27.
whiche
is
3
tymes
9
and
nothyng
remaineth
,
wherefore
I
set
a
Cipher
at
the
right
side
of
the
Crosse
as
you
see
.
Likewise
the
Figures
of
the
multiplicatour
make
14.
whereof
9
caste
away
,
the
remaine
is
5.
at
the
left
side
of
the
crosse
.
Then
saiyng
5
tymes
nothyng
is
nothyng
,
wherefore
I
set
a
Cipher
at
the
vpper
ende
of
the
Crosse
.
Lastly
the
Figures
of
the
product
together
make
45.
which
is
5
tymes
9.
and
nothyng
remaineth
,
wherefore
I
set
a
Cipher
at
the
foote
of
the
Crosse
.
And
for
that
the
toppe
and
foote
of
the
crosse
are
like
,
I
know
thereby
the
woorke
of
that
multiplication
to
be
good
,
and
so
of
all
other
,
whereof
the
effect
appeareth
in
the
former
examples
.
Howbeit
for
that
in
the
proofe
of
the
former
example
,
the
Ciphers
are
to
many
to
shewe
the
whole
effect
of
the
order
of
proofe
,
here
is
giuen
an
other
example
to
amplifie
the
same
.
|
47356
|
|
|
2573
|
|
|
142068
|
|
|
331492
|
|
236780
|
|
94712
|
|
121846988
|
|
In
the
multiplicande
of
this
example
the
figures
together
make
25.
whereof
twise
9
cast
awaie
,
reste
7
put
at
the
right
side
of
the
Crosse
.
The
figures
of
the
multiplicatour
make
17.
whereof
once
9
cast
away
rest
8
at
the
left
side
of
the
crosse
.
Then
7
and
8
being
multiplied
together
make
56.
whereof
54
cast
awaye
,
for
6
times
9.
reste
2
to
set
at
the
vpper
ende
of
the
Crosse
.
Lastly
the
Figures
of
the
product
make
together
47.
wherof
45
for
5
tymes
9
caste
away
reste
2
to
set
at
the
foote
of
the
Crosse
.
And
the
Figures
of
the
toppe
and
foote
of
the
Crosse
being
like
and
equall
,
proueth
the
worke
true
,
as
afforesaid
.
An
other
perfect
and
sure
order
of
proofe
,
of
Multiplication
is
made
by
Diuision
,
the
which
here
I
omit
,
till
I
haue
shewed
the
practise
of
Diuision
,
which
hereafter
followeth
.
¶
Diuision
.
DIuision
containeth
the
maner
how
to
shewe
the
Nomber
of
tymes
,
that
a
small
somme
or
nomber
is
contained
in
a
greater
,
and
the
effect
is
procured
in
occasions
infinite
.
And
to
the
practise
therof
belongeth
three
nombers
by
seuerall
names
distinct
,
that
is
to
say
.
The
Diuidend
,
whiche
is
the
nomber
to
be
diuided
.
The
Diuisor
,
whiche
is
euer
in
whole
nombers
lesser
then
the
Diuidende
.
And
the
Quotient
whiche
sheweth
the
nomber
of
tymes
,
that
the
Diuisor
is
contained
in
the
Diuidende
.
As
for
example
if
occasion
procured
to
bee
knowen
how
many
Poundes
were
contained
in
396
Nobles
.
Then
396
is
diuided
and
the
nomber
of
Nobles
contained
in
one
pounde
,
whiche
is
3.
muste
bee
Diuisor
.
The
whiche
Diuidend
diuided
by
the
said
Diuisor
,
the
Quotient
wil
be
found
132.
Whiche
are
so
many
tymes
as
3
Nobles
whiche
is
1
Pounde
,
are
contained
in
396
Nobles
,
whereof
the
effect
by
example
hereafter
is
practised
.
Here
the
Diuidend
396
beyng
sette
doune
,
then
the
Diuisor
3.
is
set
vnder
3.
in
the
Diuidende
,
and
the
worke
begonne
in
the
last
place
towarde
the
left
hand
,
for
that
is
the
order
in
woorkes
of
Diuision
,
though
therein
it
bee
contrary
to
the
other
partes
whiche
euer
beginne
at
the
right
hande
:
then
is
to
be
sought
how
many
times
3.
the
diuisor
is
found
in
3
,
the
diuidend
.
and
that
being
one
tyme
therfore
1
is
put
in
a
place
separate
from
the
rest
as
you
see
,
&
so
the
first
worke
ended
and
nothing
remaining
in
3.
the
diuidend
,
and
therefore
it
and
the
diuisour
is
canselled
with
a
dashe
of
a
Penne
,
thereby
to
signifie
the
woorke
to
be
ended
in
that
place
.
For
the
second
woorke
3
the
diuisour
is
set
vnder
9.
in
the
diuidend
,
and
is
founde
to
be
contaided
therein
3
times
,
and
therfore
3.
is
put
in
the
Quotient
,
and
so
the
seconde
woorke
ended
,
ane
therefore
9
and
3
canselled
as
in
the
former
woorke
.
Lastly
,
thre
the
diuisour
is
put
vnder
6.
in
the
diuidend
,
and
is
found
to
be
contained
therein
2
tymes
,
and
nothyng
remaineth
,
wherefore
2
is
put
in
the
Quotient
,
and
the
whole
worke
is
ended
.
And
by
the
Quotient
is
found
that
1
Pounde
beyng
3
Nobles
,
is
contained
in
396
Nobles
132
tymes
,
whiche
is
the
effect
required
in
the
worke
.
Here
is
to
bee
noted
,
that
the
Ciphers
set
ouer
euery
figure
of
the
deuidende
,
are
there
sett
to
signifie
nothyng
to
remaine
,
after
the
Woorke
in
the
place
,
made
vnder
any
of
the
saied
Ciphers
,
and
oft
tymes
putte
so
in
workes
,
more
for
helpe
of
memorie
,
then
for
other
neede
.
Note
also
,
that
when
the
laste
Figure
of
any
diuidende
,
is
lesser
then
the
diuisor
,
then
the
diuisor
shall
bee
sette
vnder
the
Figure
in
the
laste
place
saue
one
of
the
diuidende
,
and
so
worke
in
former
order
.
How
bee
it
,
to
make
the
matter
more
plaine
,
the
effecte
shal
appeare
in
an
example
followyng
.
If
you
would
knowe
how
many
poundes
are
contained
in
2758.
Crounes
,
then
for
that
4.
Crounes
make
one
pounde
,
therefore
4.
muste
bee
diuisor
,
and
sette
vnder
the
diuidende
,
in
the
last
place
sauyng
one
,
for
that
in
2.
in
the
laste
place
4.
is
not
conteined
,
and
so
the
worke
practised
as
followeth
.
In
this
example
you
maie
see
4.
the
diuisor
sette
vnder
27.
wherein
it
is
conteined
6.
tymes
,
and
3.
remainyng
:
therefore
6.
is
put
in
the
Quotient
,
and
3.
the
remaine
is
set
ouer
7.
and
so
the
firste
worke
ended
,
and
the
diuisor
in
that
place
,
and
the
27.
ouer
it
canselled
,
as
afore
taughte
.
Then
for
the
seconde
woorke
,
the
diuisor
is
set
vnder
fiue
in
the
diuidende
,
the
whiche
with
3.
remainyng
of
the
former
woorke
,
maketh
35.
wherein
the
diuisor
4.
is
contained
8.
tymes
,
and
3.
remainyng
,
wherefore
8.
is
putt
in
the
quotient
,
and
3.
remainyng
set
ouer
5.
and
so
the
seconde
Woorke
ended
,
and
therefore
the
diuisor
,
and
35.
ouer
it
canselled
in
former
order
.
Againe
for
the
thirde
and
laste
worke
,
the
diuisor
4.
is
set
vnder
8.
the
whiche
with
3.
remainyng
in
the
former
woorke
,
maketh
38.
wherein
the
diuisor
4.
is
contained
9.
tymes
,
and
2.
remaineth
putte
ouer
8.
and
so
the
whole
woorke
ended
,
the
diuisor
and
the
38.
beyng
canselled
as
the
other
,
and
the
2.
remainyng
of
the
whole
woorke
,
is
separate
from
the
reste
,
to
signifie
the
same
to
bée
a
remaine
of
the
worke
,
and
not
sufficient
to
containe
4.
the
diuisor
.
By
the
whiche
woorke
doeth
appeare
,
that
in
2758.
Crounes
,
4.
of
the
same
makyng
one
pounde
,
is
contained
in
the
whole
somme
689.
tymes
,
and
twoo
Crounes
remainyng
,
whiche
is
the
effecte
sought
for
by
the
worke
,
wherein
the
perfect
order
of
diuision
is
shewed
,
where
the
diuisor
is
one
figure
onely
.
Howbéeit
,
when
the
diuisor
containeth
a
number
of
Figures
,
as
more
then
one
bee
it
fewe
or
many
:
Then
the
quotient
shall
euer
bee
made
with
that
Figure
of
the
diuisor
,
whiche
standeth
next
towarde
the
left
hande
,
and
none
other
.
And
the
quotiente
so
made
,
shall
bée
multiplied
by
the
reste
of
the
Figures
of
the
diuisor
,
one
after
an
other
,
and
euery
producte
shall
bée
rebated
out
of
the
diuidende
,
standyng
right
ouer
the
Figure
of
the
diuisor
,
whiche
maketh
any
of
the
saied
productes
from
place
to
place
throughout
,
for
euery
figure
of
the
quotiente
made
.
And
the
quotient
shall
bée
made
no
greater
then
that
a
remaine
maie
bée
lefte
in
euery
worke
,
out
of
whiche
the
saied
productes
maie
bée
taken
accordyngly
,
as
in
example
practized
hereafter
,
the
effecte
more
plainly
maie
appeare
.
If
you
would
knowe
how
many
pence
are
contained
in
56847.
mites
.
Then
the
number
of
mites
makyng
one
penie
,
shall
bée
deuisor
whiche
is
24.
and
sette
vnder
the
diuidende
thus
.
In
this
example
are
4.
Figures
in
the
quotient
,
the
whiche
are
made
by
4.
seuerall
workes
in
the
diuidend
.
And
for
the
first
you
shall
set
24.
the
diuisor
,
vnder
56.
in
the
diuidende
,
and
saie
,
how
many
tymes
2.
in
5.
and
that
is
2.
tymes
,
whereof
2.
you
shall
put
in
the
quotient
,
and
sette
1.
remainyng
ouer
5.
Then
the
2.
in
the
quotient
,
multiplied
by
4.
in
the
diuisor
,
produceth
8.
to
bée
taken
out
of
16.
remaining
in
the
diuidend
ouer
4
and
so
the
first
worke
ended
8.
remainyng
of
16
set
ouer
6.
then
shall
you
cancell
your
diuisor
24
and
56
in
the
diuidend
with
1
remaining
ouer
5.
and
so
you
haue
finished
all
thinges
belonging
to
the
first
worke
.
Then
shall
you
set
your
diuisor
24.
vnder
88
and
saye
,
howe
many
tymes
two
the
diuisor
in
8.
ouer
it
,
and
that
is
3
tymes
,
and
2
remaineth
to
set
ouer
8.
The
which
3
put
in
the
quotient
,
and
multiply
the
same
by
4
in
the
diuisor
,
and
the
product
being
12.
rebated
out
of
28.
rest
16
ouer
28.
then
cancell
all
the
Figures
of
the
Diuisor
the
diuidende
and
of
the
remaines
vnder
&
behinde
16.
and
so
the
second
worke
is
ended
.
Thirdly
you
shall
put
your
diuisor
24
vnder
164
and
say
,
how
many
tymes
2
in
16.
and
that
is
6
tymes
,
&
4
remaining
to
set
ouer
6.
16
beyng
cancelled
,
then
6
multiplied
by
4
in
the
Diuisor
,
the
product
is
24
to
bee
taken
out
of
44
so
resteth
20
ouer
4
the
diuisor
,
and
the
thirde
woorke
ended
,
and
then
is
to
be
cancelled
all
figures
of
the
diuisor
diuidende
,
and
remaines
vnder
and
behinde
20.
Lastly
,
you
shall
put
the
Diuisor
24
vnder
207
and
saye
how
many
tymes
2
in
20
ouer
it
,
and
that
is
8
tymes
,
and
4
remaineth
ouer
the
cipher
in
the
second
place
:
then
8
in
the
quotient
multiplied
by
4
in
the
Diuisor
produceth
32.
to
bee
taken
out
of
47.
and
there
remaineth
15.
and
the
whole
woorke
ended
,
and
therefore
the
sayde
15
is
to
be
separated
from
all
the
other
figures
of
the
worke
plainly
to
appeare
,
all
the
other
beyng
cancelled
.
And
so
is
found
that
in
56847
mites
is
contained
2368
pence
,
and
15
mites
remainyng
,
whiche
is
the
effect
in
the
worke
required
.
Because
that
it
is
harde
for
a
learner
to
vnderstande
the
woorke
of
Diuision
where
the
example
is
practised
in
one
place
.
Therfore
in
an
other
example
the
woorkes
shall
haue
so
many
seuerall
distinctions
as
there
shal
be
figures
put
in
the
quotient
:
for
euerie
figure
of
the
saide
Quotient
doth
require
a
perticuler
worke
,
whiche
is
not
easie
to
bee
perceiued
in
the
former
example
,
as
in
an
other
folowyng
may
appeare
.
If
you
would
diuide
856942.
by
354.
you
shall
set
doune
the
diuidend
first
,
and
the
diuisor
vnder
,
as
before
is
taught
,
and
as
hereafter
appeareth
.
Then
say
how
many
tymes
3
the
diuisor
in
8.
ouer
it
,
and
that
is
2
tymes
and
2
remaineth
,
wherefore
2
for
the
tymes
is
put
in
the
quotient
,
and
the
2
of
the
remaine
is
put
ouer
8.
and
so
the
woorke
for
the
Quotient
makyng
in
that
place
is
ended
.
Then
2
in
the
Quotient
muste
bee
multiplied
by
5
in
the
diuisor
,
and
that
maketh
10
to
bee
taken
out
of
25
ouer
it
,
and
so
will
remain
15
ouer
5.
and
all
the
figures
vnder
15
to
bee
canselled
.
Also
you
must
multiply
2
in
the
quotient
by
4
in
the
diuisor
,
and
that
maketh
8.
to
bee
taken
out
of
6
ouer
4
whiche
can
not
be
but
by
borowyng
an
vnitie
out
of
5
to
make
16.
by
order
in
Substraction
,
from
whiche
8
aforesaid
rebated
,
the
rest
is
8
ouer
6
,
and
4
ouer
5.
and
so
the
whole
woorke
for
makyng
the
first
figure
put
in
the
quotient
is
ended
.
To
procede
in
the
woorke
,
you
shall
sette
doune
the
deuidende
,
whiche
is
148942.
and
set
the
diuisor
vnder
it
thus
.
Then
saie
,
how
many
tymes
3.
in
14.
that
is
4.
to
bee
set
in
the
quotient
,
and
2.
remainyng
ouer
14.
the
saied
14.
and
3.
in
the
diuisor
canselled
.
Then
saie
4.
in
the
quotient
,
multiplied
by
5.
in
the
diuisor
,
maketh
20.
to
be
taken
out
of
28.
ouer
5.
&
there
remaineth
8.
Likewise
saie
,
4.
in
the
quotiente
,
multiplied
by
4.
in
the
diuisor
,
produceth
16.
to
be
taken
out
of
9.
whiche
can
not
bee
,
but
by
helpe
of
an
vnitie
,
borowed
of
8.
to
make
19.
them
16.
out
of
19.
reste
3.
ouer
9.
and
7.
ouer
8.
and
so
the
woorke
for
makyng
the
seconde
Figure
in
the
quotient
ended
,
all
the
figures
cancelled
,
vnder
and
behinde
73.
For
the
thirde
worke
,
you
shall
set
doune
the
diuidende
remainyng
,
whiche
is
7342.
and
the
diuisor
vnder
it
,
thus
.
Likewise
saie
,
how
many
tymes
3.
in
7.
that
is
2.
to
bee
set
in
the
quotient
,
and
there
remaineth
1.
ouer
7.
beyng
canselled
,
and
also
3.
the
diuisor
vnder
it
.
Then
multiplie
2.
in
the
quotiente
,
by
5.
in
the
diuisor
&
that
is
10
to
be
taken
out
of
13.
and
so
remaineth
3
the
1
ouer
7.
beyng
cancelled
.
Also
multiplie
2.
in
the
quotiente
,
by
4.
in
the
diuisor
,
and
the
resulte
is
8.
to
bée
taken
out
of
4.
whiche
can
not
bée
but
by
helpe
of
an
vnitie
,
borowed
of
3.
and
so
8.
out
of
14.
reste
6.
ouer
4.
and
2.
ouer
3.
all
the
figures
vnder
and
behinde
26.
beeyng
cancelled
,
and
so
the
woorke
for
the
third
figure
in
the
quotiente
ended
.
For
the
fowerth
and
laste
worke
,
you
shal
set
doune
the
diuidende
remainyng
,
whiche
is
262.
and
the
diuisor
vnder
it
,
thus
.
Finallie
saie
,
how
many
tymes
3.
in
2.
ouer
it
,
and
that
is
no
tyme
,
wherefore
sette
a
Cipher
in
the
quotiente
,
to
supplie
a
place
,
and
cancell
3.
Then
saie
5.
tymes
nothyng
is
nothyng
to
bée
taken
out
of
6.
and
therefore
6.
remaineth
ouer
5.
beyng
cancelled
.
Likewise
saie
4.
tymes
nothyng
is
0.
to
bee
taken
out
of
2.
ouer
4.
and
therefore
2.
remaineth
,
and
4.
to
bée
cancelled
,
and
so
the
whole
worke
ended
,
the
quotient
made
at
fower
seuerall
woorkynges
,
and
founde
to
bee
2420.
and
so
many
tymes
is
the
diuisor
354
conteined
in
the
diuidende
,
856942.
whiche
is
the
effecte
in
the
diuision
sought
for
,
and
required
.
And
the
remaine
of
the
woorke
is
but
a
parte
of
a
tyme
,
and
therefore
to
bee
set
ouer
the
diuisor
thus
262
/
354
,
whiche
signifieth
that
the
diuisor
is
not
contained
in
the
same
,
and
therefore
appeareth
a
remaine
,
and
accordyngly
made
to
appeare
.
And
where
for
findyng
of
the
former
quotiente
,
there
hath
been
made
4.
particuler
workes
,
to
saie
,
for
euery
Figure
or
Cipher
,
one
seuerall
practise
,
you
shall
vnderstande
,
that
suche
maner
of
distinctions
is
not
furthered
,
but
onely
for
helpe
in
teachyng
,
but
the
diuision
to
bee
made
in
one
place
,
and
the
quotiente
to
bee
brought
forthe
in
one
practise
,
in
all
diuisions
generally
,
whereof
the
maner
is
hereafter
practized
in
example
,
by
the
former
diuidende
,
diuisor
,
and
quotiente
,
in
whiche
woorke
is
to
be
seen
the
former
4.
particular
workes
all
in
one
.
The
sunderie
preceptes
and
practises
of
diuision
before
shewed
,
well
noted
and
vnderstanded
,
thereby
any
diuision
is
to
bee
made
with
facilitie
:
howbeit
,
further
to
note
that
when
the
diuisor
containeth
a
greater
nomber
of
figures
,
then
hath
been
in
any
example
before
practised
.
Then
euery
of
the
same
shall
multiplie
the
quotiente
,
and
the
product
taken
out
of
the
remaine
ouer
it
,
and
other
difficultie
is
not
founde
,
wherefore
I
will
practise
sunderie
examples
,
wherein
the
effecte
maie
appeare
,
with
order
of
proofe
of
the
worke
,
and
so
proceede
to
the
next
parte
,
and
for
aide
to
the
learner
,
here
is
furthered
a
fewe
lines
in
verse
.
¶
When
the
diuidende
and
diuisor
,
are
knowen
and
how
to
stande
:
Then
to
the
place
,
make
thou
repaire
,
nexte
towarde
thy
lefte
hande
.
So
ofte
as
the
diuisor
there
,
in
diuidende
is
founde
:
By
one
figure
the
same
declare
,
in
quotient
art
thou
bounde
.
The
whiche
thy
quotient
newly
made
,
with
figure
moste
behinde
:
Thou
shalte
it
multiplie
with
the
reste
,
throughout
vnto
the
ende
.
And
euery
resulte
sée
thou
rebate
,
from
restes
in
diuidende
:
Ouer
the
figure
made
multipliar
,
so
rule
maie
thee
defende
.
Then
sée
all
figures
cancelled
bée
,
excepte
remainers
made
:
Of
euery
one
thou
wroughtest
vpon
,
whereby
true
quotient
hadde
.
The
firste
worke
finished
,
againe
beginne
,
diuisor
remoued
a
place
:
By
like
order
as
earst
was
vsed
,
and
alter
not
the
cace
.
Vntill
laste
figure
of
diuisor
,
vnder
laste
of
diuidende
séene
:
For
there
is
made
an
ende
of
all
,
so
truthe
doeth
saie
I
wéene
.
What
doeth
remaine
when
woorke
is
doen
,
set
ouer
diuisor
fine
:
In
seuered
place
from
all
the
reste
,
betwéene
them
bothe
a
line
.
¶
Examples
.
These
4.
Examples
are
set
doune
,
aswell
to
giue
the
learner
occasion
to
examine
his
skill
in
the
practice
of
diuision
,
as
also
to
see
th'order
of
proofe
of
the
worke
by
sume
men
allowed
,
whiche
is
an
vncertaine
proofe
,
by
castyng
awaie
the
nynes
by
order
vsed
in
the
other
partes
.
For
howbeit
that
in
three
of
the
examples
,
the
effecte
of
the
saied
order
of
proofe
agreeth
with
truth
,
the
same
notwithstandyng
in
one
of
the
fower
,
the
vncertaintie
of
that
order
of
proofe
doeth
plainly
appeare
:
whiche
order
followeth
.
Firste
they
caste
awaie
all
nynes
in
the
diuisor
,
and
the
reste
thei
sette
at
the
one
side
of
a
crosse
,
then
they
caste
awaie
all
the
nines
in
the
quotient
,
and
set
the
remaine
at
the
other
side
of
the
Crosse
,
and
multiplie
those
twoo
remaines
together
,
and
adde
the
resulte
to
the
remaine
of
the
same
diuision
(
if
there
bée
any
)
of
whiche
totall
all
nynes
caste
awaie
,
the
remaine
is
sette
at
the
vpper
ende
of
the
crosse
:
and
lastly
all
nynes
caste
awaie
in
the
diuidende
,
and
the
remaine
set
at
the
foote
of
the
crosse
,
and
found
to
agree
with
the
figure
in
the
toppe
of
the
Crosse
,
then
the
woorke
is
allowed
to
be
good
,
or
els
not
.
The
which
appeareth
true
,
in
thrée
of
the
former
examples
,
but
one
of
the
fower
is
founde
contrary
,
and
therefore
the
Rule
not
worthie
to
bée
allowed
.
But
when
you
desire
to
proue
any
Diuision
,
then
multiply
your
quotient
with
the
figure
or
figures
that
was
diuisor
,
and
to
the
result
adde
the
remaine
of
the
diuision
if
any
be
founde
,
and
that
totall
makyng
the
Diuidend
or
Somme
that
was
diuided
,
then
the
worke
is
true
and
else
not
.
Likewise
if
you
would
proue
the
trueth
of
any
multiplication
,
diuide
the
result
by
the
Multiplicator
,
and
the
quotient
makyng
again
the
Multiplicand
,
the
worke
is
true
or
else
not
.
So
that
the
most
certaine
proofe
of
multiplication
is
by
diuision
,
and
of
diuision
by
multiplication
,
of
the
whiche
the
effect
hereafter
may
appeare
in
Reduction
,
by
examples
seuerall
for
both
those
partes
,
wherfore
that
is
aforesaid
may
seeme
sufficient
for
the
practcse
of
Diuision
.
¶
Of
Reduction
.
REduction
is
no
proper
part
of
Arithmeticke
,
for
howbeit
that
the
change
of
one
denomination
vnto
another
,
or
the
alteration
of
thinges
from
one
title
to
an
other
may
well
bee
termed
Reduction
.
The
same
notwithstandyng
,
the
effect
is
performed
by
Multiplication
or
Diuision
,
or
else
both
.
Neuerthelesse
,
for
that
the
learner
may
haue
experience
howe
thinges
are
reduced
and
altered
in
name
and
propertie
:
the
substaunce
or
value
remainyng
perfectly
,
greatly
to
his
contentation
and
commoditie
.
I
therefore
thinke
conuenient
to
shewe
some
examples
therof
in
such
place
as
other
haue
furthered
it
as
a
parte
of
Arithmetique
,
though
as
you
may
perceiue
the
effect
furthered
by
Multiplication
and
Diuision
,
as
aforesaide
.
Reduction
of
Money
by
Multiplication
.
If
you
would
reduce
586
li.
into
Pence
,
that
is
to
say
,
if
you
would
knowe
how
many
Pence
are
contained
in
586
li.
the
same
you
may
performe
by
2
maners
.
The
one
is
by
Multipliyng
586.
by
so
many
pence
as
are
contained
in
one
pounde
which
are
240.
The
other
is
by
bringyng
586
li.
into
shillinges
,
by
multipliyng
the
same
by
20
which
are
the
nomber
of
shillinges
in
one
pounde
,
and
so
brought
into
shillinges
the
same
to
be
multiplied
by
the
pence
of
one
shillyng
,
which
are
12.
and
so
at
2
woorkes
the
saied
586
li.
brought
into
pence
of
euery
the
whiche
orders
the
effecte
is
hereafter
practized
by
example
.
Example
practized
by
the
first
Order
.
|
|
li.
|
|
586
|
|
|
240
|
d
.
|
|
23440
|
|
|
1172
|
|
|
140640
|
d
.
|
Example
practized
by
the
seconde
Order
.
|
|
li.
|
|
586
|
|
|
20
|
s
.
|
|
11720
|
s
.
|
|
12
|
d
.
|
|
23440
|
|
|
11720
|
|
|
140640
|
d
.
|
Thus
appeareth
plainly
by
2
maner
of
practizes
of
Multiplication
,
that
in
586
li.
are
contained
140640
d
.
and
so
the
denomination
chaunged
from
poundes
to
pence
,
and
therefore
saide
to
be
reduced
.
If
you
would
reduce
140640
pence
into
pounds
,
that
is
to
know
how
many
poundes
are
contained
in
the
said
nomber
of
pence
.
Then
you
shall
diuide
the
said
pence
by
so
many
as
maketh
one
Pounde
,
or
else
firste
bring
the
same
into
shillinges
,
diuidyng
by
12
whiche
are
the
nomber
of
pence
in
one
shilling
,
and
to
bryng
the
said
shillynges
into
poundes
by
20
whiche
are
the
shillinges
of
one
Pound
,
and
so
the
said
pence
by
2
maners
are
brought
into
poundes
,
whereof
the
effect
hereafter
is
practised
by
example
.
Example
practized
by
the
first
maner
.
Example
practized
by
the
seconde
Order
.
Thus
appeareth
also
that
in
140640
d
.
are
contained
586
li.
by
2
maner
of
practizes
of
Diuision
,
by
the
whiche
may
appeare
not
onely
the
efecte
of
reducing
thinges
of
one
denomination
to
an
other
.
But
also
the
perfecte
order
of
proofe
of
Multiplication
,
and
diuision
the
one
by
the
other
as
aforesaid
.
A
further
difficultie
is
founde
,
when
sondrie
denominations
are
to
bee
reduced
into
one
,
as
if
occasion
required
to
bring
749
li.
15
s
.
5
d
.
all
into
mytes
,
for
then
the
moste
conuenient
order
is
to
multiplie
the
pounds
with
the
shillinges
of
1
pound
which
is
20.
and
to
the
result
is
to
be
added
the
15
s
.
appearyng
alone
,
and
then
the
totall
of
shillinges
to
bee
multiplied
with
12
d
.
in
one
shilling
contained
and
to
the
product
is
to
be
added
the
5
pence
standyng
alone
,
and
that
totall
multiplied
by
24
mytes
in
1
peny
therby
is
brought
forth
the
whole
nomber
of
mites
in
the
foresaid
somme
contained
.
Wherof
the
effect
hereafter
by
practise
appearyng
.
¶
Example
.
|
li.
|
s
.
|
d
.
|
|
749.
|
15.
|
5
|
|
20
|
s
.
|
|
|
14980
|
s
.
|
|
|
15
|
s
.
|
|
|
14995
|
s
.
|
|
|
12
|
d
.
|
|
|
29990
|
|
|
|
149955
|
|
|
|
179945
|
d
.
|
|
|
24
|
Mytes
.
|
|
719780
|
|
|
|
359890
|
|
|
|
4318680
|
Mytes
.
|
Here
appeareth
that
in
749.
li.
15
s
.
5
d
.
is
contained
4318680
mytes
,
the
sondry
denominations
reduced
into
one
by
Multiplication
.
Likewise
to
bryng
4318680
Mytes
into
poundes
that
is
to
bee
performed
by
diuision
as
in
example
practized
the
effect
may
appeare
.
Here
you
may
see
that
.
4318680.
Mytes
diuided
by
the
mytes
of
one
peny
,
whiche
is
24.
yeldeth
in
quotient
179945
pence
,
the
whiche
also
diuided
by
pence
of
one
shillyng
,
whiche
is
12.
yeldeth
in
the
Quotient
14995
shillinges
and
5
pence
remaining
.
The
whiche
shillinges
also
diuided
by
20.
contained
in
one
Pound
yeldeth
in
quotient
749
li.
and
15
s
.
remainyng
.
The
whiche
749
li.
15
s
.
5
d
.
is
the
originall
of
the
former
examples
of
Reduction
,
firste
reducing
the
same
from
great
denomination
and
small
termes
,
into
a
small
denomination
and
great
termes
by
practice
of
multiplication
.
And
contrariwise
reducyng
the
same
again
,
from
small
denomination
and
greate
termes
into
the
firste
kinde
,
of
greate
denomination
and
small
termes
,
by
diuision
wherein
appeareth
how
to
vnderstand
of
Reduction
,
and
the
same
to
be
performed
by
Multiplication
or
Diuision
as
aforesaide
,
whereof
to
giue
further
preceptes
néedeth
not
,
howbeit
to
shewe
the
learner
wherein
partly
the
effect
to
applie
,
here
foloweth
sondrie
examples
of
Reductions
of
waights
,
measures
moneys
,
by
Exchunge
for
sondry
countries
.
¶
Reduction
of
Waightes
.
|
C.
|
quart
.
|
|
In
52.
3.
24
lib
.
What
the
whole
in
pounde
waightes
.
|
|
C.
|
qu
.
|
li.
|
|
52.
|
3.
|
24.
|
|
4
|
|
|
|
208
|
|
|
|
3
|
|
|
|
211.
|
quart
.
|
|
28
|
|
|
|
1688.
|
li.
|
|
|
422
|
|
|
|
24
|
|
|
|
5932.
|
li.
|
|
To
reduce
weightes
from
one
denomination
to
an
other
,
requireth
an
vnderstanding
of
the
seuerall
denominations
,
belongyng
to
the
kinde
of
weightes
,
procuryng
a
reduction
:
wherfore
note
,
that
the
hundred
weight
at
the
common
beame
of
London
,
containeth
112.
li.
the
halfe
hundreth
56.
li.
the
quarterne
28.
li.
The
pounde
weight
containeth
16.
onzes
,
and
are
called
weightes
Haburdepoise
.
By
whiche
kinde
of
weightes
,
the
former
example
furthered
,
note
that
52.
li.
is
multiplied
by
4
,
quarters
,
and
yeldeth
208.
quart
.
to
the
whiche
is
added
3.
quart
parcell
of
the
example
,
the
totall
whereof
multiplied
by
28.
li.
contained
in
one
quart
.
yeldeth
1688.
l.
to
the
whiche
is
added
24.
li.
parcell
of
the
example
:
the
totall
whereof
beyng
5932.
pounde
,
is
the
effecte
sought
for
in
the
example
,
whiche
is
the
number
of
pounde
weightes
,
contained
in
52.
hundred
3.
quart
.
24.
pounde
wrought
by
multiplication
.
The
whiche
to
transpose
againe
into
the
firste
kinde
by
diuision
:
hereafter
the
effecte
appereth
by
practise
.
¶
Example
.
In
5932.
pounde
,
what
hundreth
weightes
Habardipoise
.
Reduction
of
Measures
.
In
568.
yardes
,
what
Inches
are
contained
?
|
|
Yardes
.
|
|
568
|
|
|
36
|
|
|
3408
|
|
|
1704
|
|
|
20448
|
Inches
.
|
In
20448.
Inches
,
what
yardes
are
contained
?
Thus
you
maie
see
that
568.
firste
multiplied
by
36.
Inches
,
conteined
in
one
yard
produceth
20448.
Inches
,
the
whiche
againe
diuided
by
36.
yeldeth
in
the
quotient
568.
yardes
,
agréeyng
with
the
former
declaration
.
Here
it
is
necessary
to
note
,
that
when
occasion
requireth
reduction
of
one
denomination
into
an
other
,
when
neither
of
the
same
are
of
greatest
,
nor
smallest
denomination
,
belongyng
to
the
qualitie
of
that
thyng
,
which
requireth
the
reduction
,
then
the
denomination
to
be
reduced
,
requireth
multiplication
thereby
,
to
bee
brought
into
the
smallest
denomination
néedefull
,
that
by
diuision
of
the
same
,
it
maie
bee
brought
into
the
other
denomination
,
whiche
the
occasion
searcheth
:
for
any
thyng
in
small
denomination
,
maie
bee
turned
into
sonderie
sortes
of
greater
,
as
sonderie
occasions
maie
require
,
as
by
seuerall
examples
hereafter
the
effecte
maye
appeare
.
In
364.
Nobles
,
of
6.
s
.
8.
d
.
the
peece
,
what
Crounes
of
5.
s
.
peece
.
These
forenamed
Nobles
,
beyng
multiplied
by
80.
d
.
conteined
in
one
Noble
,
produceth
the
whole
noumber
of
pence
in
those
Nobles
contained
,
the
whiche
pence
diuided
by
60.
contained
in
one
Croune
,
yeldeth
in
quotient
so
many
Crounes
,
as
are
contained
in
the
saied
Nobles
,
the
whiche
beeyng
the
effecte
of
the
former
note
,
hereafter
appereth
in
example
practized
.
Nobles
.
|
368.
|
|
|
|
80
|
|
|
|
29440.
d
.
|
|
|
|
|
|
Crounes
.
|
|
490
|
|
In
,
490.
Crounes
,
and
40.
d
.
remainyng
what
Nobles
?
Crounes
,
|
490.
|
3.
s
.
|
4.
d
.
|
|
60
|
|
|
|
29400.
|
|
|
|
40.
|
|
|
|
29440.
|
d
.
|
|
|
|
Nobles
.
|
|
368.
|
|
By
the
same
maner
,
when
Englishe
money
is
to
be
reduced
into
Frenche
Crounes
,
Spanishe
Duckets
,
Flemishe
Gildrens
,
or-Dolars
,
the
somme
of
money
being
brought
into
pence
,
then
it
is
denomination
apte
to
bee
diuided
by
the
noumber
of
pence
,
beyng
price
by
exchange
of
the
saied
Croune
,
Ducket
,
Guildren
,
or
Doller
,
the
effecte
likewise
hereafter
appearyng
by
example
.
To
make
ouer
by
Exchaunge
100.
lib
.
Starlyng
for
Fraunce
,
at
4.
s
.
9.
d
.
euery
croune
,
for
Spaine
at
5.
s
.
10.
d
.
euery
Ducket
:
For
Flaunders
at
3.
s
.
11.
d
.
the
Guildren
:
or
other
place
at
4.
s
.
3.
d
.
the
Doller
.
Firste
,
reduce
the
saied
100.
l.
into
pence
whiche
maketh
24000.
the
whiche
diuided
by
57.
d
.
the
price
of
the
Croune
for
Fraunce
,
yeldeth
in
the
quotiente
so
many
Crounes
as
100.
li.
maketh
at
that
price
,
or
for
Spaine
diuided
by
70.
d
.
the
price
of
a
Duckett
,
yeldeth
in
the
quotiente
so
many
Duckettes
as
100.
li.
maketh
at
that
price
,
or
for
Flaunders
diuided
by
47.
yeldeth
in
the
quotiente
so
many
Guildrens
as
100.
l.
maketh
,
and
lastlie
diuided
by
51.
d
.
yeldeth
in
quotiente
so
many
Dolars
as
100.
lib
.
maketh
,
whereof
the
effecte
hereafter
by
examples
appeareth
.
|
lib
.
|
|
crounes
|
|
The
pence
of
100
|
421
5
/
57
|
|
The
price
of
the
|
|
|
Frenche
croune
.
|
|
|
|
|
d
.
|
|
Pence
of
100
li.
|
duc
.
|
|
price
of
the
Spanish
duket
|
342
●
/
7
|
|
li.
|
|
|
|
Pence
of
100
|
Guildrens
|
|
price
of
the
Guildren
|
510
30
/
47
|
|
li.
|
|
|
|
Pence
of
100
|
Dolars
|
|
price
of
the
Dolar
|
470
3●
/
5●
|
By
these
examples
appeareth
that
100
li.
made
into
Fraunce
by
exchaunge
at
4.
s
.
9
d
.
the
Crowne
,
maketh
421
3
/
57
Crownes
.
Also
100
li.
made
into
Spaine
by
Exchaunge
at
5
s
.
10
d
.
the
Ducket
,
maketh
342
Duckets
6
/
●
Likewise
made
into
Flaunders
at
3
s
.
11
the
Guildren
,
maketh
510
Guildrens
3●
/
47
And
at
4
s
.
3
d
.
the
Dollar
maketh
470.
Dollers
30
/
5●
.
Here
note
that
the
Exchaunge
for
Flaunders
is
for
the
moste
parte
furthered
by
the
pounde
,
aswell
Flemishe
as
starlyng
,
whereof
some
examples
followe
.
To
make
ouer
to
Andwarpe
100
li.
starlyng
at
24
s
.
8
d
.
Flemish
the
Pounde
starlyng
,
reduce
the
said
100
li.
into
Flemishe
money
by
Multipliyng
the
same
by
296
d
.
whiche
is
the
price
Flemishe
of
the
Pounde
starlyng
,
and
the
product
wil
be
so
many
Flemishe
Pence
as
the
said
100
li.
starlyng
is
worth
at
the
price
,
the
which
Pence
diuided
in
order
as
afore
taught
,
for
English
money
yeldeth
in
quotient
so
many
Flemishe
poundes
as
the
said
100
li.
starling
amounteth
to
by
Exchaunge
,
wherof
the
effect
by
example
practized
hereafter
appeareth
.
|
li.
|
|
|
100
|
starlyng
.
|
|
296
d
.
|
Flemishe
.
|
|
600
|
|
|
900
|
|
|
200
|
|
|
29600
|
pence
.
|
Thus
appeareth
that
100
li.
starlyng
reduced
into
Flemishe
Pence
by
multipliyng
the
same
by
the
price
of
the
li.
maketh
123
li.
6
s
.
8
d
.
Flemishe
But
when
Flemish
Money
is
to
be
made
from
thence
into
England
,
then
you
shall
reducd
the
same
into
pence
,
and
diuide
the
total
by
the
price
of
the
Englishe
Pounde
,
and
so
finde
in
the
Quotient
the
Englishe
Money
desired
as
in
practice
may
appeare
by
example
by
100
li.
Flemmishe
at
4
s
.
10
d
.
starlyng
.
|
li.
|
|
100
Flemmishe
.
|
|
240
|
|
4000
|
|
200
|
|
24000
|
|
|
li.
|
s
.
|
d
.
|
|
|
|
80.
|
10.
|
8.
|
253
/
298
|
starling
|
Here
appeareth
that
100
li.
Flemmishe
multiplied
by
240
d
.
contained
in
one
pound
produceth
24000
d
.
The
which
diuided
by
298
d
.
the
price
of
the
li.
starling
yeldeth
in
Quotient
80
li.
10.
8
d
.
and
a
parte
of
a
peny
,
and
is
the
value
of
a
100
li.
Flemmishe
at
24
s
.
10
d
.
the
li.
starlyng
.
Likewise
Waightes
of
what
denomination
soeuer
beeyng
reduced
into
the
smallest
denomination
nedefull
,
may
be
chaunged
into
any
other
Denomination
required
,
as
by
examples
may
appeare
.
If
you
would
reduce
Quintalles
,
containyng
100
li.
weight
simple
or
subtill
into
hundreth
waightes
containyng
112.
lib
.
or
to
the
contrary
the
C.
at
the
Beame
in
London
into
Quintalles
.
Then
bryng
the
denomination
to
be
reduced
into
Pounde
waightes
by
multiplication
,
and
beyng
in
pounde
waightes
,
they
are
apte
to
bee
brought
into
the
other
denomination
by
Diuision
.
¶
Example
.
In
54.
Quintalles
.
What
C.
waighes
.
¶
Proofe
.
In
48.
C.
24.
lib
.
what
Quintals
.
|
112
|
|
|
|
96
|
|
|
|
48
|
|
|
|
4824
|
|
|
|
5400
|
|
54
Quintals
.
|
Likewise
for
measures
,
to
tourne
yardes
into
elles
,
or
elles
into
yardes
:
either
of
the
same
brought
into
quarters
of
a
yarde
by
multiplication
,
the
other
maie
bee
brought
to
the
denomination
required
with
facilitie
.
¶
Example
.
In
568
yardes
,
what
elles
.
In
,
568
Elles
,
what
yardes
?
|
5
|
|
|
|
2840
|
|
|
|
2840
|
710.
|
yardes
.
|
|
444
|
|
|
Also
Inches
may
be
brought
into
feete
,
by
diuidyng
12.
into
yardes
,
by
36.
into
elles
,
by
45
,
and
so
of
all
other
thynges
.
Thus
muche
maie
seme
sufficient
,
to
giue
vnderstandyng
for
the
effecte
of
reduction
,
the
whiche
as
aforesaied
,
not
to
bee
accompted
a
parte
proper
of
Arithmetique
,
but
rather
an
application
of
multiplication
,
and
diuision
to
sondrie
thynges
,
whereof
the
practise
profitable
to
bee
knowen
vnto
learners
,
wherein
occasions
growyng
to
infinite
effecte
.
¶
Progression
.
PRogression
Arithmeticall
is
a
short
and
bréefe
maner
,
addyng
sonderie
figures
or
noumbers
sett
doune
,
euery
one
(
after
the
firste
)
encreasyng
by
equalle
quantitie
,
as
1.
2.
3.
4.
5.
6.
7.
8.
9.
there
is
encrease
by
an
vnitie
:
also
2.
4.
6.
8.
10.
12.
the
encrease
is
by
2.
Againe
3.
6.
9.
12.
15.
18.
&c.
euery
noumber
of
the
Progression
is
augmented
by
3.
more
then
an
other
.
The
whiche
progressions
,
and
all
other
like
,
are
to
bee
sommed
by
rule
of
Progression
with
muche
more
facilitie
then
by
Addition
,
as
by
example
the
effecte
maie
appeare
.
There
is
to
bee
noted
,
that
if
the
tymes
of
the
Progression
bee
odde
,
then
the
firste
and
laste
Noumbers
added
together
,
and
the
halfe
of
that
totall
,
multiplied
by
the
Noumber
of
tymes
of
the
progression
,
the
product
thereof
will
be
the
iust
somme
of
the
saied
progression
,
as
by
example
plainely
may
appeare
.
¶
Example
.
Here
appeareth
the
tymes
of
the
progression
to
bee
9.
and
the
firste
nomber
1.
Added
with
the
last
which
is
9.
maketh
10.
the
halfe
whereof
beyng
5.
multiplied
with
the
tymes
of
the
progression
,
which
is
9.
produceth
45
the
iust
somme
of
the
whole
progression
as
by
Addition
is
proued
,
and
this
is
the
perfecte
rule
of
Progression
when
the
tymes
be
odde
.
Howbeit
,
when
the
tymes
of
Progression
be
euen
,
then
adde
the
first
and
laste
together
and
multiplie
that
totall
with
halfe
the
nomber
of
times
of
the
Progression
,
and
the
product
will
be
the
iust
somme
of
the
Progression
,
as
may
appeare
likewise
by
example
.
¶
Example
.
Here
the
tymes
of
the
progression
beyng
8.
whereof
the
first
and
laste
makyng
9.
and
multiplied
by
4.
the
halfe
of
the
times
,
produceth
the
somme
desired
,
whiche
is
36.
as
by
Addition
is
proued
.
It
may
seeme
necessary
to
note
one
Generall
Rule
for
both
,
the
former
whiche
is
to
multiplie
the
one
hole
,
with
the
halfe
of
the
other
.
As
the
first
and
last
beyng
odde
,
multiplie
the
same
by
halfe
the
tymes
of
the
Progression
whiche
then
is
euer
euen
,
and
if
the
first
and
laste
be
euen
,
then
with
halfe
thereof
multiplie
the
tymes
of
the
Progression
beeyng
euen
or
odde
,
and
so
finde
the
iust
somme
desired
.
Some
may
by
reading
vnderstande
these
former
Rules
,
and
yet
want
experience
how
to
applie
theim
,
wherefore
not
amisse
to
giue
some
example
suche
to
contente
.
Wherefore
somwhat
thereof
followeth
.
A
Lordship
is
offered
to
sale
,
to
be
paied
the
first
day
of
.
45.
next
folowing
20.
shillinges
:
the
seconde
40.
shillynges
:
the
third
60.
shillynges
,
and
so
euery
daie
20.
shillynges
more
then
an
ather
,
till
45.
might
bée
ended
,
the
question
is
,
what
the
somme
will
amount
vnto
.
Accordyng
to
the
firste
of
the
former
rules
,
adde
the
firste
and
laste
Noumbers
of
the
Progression
together
,
as
1.
pounde
with
45
pounde
,
and
that
maketh
46.
the
halfe
wherof
23.
multiplied
by
the
tymes
of
the
Progression
,
45.
produceth
1035.
pounde
,
the
somme
required
in
the
question
,
as
by
addition
maie
appeare
.
¶
Example
.
|
1.
45
|
1
|
11
|
|
1
|
2
|
12
|
|
46
|
3
|
13
|
|
|
4
|
14
|
|
23
|
5
|
15
|
|
45
|
6
|
16
|
|
|
7
|
17
|
|
115
|
8
|
18
|
|
92
|
9
|
19
|
|
1035
|
10
|
20
|
|
55
|
155
|
|
21
|
31
|
41
|
|
22
|
32
|
42
|
|
23
|
33
|
43
|
|
24
|
34
|
44
|
|
25
|
35
|
45
|
|
26
|
36
|
215
|
|
27
|
37
|
355
|
|
28
|
38
|
255
|
|
29
|
39
|
155
|
|
30
|
40
|
55
|
|
255
|
355
|
1035
|
These
examples
,
as
well
teache
the
practise
of
Progression
,
as
also
sheweth
the
difference
of
facilitie
of
the
same
,
from
the
tedious
vse
of
Figures
in
Addition
,
the
effecte
whereof
well
noted
maie
suffice
,
for
progression
Arithemeticall
.
A
Lapidarie
solde
,
a
Iuell
to
bee
paid
the
first
wéeke
of
52.
in
one
yeare
1
Crowne
the
seconde
,
2
Crownes
,
and
so
euery
paiment
one
Crowne
more
then
an
other
.
52.
tymes
.
It
is
demaunded
what
nomber
of
Crownes
the
whole
Progression
amounteth
.
Accordyng
to
the
second
of
the
former
rules
adde
1
Crowne
the
firste
noumber
with
52.
the
last
,
and
that
maketh
53.
the
whiche
being
multiplied
with
.
26.
halfe
the
times
of
the
Progression
produceth
.
1378.
Crownes
the
iust
somme
of
the
Progression
,
as
by
Addition
will
appeare
.
Example
.
|
1
52
|
|
1
|
11
|
21
|
31
|
41
|
|
51
|
|
1
|
2
|
12
|
22
|
32
|
42
|
52
|
|
53
|
3
|
13
|
23
|
33
|
43
|
103
|
|
4
|
14
|
24
|
34
|
44
|
455
|
|
26
|
5
|
15
|
25
|
35
|
45
|
|
318
|
6
|
16
|
26
|
36
|
46
|
355
|
|
106
|
7
|
17
|
27
|
37
|
47
|
255
|
|
|
8
|
18
|
28
|
38
|
48
|
155
|
|
1378
|
9
|
19
|
29
|
39
|
49
|
55
|
|
|
10
|
20
|
30
|
40
|
50
|
1378
|
|
|
55.
|
155.
|
255.
|
355.
|
455
|
|
A
Marchaunt
solde
100.
yardes
of
cloth
to
bee
paide
in
40
wéekes
,
to
paye
the
firste
wéeke
2
s
.
the
seconde
4
s
.
the
thirde
6
s
.
so
euerie
paiment
2
s
.
more
then
an
other
,
till
40
wéekes
expired
.
It
is
demaunded
what
money
the
said
100.
yardes
of
cloth
doth
amounnt
vnto
.
Accordyng
to
the
former
generall
Rule
adde
2
s
.
the
first
noumber
of
the
progression
to
40
the
laste
of
the
same
,
and
that
maketh
42.
the
whiche
multiplied
by
20.
the
halfe
of
the
tymes
of
the
Progression
yeldeth
840.
shillinges
.
Or
otherwise
,
multiplie
the
whole
noumber
of
times
of
the
Progression
with
21.
the
halfe
of
the
Addition
of
firste
and
last
noumbers
of
the
Progression
,
and
the
result
wil
be
also
840
shillinges
as
by
example
.
Examples
.
|
2.
40.
|
2.
40
|
|
2.
|
21
|
|
42
|
840
|
|
20
|
|
|
840
|
|
There
is
an
other
kinde
of
Progression
,
and
that
is
Geometricall
,
wherein
euerie
tyme
containeth
the
nexte
before
it
,
so
often
as
the
seconde
containeth
the
firste
,
as
|
1.
|
2.
|
4.
|
8.
|
16.
|
32.
|
64.
|
|
3.
|
9.
|
27.
|
81.
|
243.
|
719.
|
|
|
4.
|
16.
|
64.
|
256.
|
1024.
|
|
|
Here
you
maie
perceiue
64.
in
the
firste
Progression
,
containeth
32.
so
often
as
2.
containeth
1.
Also
in
the
seconde
719.
containeth
243.
so
often
as
9.
containeth
3.
Likewise
in
the
thirde
1024.
containeth
256.
so
often
as
16.
containeth
4.
The
whiche
Progressions
or
suche
like
,
to
shewe
the
whole
,
you
shall
multiplie
the
laste
number
of
the
Progression
,
by
the
firste
common
multiplicator
,
and
from
the
result
you
shall
diuide
by
one
lesse
,
then
was
the
multiplier
,
and
so
haue
the
quotient
the
iuste
totall
of
that
Progression
,
as
by
examples
the
effecte
maie
appeare
.
A
Testatour
giueth
in
Legacie
to
eight
of
his
fréendes
,
a
certaine
somme
of
money
:
To
the
firste
4.
pounde
,
to
the
seconde
4.
tymes
as
muche
as
the
firste
,
whiche
is
16.
pounde
:
To
the
thirde
4.
tymes
as
muche
as
the
seconde
,
and
so
euery
of
the
other
4.
tymes
as
muche
as
he
before
hym
.
The
question
is
,
what
amounted
the
whole
legacie
.
As
before
is
shewed
,
sette
doune
all
the
8.
termes
:
Thus
.
|
4.
|
16.
|
64.
|
256.
|
1024.
|
|
4096.
|
16384.
|
65536.
|
Then
multiplie
the
laste
somme
by
the
firste
,
and
the
producte
is
.
262144.
from
whiche
rebate
the
first
4.
so
resteth
264140
to
be
diuided
by
3.
whiche
is
,
1.
lesse
thy
e
the
multiplier
and
the
quotiente
,
is
the
somme
of
the
whole
Legacie
,
whiche
is
87380.
li.
as
by
example
,
proued
by
addition
.
|
65536
|
|
|
|
4
|
|
li.
|
|
262144
|
87380
|
|
4
|
|
|
262140
|
|
|
Thus
muche
to
vnderstande
|
16
|
|
64
|
|
256
|
|
1096
|
|
4096
|
|
16384
|
|
65536
|
|
87380
|
is
sufficient
for
the
fommyng
of
any
progression
Geometricall
,
where
the
firste
Noumber
is
the
roote
in
any
worke
whatsoeuer
the
roote
be
.
¶
The
seconde
parte
containyng
the
woorke
of
Fractions
,
or
broken
numbers
,
and
firste
of
Numeration
.
AS
whole
numbers
compounde
of
vnities
maie
bee
augmented
and
encreased
to
infinite
effect
:
so
an
vnitie
maie
bee
diuided
into
sondrie
and
infinite
diminute
partes
,
whiche
partes
in
name
and
nature
are
agreable
.
For
a
fraction
is
a
parte
of
one
vnitie
,
and
not
of
many
:
for
howbeeit
that
whole
Numbers
maie
bee
diuided
into
partes
,
to
seuerall
effectes
,
the
same
notwithstandyng
,
suche
diuided
partes
are
no
proper
fractions
,
but
improperly
shewe
the
parts
of
whole
nombers
,
and
not
of
an
vnitie
,
as
40.
pounde
to
bee
parted
amongst
three
menne
:
the
firste
to
haue
¼
,
whiche
is
one
fowerth
parte
:
the
seconde
⅖
,
whiche
is
twoo
fift
partes
:
and
the
third
7
/
20
,
whiche
is
seuen
twentie
partes
.
The
saied
Partes
maie
bee
shewed
in
whole
noumbers
,
not
needyng
the
vse
of
fractions
for
the
same
.
For
the
¼
is
10.
lib
.
the
⅖
is
16.
pounde
,
and
the
7
/
20
is
14.
pounde
,
whiche
together
maketh
40.
pounde
,
and
all
suche
numbers
expressed
in
maner
like
fractions
,
are
not
proper
fractions
,
but
improperly
borowyng
the
propertie
of
fractions
,
whiche
as
aforesaied
,
are
partes
of
one
vnitie
onely
,
and
not
aboue
.
Here
is
to
bee
noted
,
that
a
fraction
is
expressed
by
twoo
figures
,
set
the
one
ouer
the
other
,
with
a
line
betwene
,
thus
⅔
,
whiche
signifieth
twoo
thirde
partes
of
an
vnitie
,
and
that
vnder
the
line
,
is
called
the
denominatour
,
because
it
doeth
euer
represent
the
partes
,
wherein
the
vnitie
is
diuided
:
and
that
aboue
the
line
is
called
the
numeratour
,
because
it
sheweth
the
number
of
partes
,
by
occasion
required
,
not
needyng
the
whole
vnitie
.
As
when
a
manne
hath
right
to
⅔
partes
of
a
pounde
in
money
,
whiche
is
twoo
Nobles
,
then
2.
ouer
the
line
,
sheweth
the
partes
of
his
right
,
and
3.
vnder
the
line
,
sheweth
wherein
the
vnitie
is
diuided
,
and
representeth
one
pounde
of
money
,
diuided
into
three
partes
.
Here
note
,
that
euery
fraction
abstract
or
free
from
denomination
,
maie
bee
applied
and
made
contracte
to
any
denomination
,
by
occasion
required
,
and
more
easie
for
the
learner
to
vnderstande
,
what
the
nature
and
valewe
of
a
fraction
is
,
when
the
Carracter
of
denomination
is
ioyned
with
it
,
then
when
it
is
without
the
same
,
as
by
example
the
effecte
maie
appeare
.
|
½
.
|
⅔
.
|
¾
.
|
⅘
.
|
⅚
.
|
⅞
.
|
9
/
10.
|
17
/
20.
|
25
/
32.
|
161
/
240.
|
Euery
of
the
denominatours
of
the
10.
former
fractions
,
doeth
represente
an
vnitie
diuided
into
so
many
partes
,
as
the
figure
or
figures
of
the
same
doeth
demonstrate
:
howbeeit
,
not
to
bee
knowen
of
what
thyng
,
for
want
of
a
Carracter
,
to
signifie
the
denomination
.
Likewise
euery
Numeratour
,
is
so
muche
lesse
thē
an
vnitie
,
as
the
difference
appeareth
,
betwene
it
and
the
denominatour
thereof
,
and
maie
bée
applied
to
sondrie
thynges
,
ioynyng
a
Carracter
for
the
same
,
bee
it
of
weightes
,
Measures
,
Moneyes
,
or
other
thynges
whatsoeuer
,
as
hereafter
appeareth
by
Carracters
for
Monies
,
seemyng
moste
apte
for
the
purpose
.
|
d
.
|
d
.
|
s
.
|
s
.
|
li.
|
li.
|
li.
|
li.
|
li.
|
li.
|
|
½
|
⅔
|
¾
|
⅘
|
⅚
|
⅞
|
6
/
10
|
17
/
20
|
25
/
32
|
127
/
240
|
The
firste
and
seconde
of
these
10.
fractions
,
hath
the
letter
d
.
for
carracter
,
signifiyng
of
a
peny
,
and
halfe
a
penie
,
and
2.
thirde
partes
of
a
peny
.
The
third
and
fowerth
haue
the
letter
s
.
for
carracter
,
signifiyng
to
bee
of
a
shillyng
:
as
3.
fowerth
partes
,
and
fower
fifte
partes
of
a
shillyng
.
All
the
reste
haue
the
letter
l.
for
carracter
,
signifiyng
euery
of
the
same
to
bee
a
fraction
,
or
a
parte
of
a
pound
of
Money
,
as
5.
sixt
partes
of
a
pound
7.
eight
partes
of
a
pounde
,
and
so
the
reste
9.
tenth
,
17.
twenteth
,
25.
thirtie
twoo
,
162
twoo
hundreth
and
fourtie
partes
of
a
pounde
and
accordyng
to
the
former
saiyng
,
so
much
as
any
of
the
numeratour
(
whiche
is
aboue
the
line
)
is
lesser
then
the
Denominatour
of
the
same
:
so
muche
it
wanteth
of
the
valewe
of
the
vnitie
by
the
Denominatour
,
and
carracter
represented
,
be
it
of
a
peny
,
a
shillyng
,
or
a
pounde
:
and
so
to
vnderstand
of
all
other
fractions
,
of
what
denomination
so
euer
,
and
for
the
learners
better
vnderstandyng
hereafter
the
same
fractions
are
applied
to
other
denominations
,
signified
by
wordes
,
for
want
of
vsuall
carracters
,
as
for
moneys
is
founde
.
½
Inche
,
⅔
Foote
,
¾
Yarde
,
⅘
Elle
,
⅚
Ounce
or
vnz
,
⅞
lib
or
pounde
weight
,
9
/
10
C.
or
hundreth
weight
,
17
/
20
Hower
,
25
/
32
Moneth
,
162
/
240
Yere
.
&c.
Thus
maie
you
see
a
fraction
to
bee
a
parte
of
an
vnitie
,
whereof
knowen
by
Carracter
,
or
woorde
of
denomination
,
and
not
hauyng
denomination
,
maie
bee
applied
to
any
thyng
,
by
occasion
required
,
and
thus
muche
maie
seme
sufficiente
to
giue
vnderstandyng
how
to
expresse
a
fraction
,
whiche
is
a
parte
of
Numeration
:
howbeit
,
now
remaineth
to
shewe
how
to
finde
the
valewe
of
a
fraction
,
whereof
the
effecte
hereafter
followeth
by
examples
in
the
former
fractions
,
applied
to
seuerall
denominations
.
½
Bushell
signifieth
a
Bushell
to
bée
diuided
in
twoo
partes
,
and
the
halfe
thereof
the
fraction
representeth
:
whereof
to
finde
the
valewe
to
bee
expressed
in
common
and
knowen
partes
,
you
shal
consider
what
diminute
partes
the
Bushell
containeth
,
and
that
is
4.
Peckes
.
Then
multiplie
the
numerator
1.
by
4.
Peckes
in
the
Bushell
,
and
the
producte
diuided
by
the
Denominator
2.
the
quotient
will
shewe
2.
Peckes
to
bee
contained
in
the
fraction
,
and
is
the
valewe
of
halfe
a
Bushell
desired
to
bee
knowne
,
and
this
take
for
a
generall
rule
,
to
bryng
a
fraction
into
common
and
knowne
partes
,
the
effect
more
at
large
appearyng
in
sondrie
examples
followyng
.
⅔
Foote
signifieth
twoo
thirde
parts
of
a
foote
,
whereof
to
finde
the
valew
in
common
knowen
partes
,
consider
what
Diminutiue
partes
a
foote
containth
,
and
that
is
12
Inches
,
by
the
whiche
multiplie
the
Numerator
.
2.
maketh
22
Inches
,
the
which
diuided
by
the
Denominator
.
3.
yeldeth
inquotient
8
Inches
for
⅔
partes
of
a
foote
.
&c.
Likewise
2
/
4
lib
.
is
3
quarteas
of
a
Pounde
weight
,
and
to
knowe
the
value
thereof
,
you
must
consider
what
knowen
partes
the
same
containeth
,
the
whiche
beeing
haberdipoys
waight
is
16
ounxes
.
Wherby
multiply
the
Numerator
3
,
and
the
product
is
48
ounzes
,
the
whiche
diuided
by
the
Denominator
4.
the
quotient
sheweth
12.
ounzes
to
bee
¾
of
the
lib
.
habardipoys
.
Howbeit
if
the
Pounde
waight
bee
Troy
weight
wherby
Gold
Siluer
and
Precious
stones
are
waied
,
then
12
ounzes
maketh
the
lib
.
the
whiche
multiplied
by
the
Numerator
3.
produceth
36.
ounze
,
the
whiche
diuided
by
the
Denominator
4
yeldeth
in
Quotient
9.
ounzes
for
¾
of
the
lib
.
Troye
.
Also
4
/
6
ell
representeth
foure
fift
partes
of
an
ell
,
the
whiche
to
bring
into
common
and
knowen
partes
,
consider
what
knowen
partes
an
ell
containeth
,
and
that
is
founde
in
3
sondrie
sortes
.
Firste
it
containeth
4.
q.
proper
to
the
same
.
Also
5
q
.
of
the
yarde
,
and
thirdly
45
Inches
.
To
haue
it
in
parts
proper
to
it
,
multiplie
the
Numerator
4
by
the
quarters
in
the
ell
,
whiche
is
also
4
,
maketh
16.
and
that
diuided
by
the
Denomitor
5.
yeldeth
3
q.
of
the
ell
,
and
⅕
of
one
of
the
same
q.
To
haue
it
in
quarters
of
the
yarde
,
multiplie
the
Numerator
by
5.
quarters
of
a
yard
in
an
ell
contained
,
the
product
wilbe
20
,
and
the
same
diuided
by
5
the
Denominator
,
sheweth
4.
q.
of
a
yard
in
the
fraction
contained
.
Lastly
to
bring
it
into
Inches
,
multiplie
the
Numerator
4
by
45
Inch
in
the
ell
contained
,
the
Product
wilbe
180.
The
which
diuided
by
the
Denominator
5.
yeldeth
in
quotient
36
Inches
for
⅘
of
an
ell
.
To
bryng
⅚
s.
into
apte
knowen
partes
,
multiply
the
Numerator
5
by
12.
d
.
in
a
shilling
contained
,
maketh
60.
and
the
same
diuided
by
6.
the
denominator
,
yeldeth
in
quotient
10.
d
.
for
⅚
of
a
shillyng
.
&c.
To
bryng
⅞
d
.
into
knowen
partes
,
multiplie
the
Numeratour
7.
by
the
Mytes
of
a
Penny
,
whiche
are
24
,
and
the
Product
wil
be
168
,
and
the
same
diuided
by
the
denominator
.
8.
the
quotient
will
shew
21.
Mytes
to
be
the
⅞
partes
of
a
penny
.
To
bring
9
/
10
Crowne
into
knowen
partes
,
multiplie
the
numerator
9.
by
15
grotes
,
or
60.
Pence
in
a
Crowne
contained
,
and
you
shall
haue
produced
135.
for
groates
,
and
540
for
Pence
,
the
whiche
products
diuided
by
the
denominator
10.
yeldeth
in
quotient
13.
groates
and
a
halfe
,
and
54
d
.
euery
of
whiche
is
4.
s
.
6.
d
.
for
9
/
10
of
a
Crowne
.
To
bryng
17
/
20
Noble
into
knowen
partes
,
multiply
the
numerator
17.
hy
20.
greates
or
80.
pence
in
a
Noble
contained
,
and
the
Producte
will
be
340.
for
the
groates
,
and
1360.
for
pence
,
the
whiche
diuided
by
the
Denominator
20.
yeldeth
in
Quotient
17
groates
and
68.
d
.
euery
of
whiche
is
5.
s
.
8.
d
.
for
17
/
20
of
a
noble
.
To
bring
25
/
32
l.
into
knowen
partes
,
multiply
the
numerator
25.
by
the
shillyngs
in
a
pound
whiche
is
20.
and
the
Product
wilbe
500.
the
which
diuided
by
the
Denominator
32.
yeldeth
in
quotient
15.
s
.
and
20
/
32
partes
of
a
shillyng
,
and
to
knowe
the
value
of
that
later
fraction
multiplie
the
numerator
20.
by
the
pence
in
a
shilling
,
which
is
12.
and
the
product
wilbe
240.
the
whiche
diuided
by
32.
sheweth
in
quotient
7.
d
.
ob
.
and
so
haue
you
15.
s
.
7.
d
.
ob
.
for
the
25
/
32
partes
of
a
pounde
.
Lastly
to
bryng
162
/
240
li.
into
knowen
parts
,
multiplie
the
Numerator
162.
by
20.
s
.
in
a
Pound
,
and
the
Product
will
be
3240.
the
whiche
diuided
by
the
Denominator
240.
yeldeth
in
quotient
13.
s
.
6.
d
.
for
162
/
240
li.
and
so
of
all
other
.
Progression
of
Fractions
.
PRogression
of
Fractions
is
in
2
sortes
,
the
one
of
property
contrary
to
the
other
.
for
the
first
which
is
½
.
⅓
.
¼
.
⅕
.
⅙
.
and
so
infinitely
,
the
greater
that
the
denominator
is
,
so
much
the
smaler
is
the
value
of
the
fraction
,
for
⅙
li.
whiche
is
3.
s
.
4.
d
.
is
of
smaller
value
then
⅕
li.
whiche
is
4.
s
.
also
¼
li.
is
5.
s
.
and
of
smaller
value
then
⅓
li.
whiche
is
6.
s
.
8.
d
.
and
so
⅓
6.
s
.
8.
d
.
is
smaller
than
½
li.
which
is
10.
s
.
But
to
the
contrary
in
the
seconde
sort
of
progression
,
whiche
is
½
.
⅔
.
¾
.
⅘
.
⅚
.
&c.
the
greater
that
the
Denominator
is
,
the
more
is
the
value
of
the
fraction
.
For
⅚
li.
beeyng
16.
s
.
8.
d
.
is
more
then
⅘
li.
whiche
16.
s
.
Also
¾
li.
whiche
is
15.
s
.
is
greater
then
⅔
li.
whiche
is
13.
s
.
4.
d
.
and
so
of
all
other
like
vnderstande
.
And
here
note
in
the
first
Progression
,
the
greater
that
the
Denominator
is
,
so
muche
the
more
is
the
vnity
decreased
,
whiche
may
bee
to
infinite
effect
and
euer
to
be
somwhat
,
and
to
the
contrary
in
the
seconde
Progression
,
the
greater
that
the
denominator
is
,
the
nearer
to
the
whole
vnitye
the
value
of
the
fraction
doth
approche
,
how
be
it
can
neuer
attaine
to
make
the
vnity
.
Reduction
of
Fractions
.
REduction
of
Fractions
containeth
the
maner
how
to
bryng
2
or
more
Fractions
into
one
,
either
such
as
be
of
one
Deuomination
,
as
other
whiche
are
of
contrary
denominations
,
the
effect
whereof
more
easie
to
vnderstand
by
a
fewe
examples
then
in
many
wordes
.
To
reduce
⅓
li.
¾
li.
into
one
,
that
is
to
make
one
Fraction
to
containe
the
value
of
them
both
.
You
shall
by
a
generall
Rule
multiplie
the
2
denominators
,
the
one
by
the
other
saiyng
,
3
tymes
4
is
is
12.
to
bee
sette
doune
twise
for
2.
newe
denominators
thus
.
12.
12.
then
multiplie
the
numerator
of
the
firste
fraction
by
the
Denominator
of
the
seconde
,
that
is
one
by
4.
maketh
4
for
a
newe
Numerator
to
stande
ouer
the
common
and
newe
denominator
thus
4
/
12
li.
Also
multiplie
the
numerator
of
the
seconde
fraction
by
the
denominator
of
the
first
which
is
3.
by
3
is
9
to
set
ouer
12
thus
9
/
12
li.
&
so
haue
you
2
new
fractions
of
one
Denomination
,
containing
the
value
of
2
first
.
For
⅓
li.
and
4
/
12
li.
is
of
one
value
which
is
6.
s
.
8.
d
.
and
¾
li.
and
9
/
12
li.
is
and
of
one
value
,
which
is
15
s
.
&
the
2
firste
beyng
of
contrary
Denominations
reduced
into
the
2
later
beyng
of
one
denomination
.
And
to
make
one
fraction
of
them
both
,
adde
together
the
2
Numerators
4
and
9
is
13.
to
set
ouer
12
thus
13
/
12.
and
so
you
haue
1
fraction
13
/
12
li.
containyng
the
iuste
value
of
⅓
li.
and
¾
li.
Note
that
when
the
Numerator
of
any
fraction
is
greater
then
the
Denominator
,
the
same
is
a
fraction
improper
,
and
made
in
suche
forme
by
néede
in
worke
or
otherwise
,
and
then
by
Rule
generall
diuide
the
numerator
by
the
Denominator
,
and
the
quotient
will
shewe
the
vnitie
or
vnities
in
the
sayde
fraction
,
and
the
remaine
if
there
be
any
will
be
a
proper
fraction
.
Wherfore
to
ende
this
reduction
,
diuide
the
Numerator
13.
by
the
Denominator
12.
and
the
quotient
will
bée
1
and
1
/
12
li.
whiche
is
21
s
.
8
d
.
the
iust
value
of
the
2
firste
fractions
⅓
li.
whiche
is
6
s
.
8
d
.
and
¾
li.
whiche
is
15
s
.
and
together
maketh
21
s
.
8
d
.
as
the
Reduction
hath
brought
forthe
.
Sometimes
occasion
may
require
reduction
of
3.
4.
or
more
seuerall
Fractions
of
sondry
Denominations
to
bee
brought
into
one
denomination
,
and
to
make
one
fraction
of
many
,
and
then
you
shall
multiplie
the
first
denominator
by
the
seconde
,
and
that
product
by
the
thirde
and
the
seconde
product
,
by
the
fourth
&c.
And
so
many
Fractions
as
there
are
to
be
reduced
,
so
many
newe
Denominators
shal
you
set
downe
in
former
order
.
And
to
finde
numerators
to
euery
of
the
same
you
shall
multiply
euery
numerator
into
all
the
denominators
of
the
other
fractions
not
belonging
to
the
numerator
multipliar
,
and
so
finde
to
euery
newe
denominator
a
newe
numerator
,
as
example
will
declare
.
To
reduce
½
li.
⅔
li.
¾
li.
and
⅘
li.
into
one
denomination
,
and
so
to
one
Fraction
firste
multiplie
the
denominators
,
one
into
anothers
product
,
as
2
by
3.
is
6.
and
that
by
4.
is
24.
the
whiche
by
5.
is
20.
for
common
denominator
to
be
set
downe
4
tymes
.
Then
by
the
numerator
of
the
firste
,
whiche
is
1.
multiplie
the
Denominators
of
the
other
,
whiche
is
3.
4.
and
5.
the
product
is
60.
to
set
ouer
the
common
Denominator
120.
thus
60
/
120
li.
and
is
in
value
equall
with
the
first
fraction
½
li.
Then
by
the
Numerator
of
the
seconde
,
whiche
is
2.
multiplie
the
denominators
of
the
other
,
whiche
is
2.
4.
and
5.
and
the
product
is
80.
to
set
ouer
the
common
denominator
thus
,
80
/
120
li.
equall
to
the
seconde
fraction
⅔
li.
Likewise
by
the
numerator
of
the
thirde
fraction
,
whiche
is
3.
multiply
the
denominators
of
the
other
whiche
is
2.
3.
and
5.
the
product
is
.
90.
to
set
ouer
120
thus
90
/
120
li.
and
is
in
value
equall
with
the
third
fraction
¾
li.
Lastly
by
4.
the
Numeratour
of
the
fowerth
fraction
,
multiplie
the
denominators
of
the
other
,
whiche
is
2.
3.
and
4.
and
the
product
is
96.
to
sette
ouer
the
common
denominator
thus
96
/
120
,
and
is
in
valewe
equal
with
⅘
li.
and
so
you
haue
fower
newe
fractions
of
one
Denomination
,
for
the
fower
firste
of
contrary
Denomination
,
whiche
is
the
effecte
causyng
the
reduction
.
Then
accordyng
to
former
instruction
,
adde
together
the
Numeratours
of
all
the
newe
fractions
,
beyng
of
one
Denomination
,
whiche
is
60.
80.
90.
96.
and
make
326.
to
sette
ouer
the
common
Denominatour
,
thus
326
/
120
,
the
whiche
appearyng
to
bée
a
fraction
improper
,
diuide
the
Numerator
by
the
Denominatour
,
and
the
quotient
will
shewe
the
vnities
in
the
same
,
and
the
proper
fraction
,
all
whiche
is
2.
and
86
/
120
li.
whiche
is
2.
li.
14.
s
.
4.
d
.
the
iuste
valew
of
the
first
fower
fractions
:
For
½
.
li.
is
10.
shillynges
,
⅔
.
li.
is
13.
s
.
4.
d
.
¾
.
li.
is
15.
s
.
and
⅘
.
li.
is
16.
s
.
and
make
together
,
2.
li.
14.
s
.
4.
d
.
as
the
woorke
of
Reduction
hath
brought
forthe
.
&c.
If
the
number
of
Fractions
bee
so
many
,
that
the
Reduction
of
them
would
bee
tedious
to
bee
made
at
one
tyme
,
then
you
maye
reduce
parte
of
theim
at
one
tyme
,
and
the
reste
at
an
other
,
and
so
make
twoo
newe
Fractions
of
all
the
firste
.
Then
reduce
the
saied
twoo
newly
made
both
into
one
,
and
so
you
haue
doen
,
as
example
maie
declare
.
To
bryng
½
.
⅔
.
¼
.
⅖
.
⅚
.
⅞
.
li.
all
into
one
fraction
,
would
séeme
tedious
to
a
learner
to
performe
.
Wherefore
reduce
three
of
the
firste
together
,
and
thei
will
make
12
/
24.
26
/
24.
6
/
24.
and
makes
in
one
3
/
2
4
/
4.
li.
Then
reduce
the
three
laste
figures
together
,
and
you
shall
haue
96
/
240.
200
/
240.
210
/
240.
and
makes
in
one
506
/
240.
and
so
haue
you
twoo
newe
Fractions
for
all
the
other
6.
Lastly
reduce
the
twoo
newly
made
into
one
and
you
shall
finde
20304
/
5760
li.
whiche
is
worthe
3.
li.
10.
s
.
6.
d
.
the
iuste
valewe
of
the
sixe
firste
.
&c.
Thus
muche
maie
séeme
sufficient
for
reduction
of
proper
fractions
,
whiche
are
partes
intire
of
an
vnitie
,
and
neither
greater
,
nor
so
muche
as
the
saied
vnitie
,
and
I
accoumpte
suche
improper
,
whiche
are
either
greater
then
an
vnitie
,
or
lesse
then
an
intire
parte
,
as
some
other
kinde
bee
,
whiche
are
but
partes
one
of
an
other
,
and
bee
called
Fractions
of
Fractions
,
whereof
the
reduction
followeth
.
To
reduce
fractions
of
fractions
,
whiche
are
partes
one
of
an
other
,
all
not
makyng
so
muche
as
an
vnitie
,
you
shall
multiplie
all
the
Denominatours
together
,
and
so
haue
one
Denominatour
,
for
an
newe
and
proper
Fraction
:
then
ye
shall
multiplie
all
the
Numeratours
together
,
and
haue
one
Numerator
to
sette
ouer
the
newe
Denominator
,
and
finde
one
proper
Fraction
for
many
other
,
as
by
example
maie
appeare
.
To
reduce
⅔
.
of
¾
.
of
⅘
li.
into
one
,
multiply
the
denominators
together
,
as
3.
by
4.
is
12
and
that
by
5.
maketh
60.
for
a
newe
Denominator
.
Then
multiply
the
numerators
together
,
as
2.
by
3.
is
6.
the
whiche
by
4.
maketh
24.
to
bee
sette
ouer
the
Denominator
thus
,
24
/
60
li.
whiche
is
the
value
of
8.
s
.
represented
by
the
three
firste
fractions
.
Sometymes
occasion
maie
procure
a
reduction
of
proper
Fractions
,
and
improper
of
bothe
sortes
all
together
(
that
is
to
saie
)
whole
numbers
,
proper
fractions
,
and
fractions
of
fractions
to
bee
brought
into
one
,
as
by
example
.
To
bryng
3.
and
⅔
.
li.
with
¾
.
li.
and
½
.
of
⅔
.
of
¾
.
li.
into
one
,
you
shall
firste
bryng
the
whole
number
,
and
the
Fraction
thereto
belongyng
,
into
one
Fraction
improper
,
the
whiche
to
performe
,
you
shall
multiplie
the
whole
number
3.
by
the
denominator
of
the
fraction
thereto
belongyng
,
whiche
is
also
3.
and
the
product
is
9.
wherevnto
adde
2
the
Numerator
of
the
same
fraction
,
so
haue
you
11
/
3.
li.
for
the
whole
number
and
first
fraction
.
Then
bryng
the
3.
fractions
of
fractions
into
one
,
as
before
is
taught
,
whiche
will
make
6
/
24.
li.
so
shall
you
haue
3.
Fractions
for
all
,
whiche
are
11
/
3.
li.
¾
.
li.
and
6
/
24
li.
and
reduced
make
1344
/
288.
li.
whiche
is
4.
li.
13.
s
.
4.
d
.
and
so
muche
representes
the
Figures
of
the
Example
.
¶
Of
diuision
in
broken
Numbers
,
and
firste
of
Abreuiation
of
greater
termes
into
smaller
.
TO
abreuiate
a
fraction
of
great
termes
(
that
is
of
many
Figures
)
into
an
other
of
smaller
termes
,
or
fewer
Figures
,
you
shall
consider
what
Digette
is
moste
apte
to
diuide
aswell
the
Numerator
,
as
also
the
Denominator
of
any
suche
fraction
,
as
is
to
bee
abreuiated
,
and
sette
the
2.
quotientes
one
ouer
the
other
,
and
you
shall
haue
a
newe
fraction
of
smaller
termes
then
the
firste
,
as
by
example
.
To
abreuiate
54
/
72
li.
giue
regard
what
Diget
or
figure
,
will
diuide
both
the
numerator
and
denominator
,
and
that
may
be
doen
by
4
sondrie
digettes
,
as
by
9.
by
6.
by
3.
and
by
2
and
the
moste
apte
of
them
is
9.
And
as
you
make
your
diuision
,
sette
the
quotiente
of
the
numerator
aboue
the
same
,
and
the
quotient
of
the
denominator
vnder
the
same
denominator
thus
.
Wherein
you
maie
perceiue
that
in
54
,
9.
is
contained
6
/
54
li.
6.
tymes
and
so
72.
8.
tymes
,
and
so
72
/
8
you
haue
a
fraction
of
twoo
Figures
6
/
8.
li.
for
the
other
of
4.
Figures
54
/
72.
the
greater
termes
abreuiated
into
smaller
,
and
the
value
not
channged
.
Likewise
by
the
same
order
,
consider
that
2.
beyng
made
diuisor
of
6
/
8.
li.
you
shall
haue
that
fraction
abreuiated
to
8
/
4.
li.
whiche
in
smallest
tearmes
that
maie
bee
,
is
of
equalle
valewe
with
the
twoo
other
:
for
euery
of
the
same
representeth
15.
shillynges
,
3
/
6.
li.
and
thus
is
the
practise
.
8
/
4.
When
the
learner
findeth
a
fraction
to
be
abreuiated
,
whiche
beyng
of
greater
termes
then
with
facilitie
to
knowe
the
Digette
,
moste
apte
for
the
abreuiation
,
then
let
hym
examine
the
example
by
mediation
thus
,
2.
beyng
alwaies
Diuisor
,
as
in
this
Fraction
48
/
96.
li.
for
example
.
|
3
|
|
6
|
|
12
|
|
24
|
|
By
2.
48
/
96
maketh
3
/
6.
li.
the
whiche
by
3.
is
1
/
●
|
|
48
|
|
24
|
|
12
|
|
6
|
Hereby
three
mediations
the
Fraction
48
/
96.
pounde
,
is
brought
to
6
/
12.
pounde
,
where
it
is
with
facilitie
perceiued
,
that
6.
is
halfe
of
12.
and
therefore
½
.
li.
is
settedoune
for
it
,
and
so
the
abreuiation
ended
.
Sometyme
a
fraction
maie
require
2.
3.
or
more
digettes
,
to
bryng
the
same
to
smallest
termes
,
as
by
sundrie
examples
the
effect
maie
appeare
by
this
fraction
160
/
240.
pounde
.
|
2
|
|
4
|
|
80
|
|
160
|
|
By
2.
240
maketh
⅔
.
|
|
120
|
|
6
|
|
3
|
|
By
3
160
it
can
not
.
|
|
240
|
|
2
|
|
40
|
|
160
|
|
By
4
240
is
⅔
.
lib
.
|
|
60
|
|
3
|
Here
note
,
that
when
a
Fraction
hath
equall
number
of
Ciphers
,
in
the
place
or
places
towarde
the
right
hande
,
then
the
abreuiation
may
bee
made
the
shorter
,
by
cuttyng
awaie
the
Ciphers
of
bothe
sides
,
in
equall
number
,
thus
.
|
2
li.
|
|
16
0
|
|
By
8.
24
0
maketh
⅔
.
|
|
3
|
|
2
li.
|
2
li.
|
|
16
00
|
16
000
|
|
24
00
|
24
000
|
|
3
|
3
|
Wherein
doeth
appeare
,
that
the
ciphers
of
euery
of
the
three
Fractions
,
separated
from
the
Figures
,
then
euery
of
the
same
is
16
/
24.
and
diuided
by
8.
sheweth
⅔
.
li.
for
smalleste
termes
,
and
so
in
al
other
like
vnto
the
same
.
To
abreuiate
75
/
120.
pounde
,
there
is
required
the
vse
of
twoo
figures
,
whiche
is
3.
and
5.
to
beginne
with
the
one
at
pleasure
to
bee
taken
,
and
to
ende
with
the
other
by
consequence
,
as
in
example
,
practise
doeth
shewe
.
|
5.
lib
.
|
|
25
|
|
75
|
|
By
3.
120
or
by
5.
|
|
40
|
|
8
|
|
5
lib
.
|
|
15
|
|
75
|
|
Or
by
5.
120
by
3.
|
|
24
|
|
8
|
To
abreuiate
112
/
192
,
there
is
required
the
vse
of
one
figure
onely
,
for
the
moste
apte
,
whiche
is
4.
and
maie
bee
doen
by
twoo
Figures
,
whiche
is
firste
by
8.
and
then
by
2.
as
practise
will
manifeste
.
|
7.
li.
|
7
lib
.
|
|
28
|
14
|
|
112
|
112
|
|
By
4.
192
|
or
by
8.
192
and
by
2
|
|
48
|
24
|
|
12
|
12
|
To
abreuiate
128
/
160.
lib
.
moste
aptly
there
is
required
twoo
figures
,
8.
and
4.
and
with
more
circumstaunce
by
4.
and
2.
as
by
example
.
|
4
lib
.
|
|
16
|
|
128
|
|
By
8.
160
and
by
4.
|
|
20
|
|
5
|
|
4
lib
.
|
|
8
|
|
32
|
|
128
|
|
By
4.
twise
160
and
by
2.
|
|
40
|
|
10
|
|
5
|
To
abreuiate
●75
/
500
li.
seeke
for
the
moste
apt
diget
to
diuide
by
,
and
that
is
5.
by
the
which
at
3
tymes
is
brought
forthe
¾
li.
whiche
is
15.
s
.
as
by
example
.
|
lib
.
|
|
3
|
|
15
|
|
75
|
|
375
|
|
By
5.
500
|
|
100
|
|
20
|
|
4
|
Thus
muche
may
seeme
to
suffice
for
Abreuiation
of
Fractions
,
whiche
is
performed
by
Diuision
practized
in
whole
noumbers
.
Howbeit
,
diuision
of
fractions
is
much
contrary
,
as
by
examples
the
effect
may
appeare
.
When
one
fraction
is
to
be
diuided
by
an
other
,
that
is
to
say
,
when
you
would
knowe
how
many
tymes
I
fraction
is
contained
in
an
other
,
set
the
diuisor
one
the
lefte
hande
the
other
,
&
a
crosse
betwéene
theim
thus
,
which
requireth
by
Diuision
to
make
knowen
how
many
tymes
⅖
li.
is
contained
in
⅞
li
.
Then
multiplie
the
numerator
of
the
diuisor
by
the
denominator
of
the
diuidende
,
and
that
product
shal
be
Diuisor
.
Likewise
multiplie
the
numerator
of
the
diuidende
by
the
denominator
of
the
diuisor
,
and
the
product
thereof
shal
be
diuidende
,
and
the
same
diuided
by
the
laste
diuisor
sheweth
in
Quotient
that
is
required
in
the
woorke
,
as
practise
may
more
amply
deelare
.
|
li.
35
li.
|
tymes
&
3
/
16
of
a
tyme
.
|
|
|
In
this
practise
appeareth
that
2.
numerator
of
the
diuisor
,
multiplied
by
8.
the
Denominator
of
the
diuidende
,
produceth
16.
set
vnder
the
Crosse
for
diuisor
,
and
5
denominator
of
the
Diuisor
multiplied
by
7.
the
Numerator
of
the
diuidende
produceth
35.
for
diuidende
to
set
ouer
the
Crosse
.
The
whiche
35
diuided
by
the
diuisor
thereof
16.
sheweth
in
quotient
that
⅖
li.
whiche
is
8.
s
.
is
contained
in
⅞
li
.
whiche
is
17.
s
.
6.
d
.
2
tymes
,
and
3
/
16
of
a
tyme
,
and
note
that
⅖
lib
.
twice
is
16
s
.
and
3
/
16
of
8
s
.
or
1
tyme
is
1
s
.
6
d
.
and
maketh
together
17
s
.
6
d
.
the
iuste
value
of
the
fraction
diuided
.
To
diuide
¾
lib
.
by
⅓
lib
.
by
the
same
order
the
practise
foloweth
.
Wherein
appeareth
that
in
¾
li
.
whiche
is
15
s
.
⅓
li.
beyng
6
s
.
8
d
.
is
contained
2
tymes
,
and
¼
in
value
equall
to
the
diuidende
whiche
is
also
15
s
.
&c.
As
in
woorkes
by
whole
numbers
a
smaler
somme
cannot
bee
diuided
by
a
greater
,
but
is
set
ouer
the
greater
,
to
shewe
in
proportion
a
part
of
a
tyme
,
geuen
so
in
diuision
of
fractions
,
when
the
diuisor
is
greater
than
the
diuidend
.
Then
the
Diuidend
produced
will
be
lesse
then
the
produced
Diuisor
,
and
therefore
to
stande
ouer
the
diuisor
,
to
shewe
the
proportionall
part
of
a
tyme
,
sought
for
by
the
woorke
,
the
effect
by
example
,
made
more
plaine
.
If
I
demaunde
how
many
tymes
⅚
lib
.
is
contained
in
⅔
li
.
reason
doth
perswade
that
no
tyme
in
the
Quotient
will
appeare
.
Neuerthelesse
procéedyng
in
the
woorke
,
the
diuidend
will
shewe
such
part
of
a
tyme
as
proportion
will
allowe
,
&
in
practise
appearing
.
Hereby
doth
appeare
that
12
/
15
parte
of
the
diuisor
is
the
value
of
the
diuidend
,
and
therfore
wanteth
of
a
tyme
,
and
12
/
15
of
16
s
.
8
d
.
the
diuisor
is
13.
s
.
4
d
.
the
iuste
value
of
the
diuidend
⅔
li.
the
effecte
sought
for
by
the
worke
.
To
shew
the
effect
in
fractions
improper
,
may
satisfie
the
desires
of
suche
as
the
same
would
knowe
,
and
therefore
is
furthered
the
example
followyng
.
If
it
be
demaunded
howe
many
tymes
¾
li.
is
contained
in
4
li.
and
⅘
.
lib
.
You
shall
firste
make
4.
li.
and
⅘
in
fraction
,
and
it
will
bee
24
/
5
which
is
the
diuidend
to
be
diuided
by
¾
the
diuisor
,
and
so
in
the
Quotient
will
appeare
,
that
is
sought
for
as
by
example
practized
.
Here
the
effect
sought
for
,
beyng
how
many
tymes
15
s
.
whiche
is
¾
li.
is
contained
in
4
li.
16
s
.
whiche
is
24
/
5
li.
the
same
in
Quotient
appeareth
to
be
6.
times
&
6
/
15
of
a
tyme
,
and
euery
tyme
containeth
the
value
of
the
Diuisor
,
whiche
is
15
s
.
maketh
in
all
4
li.
10
s
.
and
therwith
6
/
15
of
a
tyme
which
is
6
s
.
maketh
4.
li.
16
s
.
the
iuste
value
of
the
Diuidende
24
/
5
li.
whiche
is
the
effect
the
woorke
requires
.
Multiplication
of
fractions
.
THe
worke
of
Multiplication
of
Fractions
,
is
in
nature
contrary
to
the
workyng
by
whole
noumbers
,
for
as
the
one
increaseth
a
Noumber
of
Vnities
:
so
the
other
increaseth
a
Dimunition
of
a
Fraction
.
For
in
multipliyng
3
lib
.
by
2
li.
you
saye
2
tymes
3
maketh
6
lib
.
in
whole
Noumbers
,
but
¾
li.
by
⅔
lib
.
you
muste
vnderstand
the
saiyng
¾
li.
taken
⅔
of
a
tyme
maketh
halfe
a
Pounde
10
s
.
the
which
to
bring
forthe
by
order
of
Multiplication
of
Fractions
,
you
shall
multiplie
the
Denominators
together
,
and
the
product
thereof
is
an
newe
Denominator
.
Then
must
you
multiply
the
2
Numerators
together
,
and
the
product
is
the
numerator
to
the
foresaid
denominator
,
and
you
haue
done
,
as
by
example
the
effect
may
appeare
.
|
lib
.
|
|
lib
.
|
lib
.
|
lib
.
|
|
2
|
by
|
3
|
yeldeth
the
6
/
12
and
abreuiated
is
½
|
|
3
|
4
|
Here
note
,
that
as
¾
lib
.
taken
2
of
a
tyme
maketh
6
/
12
li.
which
is
10
s
.
yeuen
so
⅔
li.
taken
¾
of
a
tyme
maketh
also
6
/
12
lib
.
whiche
is
likewise
10
s
.
so
that
it
forceth
not
which
is
set
before
the
other
.
If
occasion
procure
whole
numbers
and
Fractions
to
bee
multiplied
together
,
then
your
whole
noumber
is
to
bee
brought
into
forme
of
fraction
,
and
so
multiplied
by
former
order
,
the
Producte
will
shewe
that
is
sought
for
,
as
example
may
manifest
.
To
multiplie
5
li.
⅘
by
¾
li.
reduce
the
first
fraction
,
and
the
whole
noumber
into
a
fraction
improper
,
and
it
will
be
29
/
5
li.
the
which
multiplie
by
¾
li.
produceth
87
/
20
lib
.
as
in
pratice
.
29
/
5
by
¾
yeldeth
87
/
20
whiche
is
4.
li.
7
s
.
The
whiche
product
wanteth
so
muche
of
the
firste
value
,
as
¾
li.
wanteth
of
an
Vnitie
,
whiche
is
¼
part
,
and
for
the
vnderstandyng
of
the
reason
therof
,
you
shal
note
,
that
if
5
li.
16
s
.
bee
multiplied
by
1
lib
.
it
will
not
chaunge
the
value
,
if
by
2
li.
the
value
will
double
of
by
3.
it
wil
be
treble
,
and
so
forth
infinitely
.
But
to
the
contrary
,
if
you
multiplie
the
said
5
li.
16
s
.
by
¾
lib
.
it
diminisheth
¼
in
value
,
as
practise
hath
shewed
.
If
by
⅔
lib
it
will
want
⅓
in
value
.
If
by
½
lib
.
halfe
the
value
diminisheth
,
and
so
infinitely
,
accordyng
to
the
value
of
the
fraction
multiplicator
.
To
multiplie
3
li.
⅔
with
4
li.
⅚
reduce
euery
of
the
whole
numbers
into
the
fractions
to
it
belonging
,
as
3
li.
⅔
reduced
is
11
/
3
li.
and
4
li.
⅚
maketh
29
/
6
li.
the
whiche
multiplied
together
,
produceth
39
/
18
li.
whiche
is
17
li.
13
/
18
or
14
s
.
5
d
.
⅓
.
The
trueth
whereof
by
reason
to
witnes
,
consider
,
that
3
li.
by
4
li.
produceth
12
lib
.
then
3.
li.
by
⅚
the
contrary
fraction
yeldeth
2
li.
10
s
.
and
4
li.
by
⅔
the
contrary
fraction
is
2
li.
13
s
.
4
d
.
Lastly
2
fractions
,
the
one
by
the
other
produceth
10
/
18
li.
whiche
is
11
s
.
1
d
.
⅓
.
and
together
make
the
foresaid
somme
of
17
lib
.
14
s
.
5
d
.
½
agreeyng
with
the
product
by
the
Rule
,
as
the
addition
of
the
seuerall
partes
wil
appeare
hereafter
set
doune
.
|
|
|
|
lib
.
|
s
.
|
d
.
|
|
3
|
By
|
4
|
12.
|
|
|
|
3
|
⅚
|
2.
|
10.
|
|
|
4
|
⅔
|
2.
|
13.
|
4
|
|
⅔
|
⅚
|
|
11.
|
1.
⅔
|
|
Makes
|
|
17.
|
14.
|
5.
⅓
|
Hereby
is
to
be
perceiued
aswell
the
order
of
the
rule
,
as
also
the
reason
of
the
producte
,
herevnto
hid
,
from
many
whiche
can
multiplie
broken
numbers
.
Substraction
of
fractions
.
TO
substraie
one
fraction
from
an
other
,
there
is
required
that
both
the
boken
nombers
be
of
one
denomination
,
and
then
the
lesser
numerator
rebated
from
the
greater
,
the
rest
will
appeare
to
be
set
ouer
the
common
Denominator
,
and
so
the
worke
is
ended
,
as
by
example
the
effect
may
appeare
.
To
substraie
⅜
li.
from
⅞
li.
rebate
3.
from
7.
rest
4.
to
sette
ouer
8.
the
commom
denominator
thus
4
/
8
li.
whereby
to
vnderstande
if
you
take
⅜
whiche
7
s
.
6
d
.
from
⅞
li.
whiche
is
17
s
.
6
d
.
the
reste
will
bee
4
/
8
li.
whiche
is
10
s
.
and
so
of
all
other
when
both
be
of
one
denomination
,
as
the
sondry
herereafter
set
downe
.
⅖
lib
.
from
⅗
lib
.
reste
⅕
lib
.
and
¼
lib
.
from
¾
.
lib
.
reste
2
/
4.
Likewise
4
/
10.
lib
.
from
7
/
10.
lib
.
reste
3
/
10.
lib
.
so
4
/
12.
lib
.
from
11
/
12.
lib
.
reste
7
/
12.
lib
.
&c.
Notwithstandyng
,
when
occasion
procureth
Substraction
,
the
Fractions
beyng
of
contrary
Denomination
,
then
you
muste
reduce
theim
into
one
Denomination
,
and
so
made
apt
for
the
worke
as
the
former
,
wherof
some
example
followeth
.
To
Substraie
⅔
.
li.
from
¾
.
li.
you
must
rndure
them
by
order
taught
for
reduction
of
proper
Fractions
:
and
so
you
shall
haue
for
⅔
.
li.
8
/
12.
li.
and
for
¾
.
li.
9
/
12.
li.
and
beyng
brought
to
one
denomination
Substraie
8
/
12.
from
9
/
12.
and
the
reste
is
1
/
12.
li.
and
so
you
haue
doen
,
wherein
vnderstande
,
if
you
take
⅔
.
or
8
/
12.
lib
.
from
¾
.
or
9
/
12.
lib
.
the
reste
is
1
/
12.
li.
the
whiche
is
20.
d
.
as
13.
s
.
4.
d
.
from
15.
s
.
the
reste
is
20.
d
.
as
aforesaied
.
The
like
effecte
taketh
place
in
fractions
improper
of
bothe
kindes
,
as
firste
by
example
of
Fractions
of
Fractions
shall
appere
.
To
Substraie
½
.
of
⅔
.
lib
.
from
¾
.
of
⅘
.
lib
.
firste
reduce
the
twoo
firste
into
one
proper
Fraction
,
whiche
is
2
/
6.
lib
.
and
the
twoo
laste
also
into
one
,
maketh
12
/
20.
pounde
,
whiche
beeyng
of
contrary
Denomination
,
muste
bee
brought
into
one
,
and
you
shall
for
the
firste
haue
40
/
120.
lib
.
and
for
the
last
72
/
120.
lib
.
of
the
whiche
lesser
Numerator
40.
substraied
from
the
greater
72.
the
remaine
is
32
/
120.
whiche
is
5.
s
.
4.
d
.
and
the
same
to
vnderstande
so
to
bee
note
,
that
2
/
6.
pounde
,
beyng
6.
s
.
8.
d
.
taken
out
of
12
/
20.
lib
.
whiche
12.
s
.
the
reste
is
5.
s
.
4.
d
.
as
aforesaied
,
whiche
is
30
/
120.
li.
&c.
Likewise
of
Fractions
improper
,
greater
then
an
vnitie
,
here
followeth
an
example
.
To
Substraie
2.
lib
.
⅔
.
from
4.
lib
.
¾
.
firste
reduce
2.
lib
.
⅔
.
in
one
,
maketh
8
/
32.
pounde
,
and
4.
lib
.
¾
.
also
in
one
is
19
/
4.
pounde
,
and
brought
to
one
Denomination
,
will
bee
32
/
112.
li.
and
57
/
12.
pounde
,
whereof
the
lesser
Numeratour
32.
taken
from
the
greater
57.
the
reste
is
25
/
12.
lib
.
whiche
is
2.
pounde
1.
s
.
8.
d
.
and
easely
perceiued
in
former
maner
.
For
2.
lib
.
13.
s
.
4.
d
.
taken
from
4.
lib
.
15.
s
.
the
reste
is
twoo
pounde
,
one
shillyng
eight
pence
,
as
by
the
worke
doeth
appeare
.
¶
Addition
of
Fractions
,
FOr
addition
of
Fractions
there
is
to
bee
considered
,
as
was
in
Substraction
:
that
the
broken
nombers
bee
of
one
Denomination
before
thei
bée
added
,
&
then
put
the
Numerators
into
one
,
to
sette
ouer
the
common
Denominator
,
and
so
the
woorke
is
ended
.
But
if
thei
bee
of
contrary
Denomination
,
thei
must
bee
brought
into
one
,
and
so
made
apte
for
woorke
:
as
by
example
more
at
large
,
you
maie
perceiue
.
To
adde
¾
.
2
/
4.
and
¼
.
li.
into
one
Fraction
,
adde
together
all
the
Numeratours
,
as
3.
2.
and
1.
make
6.
to
sette
ouer
the
common
Denominatour
4
,
thus
.
6
/
4.
whiche
is
1.
pounde
10.
shillynges
,
and
so
the
worke
is
ended
.
Howbeit
,
if
the
Fractions
bee
of
sonderie
Denominations
,
as
¾
.
⅘
.
and
⅚
.
pounde
,
then
thei
muste
bee
reduced
,
and
will
bee
90
/
120
96
/
120.
and
100
/
1200.
and
the
Numeratours
added
together
,
as
aforesaied
make
280
/
120
,
whiche
is
2.
lib
.
7.
s
.
8.
d
.
And
the
same
to
vnderstande
so
to
bee
,
note
that
¾
.
lib
.
15.
s
,
with
⅘
.
lib
.
16.
s
.
added
to
⅚
.
lib
.
16.
s
.
8.
d
.
make
together
2.
pounde
7.
shillynges
8.
pence
,
as
the
worke
hath
brought
forthe
.
If
you
adde
together
Fractions
of
Fractions
,
as
½
.
of
⅔
.
lib
.
to
¾
.
of
⅘
.
lib
.
then
reduce
the
twoo
firste
into
one
maketh
2
/
6.
lib
.
and
the
twoo
laste
is
12
/
20.
pounde
,
and
in
one
Denomination
is
40
/
120.
li.
and
72
/
120.
lib
.
whiche
make
112
/
120.
and
is
18.
s
.
8.
d
.
and
by
memorie
to
witnesse
the
truthe
,
consider
that
½
.
of
⅔
.
li.
is
6.
s
.
8.
d
.
and
¾
.
of
⅘
.
pounde
is
12.
shillynges
,
the
whiche
together
maketh
18.
s
.
8.
d
as
the
worke
findeth
.
Likewise
,
if
you
adde
sonderie
whole
Noumbers
,
ioyned
with
Fractions
into
one
,
you
muste
either
reduce
all
into
Fractions
improper
,
and
so
to
one
Denomination
,
addyng
the
Numeratours
together
,
to
sette
ouer
the
common
Denominatour
by
former
order
,
or
els
you
maie
adde
the
whole
nombers
firste
together
,
and
reduce
the
Fractions
onely
,
and
so
ende
the
worke
,
as
in
example
followyng
appeareth
.
To
adde
2.
lib
.
¾
.
to
5.
lib
.
⅗
.
first
reduce
2.
lib
.
¾
.
yeldeth
11
/
4.
and
againe
5.
lib
.
⅗
.
maketh
28
/
5.
li.
and
in
one
denomination
is
55
/
20.
and
212
/
20.
and
added
maketh
167
/
20.
li.
whiche
is
eight
pounde
7.
s
.
Otherwise
,
adde
the
whole
noumbers
together
,
that
is
2.
lib
.
and
5.
lib
.
maketh
.
7.
li.
Then
¾
.
lib
.
and
⅗
,
lib
.
reducted
to
one
Denomination
maketh
27
/
20.
lib
.
whiche
is
27.
s
.
and
put
to
the
foresaied
7.
lib
.
make
together
8.
lib
.
7.
s
.
as
before
.
Such
as
in
readyng
of
Substraction
and
Addition
do
not
well
vnderstande
the
effect
.
Let
them
labour
well
to
vnderstand
Numeration
and
Reduction
of
fractions
,
for
therin
is
taught
all
thinges
néedefull
to
make
the
rest
easie
.
&c.
The
third
part
containyng
the
Rules
of
Proportion
,
and
first
of
the
Rule
of
3.
THe
Rule
of
thrée
is
framed
of
the
former
partes
of
Arithmetique
,
especiallie
of
Multiltiplication
,
and
Diuision
.
And
is
called
the
Rule
of
three
,
for
that
by
three
Noumbers
knowen
,
and
set
doune
in
order
as
the
worke
requireth
,
is
founde
a
fourth
number
,
fought
for
and
desired
,
and
the
commoditie
growing
by
vse
of
the
saied
Rule
procured
Learned
writers
doe
name
it
the
Golden
Rule
,
excellyng
all
other
,
as
Golde
doth
other
mettals
.
It
is
also
called
the
Rule
of
Proportion
,
for
that
euer
the
fowerth
and
vnknowen
Number
found
by
the
worke
,
shall
beare
suche
proportion
vnto
the
thirde
of
the
knowen
numbers
,
as
the
second
beareth
to
the
firste
.
The
effect
better
appearyng
in
fewe
Examples
,
then
in
many
wordes
.
If
2.
clothes
cost
16
li.
what
15.
clothes
.
Here
you
see
3
Noumbers
knowen
,
as
2
Clothes
bought
or
prised
at
16
lib
.
and
15
Cloathes
to
bee
bought
or
prised
after
the
same
rate
the
price
of
whiche
15
Clothes
is
the
fowerth
Number
sought
for
and
desired
,
founde
by
the
woorke
in
order
as
followeth
.
First
you
shall
multiply
the
second
and
third
Numbers
the
one
by
the
other
,
and
the
product
thereof
diuide
by
the
first
Number
,
and
so
shall
you
haue
in
Quotient
the
fowerth
Number
sought
for
&
desired
,
as
by
example
.
|
Clo
.
|
lib
.
|
C.
|
|
|
If
2.
cost
16.
what
15
|
|
|
|
|
16
|
|
|
|
|
90
|
|
|
|
|
15
|
|
|
|
240
|
|
By
this
example
appeareth
that
15.
the
third
number
,
multiplied
by
16.
the
seconde
nomber
,
produceth
240.
the
whiche
diuided
by
the
firste
noumber
2.
yeldeth
in
quotiente
120.
lib
.
for
the
price
of
15.
clothes
,
and
in
suche
proportion
as
16.
beareth
to
2.
that
is
to
saie
,
8.
lib
.
for
euery
clothe
.
The
proofe
of
this
rule
is
made
changyng
the
places
of
3.
of
the
4.
numbers
,
and
so
one
of
the
2.
firste
will
bee
founde
in
quotient
,
if
the
worke
bée
true
.
As
by
example
.
|
li.
|
clothes
.
|
li.
|
|
|
If
120.
buye
15.
what
16.
|
|
|
|
|
15
|
|
|
|
|
80
|
|
|
|
|
16
|
|
|
|
240
|
|
C.
|
lib
.
|
C.
|
|
|
Or
if
15.
cost
120.
what
2
|
|
|
|
2
|
|
|
|
240
|
|
Here
is
to
bee
noted
,
that
aswell
in
practise
of
the
rule
,
as
also
in
the
proofe
,
the
firste
and
thirde
numbers
,
muste
bee
of
one
Denomination
and
nature
,
&
then
of
consequence
,
the
fowerth
number
will
bee
of
denomination
and
nature
,
as
is
the
seconde
,
the
effecte
whereof
as
in
the
former
examples
plainly
appeareth
,
so
in
other
followyng
more
at
large
may
be
seene
.
If
1
pounde
waight
of
Pepper
coste
2
s
.
8
d
.
what
9
ounzes
of
Peper
.
Here
the
first
and
thirde
Numbers
are
of
one
nature
,
but
not
of
one
Denomination
.
Wherefore
before
you
woorke
you
must
reduce
the
first
number
into
onzes
,
and
so
made
apte
for
the
worke
.
Likewise
for
that
the
seconde
Number
is
in
2.
Denominations
,
as
shillinges
and
pence
,
therefore
you
must
reduce
the
shillinges
into
pence
,
and
then
your
3
Numbers
beyng
apt
for
the
woorke
,
will
stand
thus
.
If
16.
ounzes
cost
32.
d
.
what
9.
ounzes
,
If
1.
yarde
coste
3
lib
.
7.
s
.
6
d
.
what
75.
yardes
.
The
midle
number
in
this
example
is
not
apt
for
the
woorke
,
till
the
whole
be
brought
into
pence
,
whiche
is
the
smallest
Denomination
of
3.
in
the
same
seconde
Noumber
,
wherefore
it
must
be
reduced
,
and
will
make
810
pence
,
and
will
stand
thus
apt
for
the
worke
.
If
1
yard
cost
810
d
.
what
75
yardes
.
Here
the
diuision
is
made
more
for
plainnes
in
obseruyng
the
Rule
,
then
for
any
necessitie
.
For
one
the
first
number
cannot
any
thing
diminishe
in
Diuision
,
nor
any
thyng
augment
in
Multiplication
,
as
by
the
Diuision
before
may
appeare
,
and
in
the
multiplication
required
in
the
proofe
followyng
is
manifested
.
If
75.
yardes
cost
.
60750.
d
.
what
1.
yard
Thus
you
maie
perceiue
,
that
the
Quotient
in
the
firste
woorke
,
is
equall
with
the
diuidende
in
the
same
,
and
nothyng
diminishe
by
the
diuision
.
And
likewise
the
Producte
of
the
seconde
woorke
,
is
equall
with
the
multiplicande
,
and
nothyng
augmented
by
the
multiplication
:
wherefore
it
is
good
to
note
,
that
suche
diuisions
and
multiplications
maie
bee
cutte
of
,
when
1.
is
one
of
the
3.
knowen
numbers
in
this
rule
,
as
by
some
examples
the
effecte
maie
appeare
.
If
the
C.
weight
of
Currance
coste
33.
s
.
4.
d
.
what
1.
lib
.
The
sayd
C.
reduced
into
pound
waights
to
agree
in
Denomination
with
the
thirde
number
,
and
the
seconde
number
reduced
into
pence
,
the
smaller
denomination
of
twoo
in
the
same
,
then
all
the
three
are
made
apte
for
the
whole
worke
,
and
will
stande
thus
.
If
112
li.
coste
400
d
.
what
1
lib
.
Here
the
multiplication
is
omitted
,
for
that
1.
the
Multiplicatour
can
nothynge
augmente
in
Multiplication
,
as
aforesaide
,
and
therefore
the
seconde
Noumber
is
diuidende
where
it
standeth
,
and
beeyng
diuided
by
the
firste
,
the
quotiente
is
3.
d
.
4
/
7.
whiche
fraction
is
halfe
a
penie
,
and
somthyng
more
wherefore
alwaies
when
1.
is
the
third
number
,
diuide
the
seconde
by
the
firste
,
and
the
quotient
will
bee
that
you
seeke
for
.
|
If
1.
elle
coste
20
d
.
what
48
|
960.
d
.
|
|
20
|
|
|
960
|
|
Here
the
diuision
is
omitted
,
because
that
1.
the
firste
Number
,
can
nothyng
diminishe
in
diuision
.
Wherefore
in
all
workes
where
one
is
the
firste
number
,
the
Producte
made
by
multiplication
of
the
seconde
by
the
third
is
that
you
seeke
for
in
the
quotient
,
whiche
in
this
worke
is
960
d
.
as
appeareth
.
If
4.
s
.
8.
d
.
buye
one
ounze
of
siluer
,
how
many
ounzes
buyeth
100.
li.
After
you
haue
made
the
firste
and
thirde
noumbers
to
agree
,
in
denomination
by
reduction
,
bryngyng
bothe
into
pence
,
as
the
rule
teacheth
,
then
the
question
will
stande
thus
.
Here
the
multiplication
is
omitted
in
former
respecte
,
and
the
thirde
number
the
true
diuidende
,
and
diuided
by
56.
yeldeth
in
quotient
428
ounces
4
/
7.
and
so
all
other
woorkes
,
where
1.
is
the
seconde
number
.
The
seconde
parte
of
the
Rule
of
three
,
is
of
effecte
contrary
to
the
former
,
and
is
named
the
Backer
Rule
of
three
,
vppon
cause
reasonable
:
for
as
in
the
former
Rule
,
the
fowerth
number
is
euer
so
muche
greater
thē
the
thirde
,
as
the
seconde
is
aboue
the
firste
,
so
in
the
Backer
Rule
,
the
fowerth
number
is
euer
so
muche
lesser
then
the
seconde
,
as
the
third
is
greater
then
the
firste
:
As
to
the
contrary
,
so
muche
greater
then
the
seconde
,
as
the
third
is
lesser
then
the
firste
.
And
the
order
of
this
Backer
Rule
is
suche
,
that
when
the
three
knowen
numbers
are
sette
doune
,
then
you
shall
multiplie
the
firste
and
seconde
,
the
one
by
the
other
,
and
the
Producte
thereof
diuided
by
the
thirde
number
,
and
so
finde
in
the
quotiente
,
that
is
desired
,
&
sought
for
by
the
worke
:
as
by
examples
the
effecte
more
amplie
maie
appeare
.
When
the
bushell
of
wheat
is
worth
3
s
.
4
d
.
the
Wheaten
Lofe
waiyng
20.
ounzes
for
1
d
.
what
shall
the
penny
Wheaten
Lofe
way
when
the
bushell
of
wheat
is
worth
5.
s
.
Herein
touchyng
the
woorke
,
you
shall
giue
no
respect
to
the
Bushell
of
wheate
,
but
to
the
price
thereof
,
to
be
made
the
first
number
neither
to
the
wheaten
Lofe
,
but
to
the
weight
thereof
,
for
the
seconde
number
,
and
accordyngly
of
the
bushell
of
wheate
and
the
price
thereof
,
for
the
thirde
number
,
and
then
the
thrée
numbers
agréeyng
in
denominations
apt
for
worke
,
as
was
taught
in
the
former
part
,
then
the
example
is
thus
to
bee
set
doune
and
wrought
.
d
.
If
40.
admit
20.
onz
what
60
d
.
Here
you
may
see
,
that
as
the
Bushell
of
wheate
is
augmented
in
price
,
a
thirde
parte
in
5
s
.
so
the
Lofe
of
a
peny
is
diminished
in
waight
a
thirde
parte
of
20
ounzes
.
Wherein
appeareath
the
nature
of
the
rule
,
and
the
effect
of
that
was
taught
before
touchyng
the
same
Likewise
,
if
32
d
.
admit
24.
onz
what
20
d
.
So
that
as
the
peny
Lofe
waieth
24.
ounzes
,
when
wheat
is
at
2
s
.
8
d
.
the
Bushell
,
it
shall
way
38
ounzes
⅕
,
when
wheate
is
at
20
d
the
Bushell
.
This
backer
rule
may
be
applied
to
sondry
effectes
of
greater
consequence
then
euery
man
vnderstandeth
.
Wherefore
I
will
set
doune
a
fewe
examples
whiche
to
some
men
may
seeme
not
superfluous
.
The
lode
of
Hay
at
13
s
.
4.
the
bottell
of
ob
.
waiyng
6
lib
.
what
shall
the
bottle
waye
when
the
like
Lode
of
Hay
is
worth
20
s
.
If
13
s
.
4
d
.
admit
6
li.
what
20
s
.
If
the
lode
15
s
.
admit
5.
li.
bottell
what
10
s
.
the
lode
.
The
ounze
of
fine
Golde
worth
55
s
.
The
Crowne
of
5
s
.
waiyng
2
d
.
waight
Troye
,
what
shall
the
saide
Crowne
waye
when
fine
Golde
is
at
3
li.
by
ounze
.
If
55
s
.
admit
2.
d
.
waight
,
what
60
s
.
If
60
s
.
admit
1
d
.
waight
20.
Graines
,
what
45
s
.
Reduce
and
it
will
stande
thus
.
If
60
s
.
admit
44.
graines
,
what
45
s
.
The
ounce
of
Starlyng
at
2.
s
.
8.
d
.
the
Englishe
grote
waiyng
2.
d
.
½
.
waight
,
what
ought
the
Grote
to
waie
,
when
the
ounce
of
starlyng
is
at
5.
s
.
Reduce
and
it
will
stande
thus
.
If
32.
d
.
admitted
60.
grain
,
what
60
d
.
The
ounce
of
Starlyng
at
5.
s
.
the
Englishe
Grote
waiyng
32.
graines
Troye
.
What
shall
the
said
grote
waie
,
when
Starlyng
is
at
3.
s
.
4.
d
.
the
ounce
.
Reduce
and
it
will
stande
thus
.
If
60.
d
.
admitt
32.
graines
,
what
40.
d
.
THE
double
Rule
is
so
called
,
for
that
the
aunsweres
of
suche
questions
,
as
the
same
requireth
,
are
founde
at
the
double
workyng
of
the
Rule
of
three
directe
whereof
the
order
followeth
.
If
the
100.
lib
.
waight
cost
carriage
20.
miles
18.
d
.
what
will
1500.
lib
.
waight
coste
60.
miles
.
In
this
question
and
all
other
like
,
you
maie
note
,
that
the
firste
and
thirde
number
,
must
bee
of
one
denomination
and
kinde
:
as
herein
bothe
miles
,
or
bothe
waight
to
bee
taken
at
pleasure
for
the
firste
woorke
.
And
then
of
consequence
the
other
shall
serue
in
the
saied
firste
and
thirde
noumber
in
the
seconde
worke
:
as
by
examples
the
effect
maie
appeare
.
¶
Example
.
|
C.
|
d
.
|
C.
|
|
|
If
1.
waight
coste
18.
what
15
|
|
|
|
|
18
|
|
|
|
|
120
|
|
|
|
|
15
d
.
|
s
.
d
.
|
|
|
|
270
make
|
22.
6.
|
|
s
.
d
.
|
|
|
Againe
if
20.
mile
cost
22.
6.
what
60
|
|
60
|
|
|
1320
|
|
|
30
|
|
|
1350
|
As
you
maie
perceiue
in
the
firste
worke
,
the
waight
is
vsed
,
and
not
the
miles
:
and
in
the
seconde
the
miles
is
vsed
,
and
not
the
waight
,
whiche
twoo
denominations
might
bee
chaunged
in
the
saied
examples
,
and
bryng
out
the
truthe
accordyngly
,
as
by
other
the
effecte
maie
appeare
.
If
1.
C.
waight
coste
2.
s
.
Carrage
25.
miles
:
what
8.
C.
waight
Carrage
100.
miles
.
|
miles
|
s
.
|
miles
.
|
|
Saie
if
25.
coste
2.
what
100
|
|
|
|
2
|
|
|
200
|
|
C.
|
s
.
|
C.
|
|
|
Againe
if
1.
coste
8.
what
8
|
|
|
|
|
s
.
|
li.
s
.
|
|
|
|
64
|
maketh
3.4
.
|
By
these
examples
it
is
manifeste
,
that
as
one
hundreth
costeth
2.
s
.
for
cariage
25.
miles
,
so
it
costeth
8.
s
.
for
carrage
100
miles
,
by
the
firste
woorke
brought
forthe
.
And
as
1.
C.
costeth
8.
s
.
so
8.
C.
costeth
64.
s
.
for
carrage
100.
miles
by
the
seconde
woorke
appearyng
,
wherein
is
shewed
the
effecte
purposed
,
by
furtheryng
of
the
saied
examples
,
either
of
the
same
maie
bee
taken
to
practise
of
the
firste
woorke
,
and
then
the
other
of
consequence
must
serue
in
the
later
.
If
100
li.
in
12
monthes
gaine
10
li.
what
500
in
17
monthes
.
Say
first
,
if
12
monthes
gain
10
li.
what
17
monthes
.
Againe
if
100.
li.
gaine
14
li.
3.
s
.
4.
d
.
what
500
li.
Reduce
,
Multiplie
and
diuide
,
and
finde
.
70.
l
16
s
.
8
d..
The
Rule
of
3
Compound
.
TO
the
Rule
of
3
Compound
,
belongeth
5
knowen
numbers
,
for
the
firste
parte
of
the
same
,
whereof
the
seconde
and
first
must
euer
be
of
one
Denomination
,
and
for
practise
thereof
you
shall
multiplie
the
first
and
second
Numbers
,
the
one
by
the
other
,
and
the
product
thereof
shal
be
your
diuisor
.
Then
multiply
the
other
thrée
(
that
is
)
the
third
by
the
fourth
,
and
the
product
therof
by
the
fifte
,
and
that
laste
product
shall
be
the
diuidende
,
and
diuided
by
the
forenamed
Diuisor
yeldeth
in
quotient
that
whiche
is
sought
for
and
desired
.
¶
Example
.
If
one
hundreth
weight
20
Miles
coste
carriage
18
d
.
what
15
C.
for
60
Miles
.
|
C.
|
Miles
|
d
.
|
C.
|
Miles
|
d
.
810
|
|
1.
|
20.
|
18.
|
15.
|
60
|
|
|
1
|
|
|
|
|
|
20
|
|
|
|
Herein
appeareth
that
the
first
and
second
numbers
multiplied
together
,
the
Product
is
20
for
Diuisor
,
also
the
fift
,
fourth
,
and
thirde
multiplied
together
,
produceth
16200
the
which
diuided
by
20
the
diuisor
,
yeldeth
in
quottent
810
d
.
whiche
is
3.
li.
7.
s
.
6.
d
.
for
true
aunswere
,
agréeyng
with
the
firste
example
of
the
double
Rule
practized
by
the
same
question
.
Likewise
as
in
the
thirde
Question
of
the
double
Rule
.
If
100
li.
in
12
monthes
graine
10
li.
What
500
li.
in
17
monthes
.
|
100
|
500
|
|
1200
|
5000
|
|
|
17
|
|
|
35000
|
|
|
5000
|
|
|
8500
|
|
|
|
Here
may
you
see
the
first
&
second
numbers
together
,
maketh
the
Diuisor
1200.
And
the
other
thrée
maketh
85000
for
diuidend
,
and
yeldeth
in
quotient
70
li.
16
s
.
8
d
.
for
aunswere
,
agréeyng
therein
with
the
double
Rule
.
The
seconde
part
of
the
Rule
of
thrée
compound
is
contrary
to
the
first
,
for
in
this
part
the
thirde
and
fourth
numbers
must
be
multiplied
together
,
the
product
to
bee
diuisor
.
Then
the
first
,
second
,
and
fift
to
gether
multiplied
,
the
product
shal
be
the
Diuidend
,
and
so
the
Quotient
will
shewe
that
whiche
is
sought
for
and
desired
,
and
the
thirde
and
first
number
is
of
one
Denomination
,
the
effect
by
example
appearyng
.
If
50
li.
in
6
monthes
gaine
7
li.
in
how
many
monthes
will
60
li.
gaine
10
li.
Multiplie
and
diuide
,
and
you
shall
finde
7
monthes
1
/
7
as
by
practise
.
|
li.
|
monthes
.
|
li.
|
li.
|
li.
|
|
50
|
6
|
7
|
60
|
10
|
|
6
|
|
|
7
|
|
|
300
|
|
|
420
|
|
|
10
|
|
|
|
|
|
3000
|
|
|
|
|
|
|
|
The
third
parte
of
the
Rule
of
three
compounde
,
is
contrary
to
the
twoo
former
,
for
in
the
same
,
the
firste
and
fifte
noumbers
,
bee
of
contrary
denomination
:
and
you
muste
multiplie
the
nombers
,
whereupon
the
question
dependeth
,
whiche
is
the
fite
nomber
,
by
the
firste
and
third
nombers
,
whiche
giue
the
value
,
and
the
producte
thereof
muste
bee
your
diuidende
,
then
multiplie
the
seconde
and
fowerth
together
,
whiche
are
the
numbers
valued
,
and
the
producte
shall
be
diuisor
and
so
you
shall
finde
in
quotient
,
that
which
is
sought
for
and
desired
.
as
by
example
.
If
4.
d
.
Starlyng
bee
worthe
5.
d
.
Flemishe
,
and
12.
d
.
Flemishe
bee
worthe
8.
souce
Tournoys
.
Question
,
how
many
pence
Starlyng
maketh
50.
souce
Tournoys
,
whiche
is
the
Frenche
croune
by
exchange
.
Answere
,
multiplie
50.
souce
Tournoys
(
whiche
is
the
nomber
wherevpon
the
Question
dependeth
)
by
4.
d
.
Starlyng
,
and
12.
d
.
Flemishe
,
whiche
noumbers
giue
the
value
,
and
the
producte
thereof
shall
bee
your
diuidende
.
Then
multiplie
5.
d
.
Flemishe
,
and
8.
Souce
Turnoys
(
whiche
are
the
nombers
valewed
)
the
one
by
the
other
,
and
that
producte
shall
bee
the
diuisor
,
and
so
finde
in
Quotiente
60.
d
.
Starlyng
,
the
whiche
is
worthe
the
Croune
of
50.
Souce
Tournoys
,
as
by
the
practise
maie
appeare
.
|
d
.
|
d
.
|
d
.
|
souce
,
|
souce
.
|
|
4.
Star
.
|
5.
Fle
.
|
12.
Fle
.
|
8.
Tou
.
|
5.
Tou
.
|
|
12
|
8
|
|
|
|
|
48
|
40
|
|
|
|
|
2400
|
|
|
In
the
fowerth
parte
of
the
Rule
of
three
Compounde
,
the
first
and
fiueth
(
or
laste
of
the
knowen
nombers
)
are
of
one
denomination
:
and
you
muste
multiplie
the
noumber
wherevpon
the
Question
dependeth
,
by
the
noumbers
that
haue
valuation
,
and
that
producte
diuided
by
the
resulte
of
the
noumbers
whiche
giue
the
valuation
multiplied
together
,
yeldeth
in
quotient
that
whiche
is
sought
and
desired
.
As
by
example
.
If
4.
d
.
Starlyng
be
5.
d
.
Flemishe
,
and
12.
Flemishe
bee
8.
souce
Tournoys
.
Question
,
how
many
souce
Tournoys
is
60.
d
.
Starlyng
worthe
?
Aunswere
.
Multiplie
60.
d
.
Starlyng
(
whiche
is
the
noumber
wherevpon
the
Question
dependeth
)
by
5.
d
.
Flemishe
,
&
8.
souce
Tourneys
,
the
numbers
valewed
,
and
the
product
beyng
2400
shal
be
your
diuidend
.
Then
multiplie
together
the
noumbers
whiche
giueth
the
value
,
whiche
are
4.
d
.
and
12.
and
the
producte
is
48.
for
diuisor
,
&
the
diuision
made
yeldeth
in
Quotient
50.
souce
Tournoys
,
as
practise
doeth
manifeste
.
|
d
.
|
d
.
|
d
.
|
souce
.
|
d
.
|
|
4.
Star
.
|
5.
Flem
.
|
12.
fle
.
|
8.
Tour
.
|
60.
starl
|
|
|
8
|
4
|
|
|
|
|
40
|
48
|
|
|
|
|
60
|
|
|
|
|
|
2400
|
|
|
|
|
|
|
|
¶
The
Rule
of
Companie
without
tyme
limitted
.
TWoo
menne
in
Companie
,
the
firste
put
into
stocke
45.
li.
and
the
other
put
in
68.
li.
who
gained
32.
li.
Question
,
what
portion
of
the
gaine
groweth
to
either
partie
.
To
aunswere
this
Question
,
and
all
other
suche
like
,
how
many
soeuer
are
ioyned
in
Companie
,
their
whole
stocke
shall
euer
bee
the
firste
number
in
the
Rule
of
three
directe
,
and
that
whiche
hath
been
gained
by
their
saied
stocke
,
shall
euer
bee
the
seconde
number
in
the
same
Rule
,
and
euery
mannes
proper
and
particular
stocke
shall
bee
the
third
number
,
and
so
woorkyng
euery
Quotiente
will
shewe
the
portion
of
hym
,
vnto
whom
the
particular
stocke
doeth
belong
,
as
by
example
the
effecte
more
plainly
appearyng
.
|
li.
|
li.
|
li.
|
|
If
113.
gaine
32.
what
45.
|
|
|
45
|
|
|
|
160
|
|
|
|
128
|
|
|
|
1440
|
|
|
li.
|
li.
|
li.
|
|
Likewise
if
113.
gaine
32.
what
68.
|
|
|
68
|
|
|
|
256
|
|
|
|
192
|
|
|
|
2176
|
|
Thus
appeareth
the
gaine
for
the
firste
man
is
12
li.
84
/
113
,
&
for
the
seconde
19
li.
29
/
11●
.
The
whiche
two
sommes
together
makyng
the
iuste
gaines
,
which
is
32.
li.
proueth
the
worke
true
or
els
not
.
Note
,
that
menne
in
Companie
,
hauyng
losse
by
Traffique
vpon
the
Seas
,
or
otherwise
,
their
seuerall
portions
to
bee
borne
,
is
founde
by
this
Rule
also
.
and
so
many
particulare
menne
as
are
in
Companie
,
so
many
seuerall
Quotientes
shall
bee
made
,
and
all
together
make
the
gaine
or
losse
,
euery
mannes
portion
,
accordyng
to
his
stocke
,
whereof
to
giue
many
examples
were
superfluous
,
but
onely
to
shewe
how
to
applie
the
Rule
,
whereof
a
fewe
examples
followe
hereafter
.
Three
menne
laded
a
ship
,
the
aduenture
of
the
first
was
546.
li.
of
the
second
628.
li.
and
of
the
thirde
732.
li.
By
tempest
vpon
the
sea
,
the
master
was
forsed
to
caste
ouerborde
,
to
the
value
of
640.
li.
Question
,
what
portion
of
the
losse
euery
manne
ought
to
beare
?
Aunswere
.
The
whole
aduentures
added
together
,
make
1906.
li.
for
firste
number
in
proportion
,
and
the
losse
640.
li.
must
bee
the
seconde
number
,
and
euery
particular
portion
of
the
stocke
the
thirde
number
.
The
whiche
multiplied
and
diuided
,
accordyng
to
the
Rule
,
yeldeth
three
seuerall
quotientes
,
shewyng
the
losse
of
euery
manne
,
whiche
for
the
firste
is
—
183.
li
642
/
1906.
for
the
seconde
210.
li.
1660
/
1906
,
and
for
the
thirde
245
li.
510
/
19●●
.
And
all
added
together
make
the
iuste
losse
,
whiche
is
640.
li.
|
|
|
li.
|
|
li.
|
|
If
1906
lib
.
lose
640
lib
.
|
what
|
546
|
facit
.
|
183.
46●
/
1900
|
|
628
|
210.
1000
/
190●
|
|
732
|
245.
1510
/
1906
|
|
|
|
|
|
640.
|
Three
men
in
Companie
gained
100.
li.
whereof
for
32.
lib
.
whiche
the
firste
manne
putte
in
,
he
had
of
the
gaine
25.
li.
and
of
the
reste
the
thirde
manne
had
¼
,
more
then
the
seconde
.
Question
,
what
the
seconde
and
thirde
putte
into
stocke
?
Aunswere
.
Firste
,
consider
the
25.
li.
taken
out
of
the
gaine
,
there
reste
75.
li.
for
the
seconde
and
third
whereof
the
thirde
muste
haue
5.
li.
for
4.
to
the
seconde
.
Wherefore
adde
5.
li.
and
4.
li.
together
,
and
that
maketh
9.
li.
for
firste
number
in
the
Rule
of
three
,
and
saie
,
if
9.
li.
require
75.
li.
what
4
li.
and
for
the
seconde
man
you
shall
finde
in
gaine
33.
li.
6.
s
.
8.
d
.
and
for
the
thirde
41.
li.
13.
s
.
4.
d
.
as
the
practice
sheweth
.
|
li.
|
li.
|
li.
|
|
li.
|
s
.
|
d
.
|
|
If
9.
require
|
75.
what
|
4
|
facit
.
|
33.
|
6.
|
8.
|
|
5
|
41.
|
13.
|
4.
|
Then
hauyng
founde
euery
mannes
particular
parte
of
the
gaine
,
you
shall
saie
.
If
25.
li.
of
gaine
come
of
32.
li.
in
stocke
for
the
firste
manne
,
whereof
commeth
33.
li.
6.
s
.
8.
d
.
for
the
seconde
,
and
41.
li.
13.
s
.
4.
for
the
thirde
woorke
,
and
you
shall
finde
the
seconde
man
put
in
42.
li.
13.
s
.
4.
d
.
and
the
third
53.
li.
6.
s
.
8.
d
.
|
|
|
.li
|
|
li.
|
s
.
|
d
.
|
|
If
25
li.
require
32.
l.
|
what
|
33.
⅓
|
facit
.
|
42.
|
13.
|
4.
|
|
41.
⅔
|
53.
|
6.
|
8.
|
¶
The
rule
of
Companie
with
tyme
.
THree
Marchauntes
in
Companie
,
the
firste
putte
in
50.
li.
for
fower
Monthes
,
the
second
65.
li.
for
seuen
Monethes
,
and
the
third
72.
li.
for
nyne
Monethes
,
who
gained
85
Question
.
What
euery
mannes
portion
of
the
gaine
?
Here
is
to
bee
noted
,
that
euery
mannes
money
muste
bee
multiplied
,
by
his
tyme
of
continuaunce
in
the
Companie
,
and
the
thre
productes
added
together
,
shall
bee
first
number
in
the
rule
of
three
,
the
gaine
the
seconde
and
euery
particulare
producte
the
thirde
noumber
,
and
so
proceadyng
the
woorke
,
you
shall
finde
three
seuerall
quotientes
shewyng
euery
mannes
parte
of
the
gaine
to
hym
due
,
accordyng
to
his
stocke
,
and
tyme
of
continuaunce
,
as
by
example
will
appere
.
|
1
|
2
|
3
|
|
50
|
65
|
72
|
|
4
|
7
|
9
|
|
200
|
455
|
648
|
|
|
|
455
|
|
|
|
200
|
|
|
|
1303
|
Thus
hauing
found
the
thrée
seuerall
productes
to
be
1303.
then
you
shall
go
to
the
Rule
and
say
.
|
lib
.
|
200
|
facit
|
13.
67
/
130●
|
|
If
1303.
gain
85
what
|
455
|
29.
●88
/
1383
|
|
|
648
|
42.
354
/
130●
|
|
|
|
|
85
|
Here
is
to
bee
noted
,
that
so
many
men
as
are
in
company
,
so
many
seuerall
productes
must
be
made
,
and
so
many
seueral
quotients
muste
manifest
the
gaine
to
euery
one
belongyng
.
&c.
❧
The
Rule
of
Aligation
.
THE
Rule
of
Aligation
requireth
a
certaine
circumstaunce
,
for
gatheryng
of
differences
,
of
thynges
of
sondry
Prices
,
wherof
part
may
be
better
and
parte
worse
then
a
common
price
,
whereas
a
quantitie
of
euery
sorte
occasion
may
require
to
bee
taken
,
and
the
saide
differences
added
together
,
shal
be
firste
noumber
in
the
Rule
of
three
.
The
whole
quantitie
of
the
matter
desired
the
second
,
and
euery
perticular
difference
the
thirde
noumber
,
and
so
many
perticulars
as
are
in
the
woorke
,
so
many
seuerall
quotients
will
make
the
Quantitie
of
the
matter
sought
for
.
The
effect
more
plainly
appearyng
in
fewe
examples
,
then
in
many
wordes
or
great
discourse
thereof
,
as
hereafter
you
may
see
.
An
Appoticary
for
recouery
of
health
in
a
noble
man
is
charged
to
compose
an
ingredience
of
4
sondrie
sortes
of
riche
and
costly
drogges
,
to
say
,
of
45
s
.
42
s
.
36
s
.
and
32
s
.
the
ounze
,
and
to
haue
8.
ounzes
worth
40
s
.
the
ounze
of
euery
sort
a
quantity
.
Question
.
How
muche
of
euery
sorte
is
to
be
taken
?
Aunswere
.
Firste
set
doune
the
seuerall
prises
one
vnder
an
other
,
the
highest
vppermost
,
with
the
common
price
at
the
lefte
side
thus
.
|
40
|
45
|
8
|
|
42
|
4
|
|
36
|
2
|
|
32
|
5
|
|
|
|
19
|
Then
you
muste
linke
together
one
aboue
the
common
price
with
one
of
the
other
vnder
the
common
price
,
and
the
difference
of
euery
one
aboue
the
common
price
shal
be
set
against
the
other
,
linked
with
it
vnder
the
common
price
,
and
to
the
contrary
,
the
difference
of
euery
one
vnder
the
common
price
shal
be
set
against
the
other
,
linked
with
it
aboue
the
common
price
,
the
whiche
differences
found
and
set
accordingly
,
as
aboue
appearing
,
the
totall
makyng
19.
Then
by
the
Rule
of
thrée
is
to
be
sought
the
4
Quotients
,
to
make
8
ounzes
of
40
s
.
the
ounze
of
euery
price
a
quantitie
,
whiche
is
as
by
practice
hereafter
appeareth
.
|
If
19.
require
8.
what
8
|
|
|
8
|
|
64
|
|
If
19.
require
8.
what
4
|
|
|
8
|
|
32
|
|
If
19.
require
8.
what
2
|
|
|
8
|
16
0
16
/
19
|
|
16
|
19
|
|
If
19.
require
8.
what
5
|
|
|
8
|
|
40
|
Here
you
may
perceiue
,
that
the
said
Appoticary
ought
to
take
of
45
s
.
3
ounzes
7
/
19
,
of
42
s
.
1
ounze
13
/
19
of
36
s
.
16
/
19
of
an
ounze
,
and
of
32
s
.
2
ounzes
2
/
10
the
which
together
maketh
8
ounzes
of
40
s
.
the
ounze
,
the
effect
by
the
question
required
.
Here
is
to
be
noted
,
that
although
the
former
quantities
be
truely
brought
forthe
,
as
the
question
requireth
,
the
same
notwithstandyng
,
the
same
quantities
maye
shewe
like
trueth
,
if
the
differences
chaunge
their
places
,
as
by
linkyng
the
vppermost
price
with
the
lowest
sauyng
one
,
and
the
lowest
with
the
vppermost
sauyng
one
thus
.
|
40
|
45
|
4
|
If
19.
require
8.
what
|
4
|
2.
13
/
19
|
|
42
|
8
|
8
|
3.
7
/
19
|
|
36
|
5
|
5
|
2.
2
/
19
|
|
32
|
2
|
2
|
0.
16
/
19
|
|
|
|
16
|
|
|
8.
oz
|
A
Marchaunt
hath
bought
Canuas
of
22
d
.
19
d
.
15
d
.
10
d
.
9
d
.
and
8
d
.
the
Ell.
A
frende
requireth
to
haue
a
thousande
elles
(
of
euery
sort
a
parcell
)
to
stand
hym
in
12
d
.
the
ell
one
with
an
other
,
the
Marchaunt
to
gaine
nothing
by
him
,
but
to
haue
giuen
him
a
Satten
Doublet
for
his
frendship
?
Question
.
How
muche
of
euery
sort
to
bee
taken
.
Neither
partie
to
haue
wrong
.
Aunswers
.
Firste
finde
the
differences
by
former
order
thus
.
|
12
|
22
|
4
|
|
19
|
3
|
|
15
|
2
|
|
10
|
3
|
|
9
|
7
|
|
8
|
10
|
|
|
|
29
|
The
whiche
being
found
procéede
in
the
Rule
of
thrée
,
&
so
you
shall
haue
6
Quotientes
,
whiche
shewe
the
quantitie
of
euery
sort
of
Canuas
,
to
be
taken
as
practise
will
shewe
.
|
|
|
Elles
.
|
|
If
29.
require
1000
ells
,
what
|
4
|
137.
27
/
29
|
|
3
|
103.
13
/
29
|
|
2
|
68.
28
/
29
|
|
3
|
103.
1●
/
29
|
|
7
|
241.
11
/
29
|
|
10
|
344.
24
/
29
|
|
|
|
1000.
|
A
Marchaunt
hath
4
sortes
of
Golde
,
of
seuerall
finenes
(
to
saye
)
of
23
Carratz
¾
of
22
Carratz
⅔
of
21
Carratz
⅚
,
and
of
20.
Carratz
.
½
.
fine
Question
,
what
quantitie
of
euery
sort
is
to
be
taken
,
to
haue
100.
ounzes
of
22
Carratz
fine
iust
.
Aunswere
.
First
note
,
that
forasmuche
,
as
the
Fractions
,
fine
aboue
,
and
vnder
the
common
finenes
,
are
of
sondry
Denominations
:
therfore
they
must
be
reduced
,
and
made
of
one
Denomination
,
and
will
stand
thus
.
|
22
|
22.
●●
/
12
|
18
|
|
22.
8
/
12
|
2
|
|
21.
10
/
12
|
8
|
|
20.
6
/
12
|
21
|
|
|
|
49
|
Here
you
may
perceiue
,
that
the
finer
sorts
aboue
the
common
finenes
21
/
12
and
8
/
12
are
sett
againste
the
parcells
linked
with
theym
,
whiche
are
vnder
the
common
goodnes
,
and
for
the
common
finenes
therof
2.
is
set
against
the
percell
,
linked
therewith
Also
20
Carratz
6
/
18.
is
set
against
the
parcell
linked
therewith
,
and
so
is
found
49
/
12
for
firste
nomber
in
the
Rule
of
thrée
,
and
euery
particular
difference
,
the
thirde
noumber
with
the
100.
onze
desired
the
second
,
with
which
noumbers
procéedyng
in
the
Rule
of
three
you
shall
finde
4
quotient
which
will
declare
the
quantity
of
euery
sort
of
Gold
,
to
be
taken
to
haue
100.
ounces
of
22
carrratz
fine
iust
,
the
effect
in
example
appearyng
.
|
If
49.
require
100.
what
|
18
|
36.
onz
.
36
/
49.
|
|
2
|
4.
4
/
49.
|
|
8
|
16.
16
/
49.
|
|
21
|
42.
4●
/
49.
|
|
|
|
100.
ounces
.
|
An
Assaie
master
hath
fiue
sortes
of
siluer
of
sondrie
finesse
:
that
is
to
saie
,
of
11.
onzes
14.
d
.
11.
vnzes
10.
d
.
10.
vnzes
.
5.
d
.
9.
vnzes
16.
d
.
and
9.
vnzes
.
12.
d
.
waight
fine
,
and
would
haue
100.
lib
.
weight
of
11.
vnzes
2.
d
.
fine
.
Question
.
What
quantitie
to
be
taken
of
euery
sorte
?
Aunswere
.
Firste
reduce
your
seuerall
denominations
into
one
,
and
then
it
will
stande
thus
.
|
222
|
234
|
30
|
|
230
|
26
|
|
205
|
26
|
|
196
|
11
|
|
192
|
12
|
|
|
|
105
|
The
which
differences
found
procede
with
the
totalle
for
the
firste
noumber
.
the
100.
lib
.
the
second
:
and
euery
particular
the
third
,
and
so
shall
you
haue
the
Quotiente
of
euery
sorte
to
bee
taken
,
to
make
100.
lib
.
weight
of
11.
vnzes
2.
d
.
fine
,
the
effecte
in
example
appearyng
.
|
|
|
lib
.
|
|
If
105.
require
100
li.
what
|
30
|
28.
60
/
105.
|
|
26
|
24.
80
/
105.
|
|
26
|
24.
80
/
105.
|
|
11
|
10.
50
/
105.
|
|
12
|
11.
45
/
105.
|
|
|
|
100
|
Howbeeit
that
these
woorkes
are
to
bee
proued
by
the
common
order
,
of
prouyng
the
Rule
of
three
:
The
same
notwithstandyng
,
there
are
other
sonderie
orders
of
prooues
,
for
the
commixions
of
Goldes
and
Siluers
whiche
here
I
omitte
,
in
respecte
of
seuerall
causes
,
referryng
suche
as
by
vocation
,
maie
desire
knowledge
therein
,
to
priuate
conference
who
maie
bée
satisfied
to
effecte
extraordinarie
.
The
rule
of
one
false
position
.
THE
Rules
of
false
Positions
are
so
called
(
not
that
any
vntruthes
are
furthered
,
or
taught
by
the
same
,
but
that
by
a
noumber
supposed
,
though
farre
from
truthe
.
The
same
putte
in
vse
of
the
Rule
,
bryngeth
foorthe
the
truthe
,
whiche
of
consequence
is
expected
and
desired
,
as
by
example
the
effecte
maie
appeare
.
A
Marchaunt
taketh
a
house
,
wherevpon
dependeth
suche
yerely
benefite
,
that
he
disburseth
a
somme
of
money
,
not
named
.
A
frende
requestyng
to
haue
the
bargaine
,
the
Marchaunt
is
content
to
take
10
by
C.
for
his
money
,
and
at
the
ende
of
seuen
yeres
the
tyme
of
his
vse
therof
,
receiueth
of
his
frend
606.
lib
.
of
money
,
for
that
he
had
disbursed
and
the
intreste
of
the
principall
.
The
question
is
,
what
portion
of
money
the
Marchante
disbursed
for
the
saied
house
.
Aunswere
.
The
firste
nomber
in
the
Rule
of
three
,
for
aunswere
of
this
muste
bee
furthered
by
supposition
,
the
which
for
example
,
take
300
li.
supposed
to
bee
the
money
firste
disburied
,
then
of
consequence
,
the
intreste
thereof
seuen
yeres
,
beyng
210.
lib
.
ioyned
therewith
is
to
bee
made
the
seconde
noumber
in
the
woorke
.
Then
to
proceade
,
saie
if
510.
lib
.
principall
and
gaine
come
of
300.
pounde
,
whereof
commeth
600.
pounde
,
woorke
and
finde
352.
pounde
.
1
/
1
6
/
7.
If
500.
come
of
300.
whereof
600
?
of
352.
19
/
17.
Here
note
,
that
what
nomber
or
somme
of
money
soeuer
bee
taken
for
the
supposition
as
firste
noumber
,
and
the
same
with
the
intrest
thereof
made
the
seconde
.
The
600.
li.
beeyng
thirde
in
the
woorke
,
bryngeth
the
truth
to
light
:
as
by
an
other
example
aboue
the
truthe
supposed
maie
appeare
.
Suppose
the
marchaunt
paied
at
the
first
400.
pounde
for
the
aforesaied
house
,
the
intrest
therof
is
10.
li.
by
C.
for
seuen
yeres
,
is
280.
pounde
,
whiche
putte
to
the
principall
maketh
680.
pounde
,
and
is
80.
pounde
more
then
should
bee
,
if
the
supposition
were
true
,
wherefore
saie
in
former
order
.
If
680.
li.
come
of
400.
li.
whereof
commeth
600.
woorke
saieth
as
before
of
252.
pounde
16
/
17.
The
rule
of
ij
.
false
positions
.
WHen
any
question
is
framed
,
founde
of
suche
difficultie
,
as
maie
require
the
practise
of
twoo
false
positions
:
you
shall
suppose
any
nomber
at
pleasure
for
the
first
position
,
and
by
consequence
of
worke
wil
appeare
an
errour
either
vnder
or
aboue
the
truth
,
the
which
beyng
aboue
,
shall
be
noted
with
this
caracter
,
signifiyng
more
,
&
beyng
vnder
the
truth
,
shal
haue
this
note
−
,
whiche
signifieth
lesse
.
And
euen
so
make
a
seconde
position
,
to
bryng
foorthe
a
seconde
errour
with
the
like
notes
.
Then
you
shall
multiplie
the
firste
position
,
by
the
seconde
errour
,
and
the
seconde
position
with
the
firste
errour
,
and
if
the
signes
of
the
errours
bee
like
,
to
saie
bothe
more
,
or
bothe
lesse
then
the
truth
,
then
shall
you
substraie
the
lesser
producte
from
the
greater
.
Also
you
shall
substraie
the
lesser
error
from
the
greater
,
and
with
the
remaine
thereof
you
shall
diuide
the
remaine
of
the
substraction
of
twoo
productes
:
and
the
quotiente
of
that
diuision
,
will
shewe
the
true
Noumber
sought
for
.
Howbeeit
you
shall
note
,
that
when
the
twoo
errours
haue
signes
vnlike
,
as
the
one
to
muche
,
and
the
other
to
little
,
then
you
shall
adde
the
twoo
productes
together
,
and
diuide
the
totall
by
the
somme
made
,
by
addyng
the
twoo
errours
together
,
and
the
Quotiente
will
shewe
the
truthe
sought
for
also
,
as
more
plainly
maie
appeare
by
appliyng
the
vse
of
the
Rule
,
to
the
aunswere
of
some
questions
followyng
.
Three
Marchauntes
gaines
1000.
lib
.
wherof
the
seuerall
portions
are
vnknowne
sauyng
that
the
seconde
ought
to
haue
double
the
portion
of
the
first
,
and
5.
pound
more
The
third
ought
to
haue
double
the
portion
of
the
seconde
,
and
10.
li.
more
.
The
question
is
,
what
portion
of
the
saide
gaine
belongeth
to
euery
man
Aunswere
.
You
maie
suppose
any
Number
at
pleasure
,
as
aforesaied
,
the
whiche
for
example
shall
bee
150
li.
supposed
to
bee
the
firste
mannes
due
.
Then
the
double
thereof
with
5.
pounde
more
is
305.
pounde
for
the
seconde
.
The
double
whereof
with
10.
pound
more
is
620
pounde
for
the
thirde
,
and
the
three
portions
together
make
1075.
li.
wherein
is
founde
an
errour
of
75.
pounde
to
muche
:
wherefore
for
a
seconde
woorke
,
I
suppose
the
first
mannes
portion
to
be
144.
pounde
:
then
the
second
ought
to
haue
293.
pounde
,
and
the
thirde
596.
pounde
,
whiche
together
make
1033.
pounde
,
wherein
is
founde
an
errour
of
33.
pounde
to
muche
also
.
Wherefore
I
set
the
first
position
150
with
the
errour
75.
at
the
vpper
ende
of
a
Crosse
,
with
the
signe
to
muche
thus
,
and
the
seconde
position
144.
with
the
error
33.
at
the
nether
ende
of
the
Crosse
,
with
the
signe
to
muche
,
also
as
appeareth
.
Then
the
firste
position
150.
multiplied
by
the
seconde
errour
33.
produceth
4950.
also
the
seconde
position
144.
multiplied
by
the
firste
errour
75.
produceth
10800.
And
because
the
signes
of
the
errours
bee
like
,
as
bothe
to
muche
I
substraie
the
lesser
producte
4950.
from
the
greater
10800
and
there
remaineth
5850.
for
diuidende
.
Likewise
I
substraie
the
lesser
errour
from
the
greater
75.
and
the
remaine
is
42.
for
diuisor
.
Then
diuidyng
5850.
by
42.
the
Quotiente
is
139
li.
2
/
7.
whiche
is
the
true
portion
for
the
firste
manne
,
then
the
seconde
of
consequence
hath
283.
li.
4
/
7
:
and
the
third
577.
li.
1
/
7.
and
together
make
1000.
li.
the
effecte
sought
for
by
the
worke
.
Now
to
the
ende
that
the
errours
maie
bee
bothe
to
little
,
as
in
the
firste
worke
thei
were
bothe
to
muche
,
I
will
further
an
other
supposition
to
shewe
the
agremente
.
Suppose
the
firste
mannes
portion
to
bee
130.
li.
the
double
thereof
and
5.
li.
more
is
265.
li.
for
the
second
,
the
double
thereof
and
10.
li.
more
is
540.
li.
for
the
third
,
&
maketh
together
935.
li.
wherein
is
founde
the
first
errour
to
bee
65.
pounde
to
little
.
−
.
and
set
at
the
vpper
ende
of
the
crosse
,
with
the
signe
in
former
order
.
Againe
suppose
a
biggar
somme
to
bee
his
portion
,
as
135
pound
.
Then
the
seconde
muste
haue
275.
pounde
:
and
the
third
560.
pound
,
and
maketh
together
970.
pound
,
wherein
is
found
an
errour
of
30.
pound
,
−
.
to
little
also
.
Wherefore
I
sette
the
position
with
the
errour
at
the
foote
of
the
crosse
as
you
see
with
the
signe
.
−
.
to
little
.
Then
the
firste
position
130.
multiplied
by
the
seconde
errour
30.
yeldeth
in
product
3900.
Likewise
multipliyng
the
seconde
position
135.
by
the
firste
errour
65.
the
producte
is
8775.
And
because
the
signes
of
the
errours
are
bothe
to
little
,
I
substraie
the
lesser
producte
3900.
from
the
greater
8775.
and
the
remaine
is
4875.
for
diuidende
:
also
I
substraie
the
lesser
errour
30.
from
the
greater
65.
and
the
remaine
is
35.
for
diuidende
,
Then
diuidyng
4875.
by
35.
the
Quotiente
is
139.
li.
2
/
7.
as
in
the
former
woorke
,
and
the
portions
of
seconde
and
third
followe
of
consequence
,
as
before
.
The
twoo
former
workes
with
contrary
positions
shewe
one
truthe
,
brought
foorthe
by
one
order
,
for
that
the
errours
in
eche
worke
was
like
,
though
in
the
firste
bothe
to
muche
,
and
in
the
latter
bothe
to
little
:
And
now
resteth
the
maner
of
woorke
,
when
the
errours
haue
signes
vnlike
,
as
the
one
to
much
,
&
the
other
to
little
,
where
the
productes
and
errours
will
require
addition
,
as
to
the
contrry
before
substraction
:
the
effecte
appearyng
in
a
third
worke
wherein
the
positions
made
so
farre
vnder
,
and
aboue
the
truthe
,
that
the
rule
maie
satisfie
euery
mannes
expectations
,
in
bryngyng
foorthe
the
truthe
,
notwithstandyng
the
distaunce
of
the
suppositions
from
the
same
.
Suppose
the
first
mannes
portion
of
gain
in
the
former
question
to
bee
3.
pounde
:
then
the
seconde
hauyng
5.
pounde
more
then
the
double
thereof
,
hath
11.
pounde
.
And
the
third
manne
10.
pounde
more
then
the
double
of
the
seconde
,
hath
32.
pounde
,
and
maketh
together
46.
pounde
,
whiche
is
954.
pounde
to
little
for
the
firste
errour
,
set
with
the
position
at
the
heade
of
a
crosse
in
former
order
,
with
the
signe
.
−
.
to
little
.
Then
to
haue
the
second
position
knowne
.
Suppose
the
said
first
mannes
portion
to
bée
500
pound
,
then
consequence
alloweth
to
the
seconde
1005.
li.
and
to
the
third
2020
pounde
,
whiche
together
maketh
3525.
pound
,
wherein
is
founde
an
errour
of
2525
pounde
to
muche
,
the
whiche
with
the
signe
and
position
,
I
sette
at
the
nether
ende
of
the
crosse
as
you
see
,
and
for
that
the
signes
bee
vnlike
,
as
the
one
to
little
,
and
the
other
to
greate
.
You
muste
adde
the
twoo
productes
together
for
the
diuidende
,
and
the
twoo
errours
for
the
diuisor
:
and
for
your
better
vnderstandyng
,
note
these
fewe
wordes
in
verse
.
The
signes
bothe
like
,
substraction
will
haue
:
And
contrary
found
,
addition
doeth
craue
The
which
Addition
made
of
the
two
productes
,
the
totall
is
484575.
to
bee
diuided
by
the
totall
of
the
twoo
errours
,
whiche
is
3479.
The
quotient
thereof
is
139.
li.
994
/
3479
agreyng
with
the
twoo
former
examples
,
the
effecte
required
in
euery
worke
.
Thus
hauyng
passed
through
the
common
partes
of
Arithemetique
,
in
whole
and
broken
nombers
,
appliyng
the
same
to
the
Rules
of
proportion
,
ordenarie
to
bee
founde
in
moste
authours
.
Now
followeth
other
rules
requiryng
further
circumstaunces
then
in
Schooles
(
I
meane
in
Vniuersities
been
taught
)
to
saie
of
gaine
and
losse
vppon
the
hundreth
,
of
Barters
,
and
of
Exchaunge
for
sondrie
nations
.
Of
gaine
and
losse
by
the
.
C.
A
Marchaunte
hath
100.
Clothes
,
whiche
coste
425.
lib
.
he
desireth
to
knowe
how
to
sell
euery
Clothe
to
gaine
8.
li.
vpon
the
hundreth
.
To
aunswere
this
qustion
and
suche
like
,
you
must
vse
this
circumstaunce
,
saiyng
,
by
the
Rule
of
three
directe
.
If
100.
lib
.
doe
gaine
8.
li.
what
gaineth
425.
li.
paied
for
the
forenrmed
100.
Clothes
:
worke
by
the
foresaied
Rule
,
and
finde
34.
li.
gained
,
as
practise
will
shewe
.
|
If
100.
li.
gaine
8.
li.
what
|
425.
|
|
|
8
|
|
|
3400
|
34
lib
.
gained
.
And
hauyng
founde
the
gaine
,
adde
thereto
the
principall
,
whiche
the
Clothes
coste
,
and
you
shall
haue
459.
lib
.
the
value
of
the
saied
Clothes
,
sold
after
the
rate
of
8.
pound
gained
vpon
the
C.
li.
Then
to
finde
the
price
of
euery
Clothe
,
after
the
rate
iuste
,
you
shall
saie
.
If
100.
Clothes
solde
,
yelde
459.
lib
.
plincipall
and
gaine
,
what
one
Clothe
,
multiplie
and
diuide
,
and
you
shall
finde
4.
pound
11.
s
.
9.
d
.
⅗
:
euery
clothe
as
practise
sheweth
.
If
100.
yelde
459.
li.
what
one
4
lib
.
59
/
100.
Likewise
if
one
peece
of
Clothe
containyng
84.
yardes
,
coste
60.
pound
:
how
ought
the
yarde
to
bee
solde
to
gaine
10.
li.
by
C.
li
Aunswere
in
former
order
saiyng
,
if
100
li.
gaine
10.
li.
what
60.
li.
woorke
by
the
rule
of
three
,
you
shall
finde
6.
pounde
.
Then
saie
again
if
84.
yardes
yelde
66.
pound
in
principall
and
gaine
,
what
one
,
worke
accordingly
,
and
you
shall
finde
15.
s
.
8.
d
.
12
/
21.
euery
yarde
.
Clothes
60.
costyng
53.
pounde
,
howe
maie
12.
peeces
thereof
bee
solde
to
gaine
9.
li.
by
C.
Aunswere
former
order
,
saiyng
:
If
100.
li.
gaine
9.
li.
what
getteth
53.
pounde
:
woorke
and
fide
—
47.
li.
14.
s
,
the
whiche
gaine
with
the
principall
maketh
577.
li.
14.
s
.
the
whiche
founde
,
saie
again
.
If
60.
Clothes
solde
,
yelde
in
principall
and
gaine
577.
li.
14.
s
.
what
12
?
woorke
by
the
rule
,
and
finde
115.
li.
10.
s
.
9.
d
.
3
/
7.
and
so
muche
ought
12
Clothes
to
bee
sold
to
gaine
9.
li.
by
.
C.
If
apeece
of
Veluet
coste
euery
yarde
18
shillynges
,
howe
maie
the
yarde
bee
solde
againe
,
to
profite
9.
li.
by
C
:
Saie
if
100.
li.
gaine
10.
li.
what
18.
s
?
woorke
and
finde
1.
s
.
9.
d
.
⅗
.
whiche
makes
for
euery
yarde
to
bee
19.
s
.
9.
d
.
⅗
.
to
gaine
after
10
li.
by
C.
If
in
sale
of
100.
yardes
of
Satten
for
48.
li.
there
bee
gained
3.
li.
10
s
.
I
demaunde
what
coste
euery
yarde
the
firste
penie
.
Aunswere
.
Rebate
the
gaine
3.
pounde
10.
s
.
from
the
totall
48.
li.
and
the
principall
will
appeare
44.
pounde
10.
shillynges
wherefore
saie
:
If
100.
yardes
coste
firste
penie
44.
li.
10.
shillynges
,
what
one
yarde
,
woorke
by
rule
,
and
finde
8.
s
.
10.
d
.
⅘
.
200.
ounces
of
Golde
taken
in
a
shifte
for
645.
li.
and
solde
againe
to
losse
10.
li.
in
the
hundred
.
I
demaunde
what
is
losse
in
euery
ounze
?
Aunswere
,
saie
if
100.
lose
10
pounde
,
what
145.
li
?
worke
by
rule
,
and
finde
64.
li.
10.
s
.
then
saie
gaine
.
If
200.
ounzes
,
lose
64.
li.
10.
s
.
what
one
ounze
,
woorke
and
finde
6.
s
.
5.
4
/
10.
If
the
pounde
of
Saffron
,
whiche
coste
18.
s
.
bee
solde
againe
for
18.
s
.
6.
d
.
I
demaunde
what
is
loste
by
the
hundred
pounde
in
money
?
Aunswere
.
If
18.
s
.
lose
6.
d
.
what
100.
pounde
,
woorke
by
rule
,
and
finde
2.
li.
15
s
.
6.
d
.
in
the
C.
If
100
yardes
of
Damaske
coste
65.
li.
and
the
buier
repentyng
,
would
lose
5.
li.
in
the
hundred
of
money
.
I
demaunde
how
the
yarde
maie
bee
solde
,
his
losse
to
bee
neither
more
nor
leffe
then
after
the
rate
aforesaied
,
of
5.
by
hundred
.
Aunswere
by
rule
and
saie
.
If
100.
li.
lose
5.
li.
what
65.
li.
woorke
and
finde
3.
li.
5.
s
.
the
whiche
rebated
from
the
principall
65.
li.
rest
61.
li.
15.
s
.
Lastly
say
,
if
100
yardes
yelde
61.
li.
15.
s
.
what
1.
yardes
,
worke
and
finde
12.
s
.
4.
d
.
⅕
euery
yarde
.
Of
the
Rule
of
Barteryng
.
TWo
Marchaunts
willing
to
chaunge
their
Marchaundize
together
,
the
one
hauyng
Carsies
of
35.
s
.
the
péece
redy
Money
will
deliuer
theim
in
Barter
at
40.
s
.
the
péece
.
The
other
hauyng
Holland
clothe
worth
2.
s
.
6.
d
.
the
Ell
ready
money
,
would
know
how
to
put
away
an
ell
to
make
the
Barter
equall
.
To
Aunswere
herein
,
and
by
like
order
all
other
,
say
by
Rule
,
if
35.
s
.
for
a
Carsey
,
make
in
barter
40.
what
will
2.
s
.
6.
d
.
for
an
ell
of
Hollande
yelde
in
Barter
,
worke
and
you
shall
finde
2.
s
.
10.
d
.
10
/
35
the
ell
to
equall
the
Barter
.
A
Marchaunt
hath
100.
Clothes
to
sell
for
ready
money
at
14
li.
a
péece
,
and
in
barter
hee
will
put
theim
away
at
15.
li.
10.
s
.
euery
clothe
,
an
other
will
giue
for
theim
in
Barter
,
silkes
that
are
worth
9
li.
a
péece
redie
money
.
I
demaunde
at
what
price
the
silkes
are
to
be
deliuered
in
barter
,
&
how
many
péeces
paieth
for
the
clothes
,
neither
partie
to
haue
aduauntage
of
other
.
Aunswere
by
former
order
and
say
.
If
14
li.
for
a
Clothe
redy
Money
yelde
15.
li.
10.
s
.
in
Barter
,
what
giueth
9.
li.
for
a
péece
of
Silke
in
Barter
,
to
make
the
trucke
equall
,
woorke
and
finde
9.
li.
19.
s
.
3.
d
.
●
/
7
,
the
price
of
a
peece
of
Silke
.
Then
say
,
if
9.
li.
19.
s
.
3.
d
.
3
/
7
,
require
1.
péece
of
silke
?
how
many
péeces
of
Silke
is
bought
with
1550
li.
whiche
is
the
value
of
the
100.
péeces
of
clothes
in
Trucke
,
worke
by
the
Rule
of
3.
direct
,
and
you
shall
finde
that
,
155.
péeces
,
and
10230
/
16734
,
at
the
former
price
paieth
for
the
100.
Clothes
,
and
neither
party
hauyng
aduauntage
of
the
other
.
Two
Marchauntes
desirous
to
chaunge
their
Marchaundize
together
.
The
one
hauyng
Allam
,
worthe
25.
s
.
by
C.
ready
Money
,
and
will
put
it
awoy
for
30.
s
.
by
C.
in
Trucke
,
to
take
Pepper
at
3.
s
.
4
d
.
the
lib
.
whiche
is
worthe
but
3.
s
.
the
lib
.
The
Peper
Marchaunte
not
of
skill
to
equall
the
chaunge
,
giueth
Pepper
for
100.
Quintals
of
the
Allam
at
the
prises
aforesaide
.
I
demaund
what
aduauntage
the
one
hath
of
the
other
and
who
is
the
loosar
,
Aunswere
.
First
séeke
at
what
price
a
lib
.
of
Pepper
maketh
the
Barter
equall
saiyng
.
If
25
s
.
make
30.
s
.
in
Allam
,
what
3.
s
.
for
Pepper
,
woorke
and
you
shall
finde
3.
s
.
7.
d
.
wherby
appeareth
3.
d
.
⅕
lest
in
euery
lib
.
of
Pepper
deliuered
.
Then
to
finde
the
state
of
the
chaunge
,
say
by
the
Rule
of
3.
If
3.
s
.
4.
d
.
by
1.
lib
.
of
Pepper
what
bieth
150.
li.
the
value
of
the
100.
Quintalls
of
Allam
,
woorke
and
you
shall
finde
900
lib
.
of
Pepper
paieth
for
the
said
Allam
.
Againe
to
finde
the
losse
,
searche
what
quantitie
of
Pepper
would
haue
paid
for
the
Allam
,
if
the
Bartar
had
bene
equall
,
saiyng
.
If
3.
s
.
7.
d
.
⅕
requireth
1.
lib
.
of
Pepper
,
what
150.
lib
.
the
value
of
the
Allam
?
worke
and
you
shall
finde
833
,
lib
.
⅓
would
haue
paid
for
the
Allam
,
the
Barter
made
equall
.
The
which
833.
lib
.
waight
⅓
rebated
from
900.
lib
.
deliuered
the
rest
,
lost
is
66.
li.
waight
⅔
,
and
so
much
gained
the
Allam
of
the
Pepper
.
The
effect
sought
for
by
the
woorke
.
Here
you
shall
vnderstande
,
that
if
the
one
partie
require
to
haue
a
portion
in
redy
Money
,
as
½
.
⅓
.
¼
.
or
any
other
,
you
shall
rebate
the
said
such
portion
what
it
bee
,
aswell
from
the
price
of
his
Wares
worth
in
ready
Money
,
also
rated
in
Barter
,
and
the
2.
remaines
shal
be
the
first
and
seconde
noumbers
in
the
Rule
of
three
,
and
the
thirde
shal
be
the
price
of
the
Ware
of
the
contrary
partie
,
as
hereafter
by
example
the
effect
may
appeare
.
Two
Marchauntes
willyng
to
chaunge
Marchandises
,
the
one
with
the
other
,
the
firste
hath
Oyles
of
24.
li.
by
Tunne
,
redy
money
,
and
in
Barter
he
will
put
it
away
at
27.
li.
by
Tunne
,
and
will
haue
⅓
in
readie
money
.
The
other
hath
Bayies
of
2.
s
.
6.
d
.
the
yarde
ready
mony
.
I
demaunde
how
the
yarde
of
Bayes
ought
to
bee
rated
,
to
make
the
Barter
equall
?
Aunsware
.
First
rebate
9.
li.
whiche
⅓
of
27.
li.
from
24.
li.
the
rest
is
15.
li.
for
first
number
in
the
Rule
of
thrée
,
also
rebate
the
same
9.
li.
from
27.
li.
the
value
of
the
Oyle
in
Barter
,
and
the
rest
is
18.
li.
for
second
number
in
the
said
rule
,
and
the
third
number
shal
be
2.
s
.
6.
d
.
to
finde
howe
the
yarde
of
Bayes
shal
be
deliuered
in
Barter
,
the
which
to
finde
,
say
,
if
15.
li.
yelde
18.
li.
a
Tunne
of
Oyle
,
what
2.
s
.
6.
d
.
for
a
yarde
of
Bayes
,
woorke
and
you
shall
finde
3.
s
.
for
euery
yard
of
Bayes
in
Barter
,
and
so
of
all
other
.
Twoo
Marchauntes
will
chaunge
Marchaundizes
,
the
one
hath
wines
of
13.
li.
6.
s
.
8.
d
.
redy
Money
by
Tunne
,
and
in
barter
he
will
put
them
awaie
at
16.
li.
13.
s
.
4.
d
.
by
Tunne
,
and
also
will
haue
¼
money
content
.
The
other
hath
Tynne
at
3.
li.
the
C.
in
barter
.
I
demaunde
what
the
C.
of
Tynne
is
worth
ready
money
.
Answere
.
Take
the
one
fourth
parte
of
the
price
of
a
Tunne
of
wine
in
Barter
,
which
is
4.
li.
3.
s
.
4.
d
.
from
the
price
of
a
Tunne
readie
money
,
which
is
13.
li.
6.
s
.
8.
d
.
so
resteth
9.
li.
3.
s
.
4.
d
.
for
seconde
number
in
the
Rule
of
3.
Likewise
take
the
said
4.
li.
3.
s
.
4.
d
.
from
the
price
of
the
Wine
in
Barter
,
and
the
rest
wilbe
12
li.
10.
s
.
for
first
number
in
the
said
Rule
.
Lastly
,
put
the
price
of
the
C.
of
Tinne
the
thirde
number
,
whiche
is
3.
li.
in
Barter
,
and
woorke
the
Rule
,
and
you
shall
finde
44.
s
.
the
value
of
the
C.
of
Tynne
readie
Money
.
Twoo
Marchauntes
will
chaunge
their
Marchaundizes
the
one
with
the
other
,
one
hath
Cottons
of
10.
li.
the
Packe
ready
money
,
and
will
put
theim
awaie
in
Barter
,
at
13.
li.
6.
s
.
8.
d
.
the
Packe
,
and
will
gaine
10.
li.
by
C.
and
also
haue
the
halfe
in
ready
money
.
The
other
hath
Burrace
of
6.
d
.
the
li.
ready
money
.
I
demaunde
how
the
li.
of
of
Burrace
shall
be
put
away
in
Barter
.
Answere
.
First
say
,
if
100.
li.
giue
10.
li.
what
giueth
13
li.
6.
s
.
8.
d
.
the
price
of
a
Packe
of
Cottons
in
Barter
:
Worke
by
the
rule
,
and
you
shall
finde
14.
li.
13.
s
.
4.
d
.
whereof
the
one
halfe
demaunded
in
ready
money
,
rebated
from
10.
li.
price
of
the
Cottons
ready
money
,
the
rest
is
2.
li.
13.
s
.
4.
d
.
for
firste
number
in
the
Rule
of
three
,
and
the
same
also
rebated
from
14.
li.
13.
4.
d
.
price
of
the
Cottons
in
Barter
,
the
rest
is
7.
li.
6.
s
.
8.
d
.
for
second
number
,
then
make
the
6.
d
.
price
of
Burrace
the
thirde
number
,
and
worke
by
the
Rule
,
ond
you
shall
finde
16.
d
.
½
for
the
lib
.
of
Burrace
in
Barter
.
Of
the
exchaunge
of
Moneys
from
one
country
to
another
.
FOrasmuch
as
by
the
Lawes
and
statutes
,
of
euery
or
most
nations
it
is
defended
to
transporte
or
carry
out
Gold
and
Siluer
either
in
coine
or
Bullion
,
therefore
was
diuised
and
ordained
the
exchaunge
of
moneis
betwene
country
&
country
,
that
is
to
say
.
For
a
somme
of
money
,
the
value
great
or
small
,
in
one
nation
deliuered
from
one
man
to
an
other
.
The
said
deliuerar
to
receiue
the
value
therof
in
money
of
an
other
contry
wherwith
to
furnish
his
affaires
for
traffique
or
otherwise
,
in
that
place
,
the
effect
by
examples
more
plainly
apearyng
.
A
Marchaunt
deliuereth
in
London
100.
li.
starling
to
receiue
in
Andwarp
at
sight
of
the
bills
made
for
exchaunge
therof
,
for
euery
li.
starlyng
24.
s
.
9.
d
.
Flemmishe
.
I
demaunde
what
money
Flemmishe
paieth
the
bills
in
Andwarp
.
Aunswere
.
Say
,
if
20.
s
.
starlyng
,
bee
worth
24.
s
.
9.
d
.
Flemmishe
,
what
100.
li.
starling
,
worke
by
the
Rule
of
3.
direct
and
finde
123.
li.
15.
s
.
Flemmish
paieth
the
bills
of
the
said
100.
starlyng
.
A
Marchaunt
deliuereth
in
Andwarp
100
li.
Flemmishe
,
to
receiue
in
London
20.
s
.
starlyng
for
24.
s
.
9.
d
.
Flemmishe
,
I
demaund
.
what
starling
money
paieth
the
Bills
for
the
saide
100
li.
Flemmishe
.
Aunswere
and
saye
If
24.
s
.
9.
d
.
Flemmish
,
giue
20.
s
.
starlyng
,
what
100.
li.
Flemmishe
,
multiplie
and
diuide
,
and
you
shall
finde
80.
li.
16.
s
.
1.
d
.
48
/
297
,
and
so
muche
starling
money
paieth
the
said
bills
of
100.
li.
Flemmishe
.
A
Marchaunt
Deliuereth
in
london
100.
li.
starlyng
,
to
receiue
in
Parris
50.
s
.
Turnois
for
euery
Frenche
Crowne
of
5.
s
.
3.
d
.
starlyng
.
To
saye
,
valued
at
that
price
.
I
demaund
how
much
Turnois
or
Frenche
money
paieth
the
bills
for
the
saide
100.
li.
starlyng
.
Aunswere
.
Say
by
the
Rule
of
3.
If
5.
s
.
3.
d
.
starlyng
,
make
1.
Crowne
,
what
100.
li.
multiplie
&
diuide
,
and
you
shall
finde
380.
▿
and
60
/
63
parte
of
a
Crowne
,
and
note
that
the
Caracter
▿
representeth
the
crown
by
exchaunge
,
and
is
euer
50.
s
.
Turnois
or
Frenche
money
.
Then
say
againe
,
if
1.
▿
be
worth
50
s
.
what
380.
60
/
63
▿
woorke
by
the
Rule
,
and
finde
952
li.
or
franks
7.
sowce
,
and
7.
d
.
47
/
6●
paieth
the
Billes
for
the
saide
100.
li.
starlyng
.
A
Marchaunt
deliuereth
in
Parris
1000.
li.
or
franks
,
the
whiche
franke
or
li.
is
20.
sounce
or
pounde
Turnois
Frenche
money
to
Receiue
in
London
4.
s
.
10.
d
.
starlyng
for
euery
▿
of
50.
souce
Turnois
.
I
demaund
how
muche
starlyng
money
paieth
the
billes
of
exchaunge
for
the
said
1000.
li.
Turnois
.
Aunswere
.
Saye
first
,
if
50.
souce
Turnois
make
1
▿
howe
manye
Crownes
maketh
1000
li.
worke
by
the
Rule
&
finde
400.
▿
.
Then
say
againe
,
if
1.
▿
giue
4.
s
.
10.
d
.
starlyng
,
what
400.
▿
.
woorke
accordingly
,
and
find
96
li.
13.
s
.
4.
d
.
starlyng
,
paieth
the
Billes
of
exchaunge
for
the
saide
1000.
li.
Turnoys
.
A
Marchaunt
deliuereth
in
London
100.
li.
starlyng
,
to
receiue
in
Bayon
for
euery
5.
s
.
10.
d
.
1.
ducket
of
374.
Maruedies
?
I
demaunde
how
manie
Maruedies
paieth
the
billes
for
the
said
100.
li.
starling
.
Aunswere
.
Say
first
,
if
5.
s
.
10.
d
.
make
1.
Ducket
,
what
100.
li.
multiplie
and
diuide
,
and
you
shall
finde
342.
Duckets
.
6
/
7.
Then
say
againe
,
if
1.
Ducket
giue
374.
Maruedies
,
what
giueth
342.
Duckets
●
/
7.
woorke
accordingly
,
and
finde
128228.
Maruedies
4
/
7.
A
Marchaunt
deliuereth
in
Bayon
100.
M.
Maruedies
,
to
receiue
in
London
5.
s
.
10.
d
.
for
euery
Ducket
of
374.
Maruedides
:
I
demaunde
how
muche
Starlyng
money
paieth
the
billes
of
Exchaunge
for
the
saied
100.
M.
Maruedies
.
Aunswere
.
Say
if
374.
Maruedies
make
one
Ducket
,
what
100.
M.
worke
by
the
Rule
,
and
finde
267.
Duckettes
.
331
/
374.
Then
saie
againe
.
If
one
Ducket
giue
5.
s
.
10.
d
.
Starlyng
,
what
giueth
267.
Duckettes
331
/
374.
woorke
and
finde
78.
lib
.
2.
s
.
7.
d
.
356
/
374.
And
so
muche
paieth
the
Billes
of
Exchaunge
for
the
saied
100.
M.
Maruedies
.
&c.
Thus
hauyng
runne
ouer
the
seuerall
common
partes
of
Arithemetique
,
aswell
in
whole
as
broken
Noumbers
,
now
followeth
the
Rules
of
Breuetie
,
of
rare
and
profitable
effecte
,
the
originall
cause
of
furtherance
of
this
my
woorke
.
¶
The
fowerth
and
last
part
containyng
the
Rules
of
Breuetie
,
of
rare
and
singular
effect
.
THe
Rules
of
Breuetie
in
workes
of
Arithemetique
,
are
sondrie
and
many
,
and
to
further
a
woorke
,
wherein
to
shewe
all
that
might
bee
expected
,
would
not
onely
be
a
tedious
and
superfluous
toile
,
but
also
cunnyng
might
wante
in
the
beste
learned
the
same
to
performe
.
Wherefore
I
minde
not
to
enlarge
my
trauaile
with
suche
Rules
,
as
menne
are
ordinarily
acquainted
withall
,
neither
so
muche
to
saie
of
other
,
(
which
maie
séeme
more
rare
,
and
not
in
familiaritie
with
many
menne
)
as
might
bee
furthered
to
good
and
profitable
purpose
.
Notwithstandyng
as
euery
manne
desireth
the
nearest
waie
to
ende
a
wearie
iourney
:
so
I
intende
to
shewe
practise
first
,
how
to
giue
thee
some
of
any
nomber
,
whereof
the
value
of
an
vnitie
,
is
an
euen
parte
of
a
pounde
,
with
as
small
circumstance
and
fewe
figures
as
maie
be
,
therein
,
auoydyng
the
tedious
vse
of
figures
in
Multiplication
,
and
Diuision
,
commonly
practized
in
the
Rule
of
three
.
And
againe
,
as
many
menne
in
respecte
of
Benefite
,
or
to
withstande
a
detrimente
,
maie
contente
theim selues
to
take
a
compasse
out
of
the
nearest
waie
,
to
stoppe
a
breache
in
a
hedge
of
a
Corne
fielde
,
or
to
see
his
pasture
voyde
of
other
mennes
Cattell
:
so
I
thinke
it
bothe
profitable
and
necessary
,
to
further
a
more
large
walke
by
sondrie
orders
,
in
searching
the
totall
of
sondry
sommes
,
whereof
the
value
of
an
vnitie
,
may
be
either
some
euen
parte
of
a
pounde
,
or
sondrie
euen
,
or
odde
partes
of
a
pounde
.
From
one
penie
to
twentie
shillynges
,
and
so
muche
aboue
as
maie
séeme
néedefull
,
the
effect
not
so
hard
to
vnderstande
in
woordes
,
as
with
facilitie
to
bee
perceiued
in
example
,
whiche
hereafter
followe
in
plentifull
maner
,
and
so
full
of
chaunge
as
procured
cause
,
wherfore
this
Booke
is
named
the
storehouse
of
Breuetie
.
It
is
good
for
euery
learner
to
printe
in
memorie
the
euen
partes
of
a
pounde
of
money
,
before
he
meddle
with
the
briefe
rules
.
The
whiche
partes
are
put
in
the
table
folowyng
.
|
d
.
|
l.
|
|
1.
|
1
/
24●
|
|
2.
|
1
/
120
|
|
3.
|
1
/
80
|
|
4.
|
1
/
60
|
|
6.
|
1
/
40
|
|
8.
Take
|
1
/
30
At
|
|
10.
|
1
/
24
|
|
12.
|
1
/
2●
|
|
15
|
1
/
16
|
|
16
|
1
/
51
|
|
20.
|
1
/
12.
or
½
of
⅙
,
or
¼
of
⅓
|
|
2.
s
.
|
1
/
10
|
|
3.
s
.
4.
d
.
|
⅙
|
|
4.
s
.
|
⅕
|
|
5.
s
.
|
¼
|
|
s
.
d
.
|
|
|
6.
8.
take
|
⅓
¶
The
price
of
an
vnitie
.
|
|
10.
s
.
|
½
|
|
13.
s
.
4.
d
|
⅔
|
|
15.
s
.
|
¾
|
|
16.
s
.
8.
d
.
|
5
/
6
|
WHen
occasion
doth
procure
anie
noumber
to
bée
summed
,
whereof
the
vnitie
beareth
any
euen
parte
of
a
pounde
.
Then
the
saide
nomber
beyng
diuided
by
the
Denominator
of
suche
parte
as
is
the
value
of
the
said
vnitie
,
the
quotient
of
that
diuision
wil
be
the
totall
,
sought
for
of
any
suche
nomber
,
as
by
example
the
effect
more
plainly
may
appeare
.
At
4.
s
.
the
yarde
,
what
2156.
yardes
?
Aunswere
.
Forasmuche
as
4.
s
.
is
the
1
/
5
of
a
pounde
,
therefore
if
the
noumber
of
yardes
beeyng
2156.
bee
diuided
by
5.
the
Denominator
of
1
/
5
li.
which
is
4.
s
.
the
price
of
euery
vnitie
in
the
said
nomber
,
the
quotient
wilbe
431.
4.
s
.
the
true
totall
required
as
practise
will
manifest
.
Thus
Diuision
hath
brought
forth
the
totall
of
2156.
yardes
at
4.
s
.
the
yarde
,
the
effect
whereof
I
further
not
as
a
woorke
of
breuity
,
though
in
some
respects
in
déed
it
is
a
breuety
,
but
rather
for
an
example
therby
the
better
to
vnderstande
the
maner
of
abreuiation
of
woorke
in
that
example
,
and
in
all
other
like
,
by
practising
the
same
,
and
like
diuision
reteinyng
in
memory
the
diuisor
,
and
remaine
of
euery
such
Diuision
,
and
settyng
the
totall
in
one
line
vnder
the
number
giuen
,
as
by
an
other
example
of
perfect
breuetie
the
effect
may
appeare
.
|
At
4.
s
.
the
yard
what
|
2156.
yards
.
Take
⅕
.
|
|
Makes
|
431.
4.
s
.
|
Here
I
haue
kept
in
memory
the
Diuisor
.
5.
the
Denominator
of
⅕
li.
whiche
is
4.
s
.
the
value
of
euerie
vnitie
in
the
number
giuen
for
example
,
and
haue
founde
that
the
same
is
contained
in
21.
4.
tymes
,
and
1
remainyng
.
Wherefore
I
set
4.
vnder
21.
and
a
line
betwéene
.
Then
I
finde
also
that
the
said
diuisor
5.
is
contained
in
15.
3
tymes
,
and
nothyng
remaineth
,
wherefore
I
set
3.
vnder
15.
as
the
former
.
Then
lastly
I
finde
that
5.
the
Diuisor
is
contained
in
6.
the
last
figure
1
time
,
and
one
remainyng
,
wherefore
I
set
one
vnderline
as
the
other
,
and
the
one
remainyng
beyng
1
/
5
of
a
pounde
for
the
same
I
put
4.
s
.
also
in
the
Quotient
,
and
so
the
woorke
is
ended
with
the
vse
of
as
fewe
figures
set
doune
,
as
can
be
,
whiche
is
the
effect
ment
by
this
last
part
,
as
in
sondry
examples
followyng
you
may
perceiue
.
At
1.
d
.
what
54368.
elles
.
Aunswere
.
Forasmuch
as
1.
d
.
is
the
1
/
240
part
of
a
pound
,
therefore
,
if
this
giuen
number
bee
diuided
by
the
denominator
240.
the
quotient
would
be
the
poundes
,
containyng
the
value
of
the
said
giuen
number
,
as
aforesaid
,
howbeit
,
for
that
I
pretende
the
omittyng
vse
of
the
Figures
,
aswell
in
Multiplication
as
Diuision
.
I
therefore
imagine
what
euen
parte
of
a
pounde
I
may
worke
by
.
Whereof
a
peny
beyng
a
perfite
parte
,
may
be
taken
from
it
,
and
so
my
desire
furnished
.
The
whiche
findyng
to
be
sondrie
,
as
8.
d
.
the
1
/
30
parte
,
wherof
⅛
parte
serueth
,
and
6.
d
.
1
/
40
parte
whereof
⅙
parte
serueth
.
Also
4.
d
.
1
/
60
parte
whereof
¼
parte
serueth
,
the
whiche
last
to
mée
séemyng
most
apt
,
I
further
for
example
as
foloweth
.
|
At
1.
d
.
what
|
54368.
ells
.
Take
¼
of
1
/
60.
|
|
for
4.
d
.
|
906.
2.
8.
d
.
|
|
wherof
¼
facit
226.
10.
8.
d
.
|
As
I
know
that
4.
d
.
is
1
/
60
part
of
a
pound
,
so
1
/
60
part
of
the
giuen
number
,
is
the
pounds
containyng
the
value
sought
for
at
4.
d
.
the
ell
,
howbeit
,
for
that
1.
d
.
is
the
value
admitted
for
euery
vnitie
,
and
is
¼
of
4.
d
.
therfore
¼
of
the
quotient
yelded
for
4.
d
.
is
the
totall
sought
for
,
whiche
as
aboue
appeareth
is
226
li.
10.
s
.
8.
d
.
founde
without
vse
of
moe
figures
set
doune
,
then
aboue
appeareth
And
note
that
the
Diuisor
beyng
60.
the
Cipher
is
imagined
to
stand
vnder
8
the
last
Figure
of
the
diuidend
so
that
6.
diuiding
all
the
other
Figures
,
yeldeth
906.
li.
and
8
/
60
remainyng
whiche
is
2.
s
.
8.
d
.
as
also
aboue
you
may
see
,
whereof
¼
is
the
totall
sought
for
,
as
aforesaid
.
|
At
2.
d
.
what
|
45682
foote
Take
½
of
1
/
60.
|
|
for
4.
d
.
|
761.
7.
4.
d
.
|
|
wherof
½
facit
.
380.
13.
8.
d
.
|
This
Diuision
is
made
in
former
order
,
and
the
trueth
shewed
accordingly
.
At
3.
d
.
pounde
waight
what
4356.
li.
|
Take
|
1
/
80
▪
|
|
|
|
|
|
facit
|
54.
li.
9.
s
.
0.
d
.
|
|
At
4.
d
.
what
|
|
3986.
Take
1
/
60.
|
|
|
facit
|
66.
8.
s
.
8.
d
.
|
|
At
6.
d
.
what
|
3245.
Take
1
/
40.
|
|
facit
|
81.
2.
6.
|
|
At
8.
d
.
what
|
2678.
Take
1
/
30.
|
|
facit
|
89.
5.
s
.
4.
d
.
|
|
At
10.
d
.
what
|
2576.
Take
¼
of
⅙
|
|
for
⅙
|
429.
6.
8.
|
|
whereof
¼
facit
|
107.
6.
s
.
8.
d
.
|
|
At
12.
d
.
what
|
2432.
Take
1
/
20.
|
|
facit
|
121.
12.
s
.
0.
d
.
|
|
At
15.
d
.
what
|
2354.
|
|
Take
1
/
16
or
½
of
⅛
.
|
|
|
For
⅛
|
|
|
whereof
½
facit
|
147
li.
2.
6.
d
.
|
|
At
16.
d
.
what
|
2216.
Bushelles
.
|
|
Take
1
/
15
or
1
/
20
and
⅓
thereof
,
|
|
For
1
/
20
|
110.
16.
s
.
0.
|
|
For
⅓
thereof
|
36.
18
s
.
8.
|
|
facit
|
147.
14.
8.
d
.
|
|
d
.
|
|
|
At
20.
what
|
1864.
Take
½
of
⅙
.
|
|
For
⅙
|
|
|
Whereof
½
facit
|
155.
6.
8.
|
|
At
2.
shillynges
,
what
|
1568.
Take
1
/
10
|
|
facit
|
156
l.
.
16.
0.
d
.
|
|
At
2
s
.
6.
d
.
what
|
1453.
Take
⅛
.
|
|
facit
|
181.
12.
s
.
6.
d
.
|
|
At
3
s
.
4
d
.
what
|
1263.
Take
⅙
|
|
facit
|
210
li.
10.
s
.
0
d
.
|
|
At
4.
shillynges
,
what
|
1144.
Take
⅕
.
|
|
facit
|
228.
li.
16.
0.
d
.
|
|
At
5
s
.
what
|
1123.
Take
¼
|
|
facit
|
280.
15
s
.
0.
d
.
|
|
At
6
s
.
8.
what
|
1042
,
Take
1
/
●
|
|
facit
|
347.
6.
s
.
8
d
.
|
If
you
marke
the
former
practizes
,
you
maie
perceiue
that
in
euery
example
,
wherein
the
price
of
an
vnitie
in
the
giuen
nomber
is
conteined
in
a
diget
,
or
an
article
nomber
,
beyng
either
of
shillynges
or
pence
.
The
totall
of
that
example
is
shewed
in
one
line
done
,
without
vse
of
mo
figures
,
then
in
the
same
line
doeth
appeare
:
Howbeit
,
where
the
value
of
the
vnitie
is
conteined
,
in
a
mixed
or
compounde
nomber
,
then
is
required
two
lines
,
three
lines
,
fower
or
more
,
as
the
sondrie
partes
in
the
example
maie
proclure
.
For
sometymes
the
totall
is
giuen
by
one
euen
parte
,
and
that
requireth
but
one
line
.
Sometymes
by
a
parte
of
a
parte
,
and
that
requireth
two
lines
,
the
one
substraied
from
the
other
:
Sometymes
by
euen
and
sonderie
partes
,
and
partes
of
partes
also
,
whiche
wil
require
so
many
lines
,
as
the
sondrie
partes
will
procure
.
As
in
example
followyng
,
the
effecte
more
at
large
appearyng
.
At
1
d
.
the
yarde
,
what
24568
yardes
?
Take
¼
of
1
/
60
or
⅓
of
1
/
80.
or
⅙
of
1
/
40
or
⅛
of
1
/
30
or
1
/
1●
of
1
/
20
,
or
¼
of
⅙
of
1
/
10
or
⅙
of
⅕
of
⅛
.
By
euery
of
whiche
directions
,
the
true
totall
is
brought
foorthe
,
as
by
the
seuerall
practizes
maie
appeare
.
|
The
giuen
number
.
|
24568.
at
1.
d
.
the
yard
.
|
|
For
1
/
16
|
|
|
Whereof
¼
facit
102.
7.
4.
|
|
Also
the
giuen
nomber
.
|
24568.
at
1.
d
.
the
|
|
yarde
.
For
1
/
80.
|
|
|
Whereof
⅓
facit
|
102.
7
,
4.
|
|
Likewise
the
giuen
nomber
|
24546.
at
1.
d
|
|
the
yarde
.
For
1
/
40
|
614.
4.
0.
d
|
|
Wheref
⅙
facit
|
102.
7.
4.
|
|
Againe
the
giuen
nomber
|
24568.
at
1.
d
.
|
|
the
yarde
.
For
1
/
30
|
|
|
Whereof
⅛
facit
|
102.
7.
4
d
.
|
|
Accordingly
the
giuen
nomber
|
24568
at
1.
d
|
|
the
yarde
.
For
1
/
20
|
1228.
8.
s
.
0.
d
|
|
Whereof
1
/
12
facit
|
102.
7.
4.
|
|
Also
the
giuen
nomber
.
|
24568.
at
1.
d
.
the
|
|
yarde
.
For
1
/
10
|
2456.
16
s
.
0.
d
.
|
|
For
⅙
thereof
.
|
409.
9.
4.
|
|
Whereof
¼
facit
|
102.
7.
4.
|
|
Againe
the
giuen
nomber
|
24568.
at
1.
d
.
|
|
the
yarde
.
For
⅛
|
3071.
|
|
For
⅕
thereef
|
614.
4.
s
.
0.
d
.
|
|
Whereof
⅙
facit
|
102.
7.
4.
|
As
necessitie
requireth
,
not
suche
plentie
of
examples
for
one
thyng
,
so
delectation
in
a
desirous
studente
,
maie
accepte
the
good
will
of
the
trauailer
herein
.
And
neuerthelesse
,
for
that
euery
order
is
witnesse
of
truth
one
in
an
other
,
none
of
the
same
are
without
profite
,
for
suche
as
are
exercized
in
accomptes
.
And
in
respecte
aswell
thereof
,
as
also
to
adorne
the
pearlesse
Science
(
Mathematicall
)
of
Arithemetique
,
with
the
Iewelles
of
her
owne
closet
:
here
after
followeth
sondrie
other
examples
of
the
same
matter
.
|
At
1.
d
.
the
yarde
.
what
.
|
24586.
yardes
.
|
|
Take
¼
of
1
/
10
of
⅙
for
⅙
|
4094.
13.
4.d
.
|
|
For
1
/
10
thereof
|
409.
9.
4.
d
.
|
|
Whereof
¼
facit
|
102.
7.
4.d
.
|
|
Also
at
1
d
.
the
yarde
,
what
.
|
24568.
yardes
|
|
Take
1
/
12
of
¼
of
⅕
for
⅕
|
4913.
12.
0.
|
|
For
¼
thereof
|
1228.
8.
0.
|
|
Whereof
1
/
12
facit
|
102.
7.
4.
|
Also
at
1.
d
.
the
yarde
what
.
24568
yardes
.
Take
¼
of
⅓
of
⅕
of
¼
.
|
The
giuen
nomber
.
|
24568.
|
|
For
¼
|
6142.
li.
|
|
For
⅕
thereof
|
1228.
8.
s
.
0
d
.
|
|
For
⅓
thereof
|
409.
9.
4
|
|
Wherof
¼
facit
|
102.
7.
4.
d
.
|
Thus
appeareth
that
by
10.
sondrie
orders
of
breuetie
,
without
the
vse
of
the
rules
of
3.
is
brought
forth
the
totall
of
24568.
yardes
at
1.
d
.
the
yarde
,
and
because
it
may
appeare
to
the
sight
of
euerie
man
,
what
difference
of
circumstaunce
is
betwéene
any
of
the
said
orders
,
and
the
saide
Rule
of
3.
here
●…
olloweth
the
practice
of
the
same
by
the
said
Rule
.
At
1.
d
.
the
yarde
what
14568.
yards
.
Because
1.
doth
not
increase
or
augment
in
Multiplication
,
I
omit
the
saide
multiplication
,
and
diuide
the
giuen
noumber
by
so
many
pence
as
is
in
a
pound
contained
,
which
is
240.
&c.
At
2.
d
.
the
ell
what
.
23647
ells
.
Take
for
most
bréefe
½
of
1
/
60
or
⅔
of
1
/
80
or
⅓
of
1
/
40
or
¼
of
1
/
30
or
⅙
of
1
/
20
or
½
of
⅙
of
1
/
10
or
⅓
of
⅕
of
⅛
or
½
of
⅓
of
¼
of
⅕
.
|
The
giuen
number
.
|
23647.
|
|
For
1
/
60
|
394.
2
s
.
4
d
.
|
|
Whereof
½
facit
.
|
197.
1
s
.
2
d
.
|
And
only
for
proofe
½
of
1
/
10
of
⅙
.
|
The
giuen
nomber
.
|
23647.
|
|
For
1
/
06
|
3941.
3.
s
.
4.
d
.
|
|
For
⅙
thereof
|
394.
2.
4.
|
|
Whereof
½
facit
.
|
197.
1.
2.
|
At
3.
d
.
lib
.
whaight
what
4875.
lib
.
Take
for
most
bréefe
1
/
80
|
The
giuen
number
.
|
4875.
|
|
facit
.
|
60
li.
18
s
.
9.
d
.
|
And
for
proofe
Take
½
of
1
/
40
or
¼
of
1
/
20
or
⅛
of
1
/
10
,
or
½
of
⅕
of
⅛
or
¼
of
¼
of
⅕
or
½
of
1
/
60
,
and
½
thereof
,
or
½
of
1
/
40
,
&c.
Euery
of
whiche
facit
18.
li.
17.
s
.
9.
d
.
|
At
4.
d
.
what
.
|
457.
Take
for
most
bréef
1
/
60●
|
|
facit
|
76.
li.
5.
s
.
4.
d
.
|
And
for
proofe
.
Take
½
of
⅓
or
⅓
of
1
/
20
or
⅙
of
1
/
10
or
½
of
⅙
of
⅕
or
⅕
of
¼
of
⅓
.
&c.
Euery
of
whiche
facit
76
li.
5.
s
.
4.
d
.
|
At
5
d
.
what
.
|
4269.
Take
for
bréefe
1
/
60
and
¼
thereof
.
|
|
For
1
/
60
|
71.
3.
s
.
0.
d
.
|
|
For
¼
thereof
|
17.
15.
9.
d
.
|
|
Whiche
together
facit
|
88.
18.
9.
d
.
|
And
for
proofe
Take
1
/
40
lackyng
⅙
thereof
as
by
example
.
|
At
5.
d
.
what
.
|
4269.
|
|
For
1
/
40
|
106.
14.
6.
|
|
From
whiche
⅙
|
17.
15.
9.
|
|
per
rest
facit
|
88.
18.
9.
|
Or
for
the
same
proofe
Take
1
/
20
and
½
of
1
/
60
or
¼
of
⅓
of
¼
or
¼
of
½
of
⅙
or
⅕
of
⅛
lacking
⅙
thereof
.
Euery
of
whiche
facit
88
li.
18
s
.
9
d
.
|
At
6.
d
.
what
|
3896.
Take
for
most
bréef
1
/
40.
|
|
facit
|
97.
8.
s
.
|
And
for
proofe
and
pleasure
Take
1
/
60
and
½
thereof
,
or
1
/
80
double
,
or
½
of
1
/
20
or
¼
of
1
/
10
,
or
⅕
of
1
/
●
or
½
of
⅕
of
¼
.
Euery
of
whiche
facit
97.
li.
8.
At
7.
d
.
what
3648.
li.
Take
for
breef
1
/
40
and
⅙
thereof
|
The
giuen
nomber
|
3648.
li.
at
7
d
.
|
|
For
1
/
40
|
91.
li.
4.
s
.
0.
d
.
|
|
For
⅙
thereof
|
15.
4.
0.
|
|
whiche
together
facit
|
106.
8.
0.
|
And
for
proofe
.
Take
1
/
30
lackyng
⅛
thereof
,
or
1
/
60
and
1
/
80
,
or
½
of
1
/
20
and
⅙
thereof
,
or
¼
of
1
/
10
and
⅙
thereof
,
or
1
/
60
double
lackyng
¼
of
1
/
60.
Euery
of
whiche
waies
facit
—
106
li.
0.
d
.
|
At
8
d
.
what
|
3579.
Take
for
moste
ree1
/
3●
|
|
facit
|
119.
6.
0.
|
And
for
proofe
.
Take
1
/
60
double
or
1
/
40
and
⅓
thereof
,
or
⅔
of
1
/
02
,
or
⅓
of
1
/
10
,
or
⅕
or
⅙
.
&c.
Euery
of
whiche
waies
facit
119.
6.
0
|
At
9.
d
.
what
|
3648.
Take
1
/
40
and
½
thereof
.
|
|
For
1
/
40
|
91.
4.
s
.
0.
d
.
|
|
For
¼
therof
|
45.
12
0.
|
|
facit
|
136.
16.
s
.
0.
|
And
for
the
proofe
.
Take
1
/
30
and
⅛
thereof
,
or
¾
of
1
/
20
,
or
1
/
60
do●ble
,
and
¼
of
1
/
60
,
or
1
/
80
treble
,
or
⅕
of
⅛
and
½
thereof
.
&c.
Euery
of
whiche
waies
facit
136
▪
li.
16
s
.
|
At
10
d
.
what
|
2973.
|
|
Take
¼
of
⅙
for
moste
breefe
.
|
|
The
giuen
nomber
|
2973.
|
|
For
⅙
|
495.
10.
s
.
0.
d
.
|
|
Whereof
¼
facit
|
123.
17
▪
s
.
6.
|
And
for
proofe
.
Take
½
of
¼
of
⅓
,
or
⅚
of
1
/
20
,
or
1
/
30
and
¼
thereof
,
or
1
/
40
and
1
/
60
,
or
1
/
40
and
½
thereof
,
and
⅕
thereof
,
or
1
/
80
treble
,
and
⅓
of
1
/
80.
Euery
of
whiche
waies
facit
136.
l.
16.
s
.
|
At
11.
d
.
the
bushell
what
|
2684.
|
|
Take
1
/
20
lacke
1
/
12
thereof
|
|
|
The
giuen
nomber
|
2684.
at
11.d
.
|
|
For
1
/
20
|
134.
li.
4
s
.
0.
d
.
|
|
From
whiche
1
/
12
|
11.
3.
8.
d
.
|
|
Reste
facit
|
123.
0.
4.
d
.
|
And
for
proofe
.
Take
1
/
30
and
1
/
80
as
in
example
.
|
At
11.d
.
what
|
2684.
|
|
|
For
1
/
30
|
89
|
9.
4
▪
|
|
For
1
/
80
|
33.
|
11.
|
|
Together
facit
|
123
|
4
|
Or
for
the
same
proofe
.
Take
¼
of
⅙
and
1
/
10
thereof
,
or
1
/
40
and
1
/
60
and
¼
of
1
/
60
or
1
/
30
,
and
the
½
thereof
,
and
⅔
thereof
,
or
1
/
30
and
¼
thereof
and
½
thereof
.
Euery
of
whiche
orders
facit
120
l.
s.
4.
d
|
At
12.
d
.
what
|
2568.
Take
for
moste
breee
1
/
20
|
|
facit
|
128.
li.
8
.
s
.
0.d
.
|
|
Foproofe
at
12
d
.
what
|
2568.
Take
⅕
of
¼
|
|
For
¼
|
642.
|
|
Whereof
⅕
faeit
|
128.
8.
0.
|
Whiche
is
sufficiente
,
for
suche
as
will
●…
ue
onely
the
nearest
waie
:
howbeeit
suche
as
vpon
pleasure
will
range
abroade
.
Take
for
the
same
proofe
½
of
1
/
10
,
or
1
/
30
and
½
thereof
,
or
1
/
40
double
.
Euery
of
whiche
facit
—
128.
li.
8.
s
.
0.
d
.
At
13
▪
d
.
what
2357.
Take
1
/
20
and
1
/
1●
therof
.
|
For
1
/
20
|
117.
17.
0.
|
|
|
|
|
For
1
/
12
therof
|
9.
16.
5.
|
|
Whiche
facit
|
127.
13.
5.
|
Here
because
1
/
12
to
bee
taken
from
1
/
10
requireth
some
difficultie
.
Therefore
⅙
is
firste
taken
,
whereof
½
serueth
,
and
the
⅙
canselled
and
the
reste
added
,
maketh
the
totall
.
|
And
for
proofe
at
13.
d
.
what
|
2357
|
|
Take
1
/
30
and
½
thereof
,
and
¼
thereof
.
|
|
The
giuen
nomber
|
2357.
at
13
d
.
|
|
For
1
/
30
|
78.
li.
11.
s
.
4.d
.
|
|
For
½
thereof
|
39.
5.
8.
|
|
For
¼
thereof
|
9.
16.
5.
|
|
Whiche
together
facit
|
127.
13.
5.
|
Or
for
the
same
proofe
Take
1
/
40
double
,
and
⅙
of
1
/
40
or
1
/
60
treble
,
and
¼
of
1
/
60
or
1
/
80
quadruple
,
and
⅕
of
1
/
80
&c.
Euery
of
whiche
facit
127.
li.
13.
s
.
5.
d
.
|
At
14
d
.
what
|
1926.
Take
¼
of
⅕
,
and
⅛
thereof
.
|
|
For
⅕
|
385.
li.
4.
s
.
0
d
.
|
|
For
¼
thereof
|
96.
6.
0
d
.
|
|
For
1
/
●
thereof
|
16.
1.
0
|
|
facit
|
112.
7.
0
d
.
|
|
And
for
profe
at
14.
d
.
what
|
1926.
|
|
Take
½
of
1
/
10
and
⅙
therof
|
|
|
The
giuen
nomber
at
14.
d
.
|
1926.
|
|
For
1
/
10
|
192.
12.
0
|
|
For
½
thereof
|
96.
6.
0
|
|
For
⅙
thereof
|
16.
1.
0
|
|
facit
|
112.
7.
0
|
Or
for
the
same
proofe
Take
1
/
20
and
⅙
thereof
for
moste
bréefe
,
take
1
/
30
and
1
/
40
or
1
/
60
treble
,
and
½
of
1
/
60
&c.
li.
Euery
of
whiche
facit
112.
7.
s
.
0
d
.
|
At
15.
d
.
what
|
1884.
|
|
Take
1
/
20
and
¼
thereof
|
|
|
For
1
/
20
|
94.
4.
s
.
0
d
.
|
|
For
¼
thereof
|
23.
11.
0
|
|
facit
|
117.
15.
0
|
|
And
for
profe
at
15.
d
.
what
.
|
1884.
|
|
Take
½
of
⅛
|
|
|
For
⅛
|
235.
10.
0
d
.
|
|
Whereof
½
facit
|
117.
15.
0
d
.
|
Or
for
the
same
proofe
Take
¼
of
⅕
and
¼
thereof
,
or
½
of
1
/
10
and
1
/
●
thereof
,
or
1
/
40
double
and
½
of
1
/
●0
,
or
1
/
30
and
1
/
60
and
1
/
●0
.
&c.
Euery
of
which
facit
117.
li.
15.
s
.
0
d
.
Take
for
bréefe
1
/
20
and
1
/
●
thereof
.
The
geuen
nomber
at
16
d
.
1468.
take
1
/
20
〈◇〉
⅓
of
it
.
|
For
1
/
20
|
73.
8.
0
d
.
|
|
For
⅓
thereof
|
24.
9.
4
|
|
facit
|
97.
17
4
|
|
And
for
proofe
at
16.
d
.
what
|
1468.
|
|
Take
⅕
of
⅓
|
|
|
For
⅓
|
489.
6.
8
|
|
For
⅕
thereof
|
97.
17.
4
|
Or
for
the
same
proofe
.
Take
⅔
of
1
/
10
or
1
/
20
and
⅓
thereof
or
1
/
30
double
,
or
1
/
40
double
,
and
1
/
60
or
1
/
60
quadruple
.
Euery
of
whiche
facit
.
97.
17.
4.
d
.
|
At
17.
d
.
what
|
1376.
|
|
Take
1
/
20
and
⅓
thereof
,
and
¼
thereof
|
|
The
giuen
nomber
|
1376.
at
17
d
.
|
|
For
1
/
20
|
68.
16.
0
|
|
For
—
½
thereof
|
22.
18.
8
|
|
For
¼
thereof
|
5.
14.
7
|
|
facit
|
97.
9.
0
3
|
And
for
proofe
at
17.
d
.
what
1376.
Take
¼
of
⅕
and
1
/
60
and
¼
thereof
.
|
The
giuen
nomber
|
1376.
at
17.d
.
|
|
For
⅕
|
275.
4.
0
|
|
For
¼
thereof
|
68.
16.
|
|
For
1
/
60
|
22.
18.
8
|
|
For
¼
thereof
|
5.
14.
7
|
|
Whiche
together
facit
|
97.
9.
3
|
Or
for
the
same
proofe
.
Take
⅓
of
1
/
10
and
⅓
thereof
and
¼
therof
or
1
/
30
double
and
⅛
of
1
/
30
or
1
/
30
add
1
/
40
and
1
/
80.
|
Euery
of
whiche
facit
|
97
li.
9
s
.
3
d
.
|
|
At
18
d
.
what
|
1674.
|
|
Take
¼
of
⅕
&
½
therof
.
|
|
|
For
½
|
|
|
For
¼
thereof
|
83.
14.
0
|
|
For
½
thereof
|
41.
17.
0
|
|
facit
|
125.
11.
0
|
And
for
proofe
at
18
d
.
what
1674.
Take
½
of
1
/
10
and
½
thereof
.
|
The
giuen
noumber
|
1674.
at
18d
|
|
For
1
/
10
|
|
|
For
½
thereof
|
83.
14.
0
|
|
For
½
thereof
|
41.
17.
0
|
|
facit
|
125.
11.
0
|
Or
for
the
same
proofe
.
Take
1
/
20
and
½
thereof
,
or
1
/
30
double
,
and
¼
of
1
/
30
,
or
1
/
40
treb●e
,
or
1
/
30
and
40
and
1
/
60.
&c.
|
Euery
of
whiche
facit
|
125.
11.
0
|
|
At
19
d
.
what
|
1735.
|
Take
1
/
20
and
½
therof
and
⅙
thereof
|
The
giuen
noumber
|
1735.
at
19
d
.
|
|
For
1
/
2●
|
86.
15.
0
d
.
|
|
For
½
thereof
|
43.
7.
6
|
|
For
⅙
thereof
|
7.
4.
7
|
|
facit
|
137.
7.
1
|
|
And
for
proofe
at
19
d
.
|
1735.
|
|
Take
1
/
30
double
and
⅛
|
|
|
For
1
/
30
|
|
|
Whereof
the
double
|
115.
13.4
|
|
For
1
/
80
|
21.
13.
9
|
|
facit
|
137.
7.
1
|
Oor
for
the
same
proofe
.
Take
¼
of
⅕
and
½
thereof
,
and
⅙
thereof
,
or
½
of
1
/
10
and
the
½
thereof
and
the
⅙
thereof
.
&c.
|
Euery
of
whiche
facit
|
137
li.
7
s
.
1
d
.
|
|
At
20
d
.
the
péece
,
what
|
1876.
|
|
Take
¼
of
⅓
|
|
|
For
⅓
|
|
|
Whereof
¼
facit
|
156.
6.
8
d
.
|
And
for
proofe
20
d
.
what
1876.
|
Take
½
of
⅙
|
|
|
For
⅙
|
|
|
Whereof
½
facit
|
156.
6.
8.
|
Or
for
the
same
proofe
.
Take
⅓
of
¼
,
or
⅔
of
½
or
⅚
of
1
/
30
o●
1
/
12
,
or
1
/
20
and
½
thereof
and
⅓
thereof
or
1
/
30
double
and
1
/
60
&c.
|
Euery
of
whiche
facit
|
156
li.
6
s
.
8
d
.
|
|
At
21
d
.
what
|
1289.
|
|
Take
½
of
⅙
and
¼
of
1
/
60.
|
|
|
For
⅙
|
|
|
Whereof
½
|
107.
8.
4
|
|
For
1
/
60
|
|
|
Whereof
¼
|
5.
7.
5
|
|
And
the
vncanseld
,
facit
|
112.
15.
9
|
And
for
proofe
at
21
d
.
what
1289.
Take
1
/
20
and
½
thereof
and
½
thereof
.
The
giuen
number
1289.
at
21
d
.
|
For
1
/
20
|
64.
9.
0
d
.
|
|
For
½
therof
|
32.
4.
6
|
|
For
½
therof
|
16.
2.
3
|
|
which
together
facit
|
112.
15.
9
|
Or
for
the
same
proofe
.
Take
1
/
10
lacke
⅛
therof
,
or
1
/
30
and
1
/
40
and
1
/
60
and
1
/
80
,
or
1
/
40
treble
&
1
/
80.
|
Euery
of
whiche
facit
|
112.
15.
9
|
At
22.
d
.
The
yarde
,
what
1578.
Take
1
/
10
lacke
½
of
1
/
60.
|
The
giuen
nomber
|
1578
at
22.d
.
|
|
For
1
/
10
|
157.
16
.
s
.
0.d
.
|
|
For
1
/
60
|
|
|
For
½
thereof
|
13.
3.
0.
|
|
Whiche
rest
facit
|
144.
13.
0.
|
For
proofe
at
22.d
.
what
1578.
Take
½
of
⅙
and
1
/
10
thereof
.
|
The
giuen
nomber
.
|
1578.
|
|
For
⅙
|
|
|
For
½
thereof
.
|
131.
10.
0.
|
|
For
1
/
10
thereof
|
13.03.0
.
|
|
facit
|
144.
13.
0.
|
Or
for
the
same
proofe
.
Take
1
/
20
and
½
thereof
,
and
½
thereof
,
and
⅓
thereof
,
or
1
/
20
and
1
/
40
and
1
/
60
,
or
1
/
30
double
and
1
/
40
,
or
1
/
40
treble
,
and
1
/
60.
|
Euery
of
whiche
facit
|
144
l.
.
13
.
s
.
0.
d
.
|
At
23.d
.
what
1627.
Take
1
/
10
lacke
⅓
of
1
/
80
|
For
1
/
10
|
162.
14.
0.
|
|
For
1
/
80
|
|
|
whereof
⅓
|
6.
15.
7.
|
|
Per
rest
facit
|
155.
18.
5.
|
|
For
proofe
at
23.d
.
what
|
1627.
|
|
Take
½
of
⅙
and
⅛
of
1
/
10.
|
|
The
giuen
nomber
at
23.d
.
1627.
|
For
—
⅙
|
|
|
For
½
thereof
|
136.11.8
.
|
|
For
1
/
10
|
|
|
For
⅛
thereof
|
20.9
.
6.
|
|
Whereof
the
vncanselled
|
155.18
.
5.
|
Or
for
the
same
proofe
take
1
/
20
and
½
therof
and
½
thereof
,
and
⅔
thereof
,
o●
1
/
30
double
,
and
1
/
60
and
1
/
80.
or
1
/
20
1
/
30
and
1
/
80
or
1
/
20
,
and
1
/
40
and
1
/
60
and
¼
thereof
.
|
Euery
of
whiche
facit
|
155
li.
18
.
s
.
5.
|
|
At
2
.
s
the
elle
what
|
1243.
|
|
Take
1
/
10
moste
breefe
.
|
|
|
The
giuen
nomber
at
2
.
s
.
|
1243.
.
|
|
facit
|
124
.
6.s
.
0.
d
.
|
For
proofe
,
at
2
.
s
.
what
1243.
Take
½
of
⅕
|
For
⅕
|
|
|
Whereof
½
facit
|
124.
6.
0.
|
Or
for
the
same
proofe
.
Take
1
/
20
double
or
1
/
30
treble
,
or
1
/
40
quadruple
,
or
1
/
60
sextuple
.
&c.
Euery
of
the
whiche
facit
124
.
li
.
6.d
.
0.d
.
|
At
2
.
s
.
and
1.d
.
what
|
1468.
|
|
Take
1
/
10
and
¼
of
⅙
thereof
.
|
|
|
The
giuen
nomber
|
146.
at
2
.
s
.
1.d
.
|
|
For
1
/
10
|
146
.
16.s
.
0.d
.
|
|
For
⅙
thereof
|
|
|
For
¼
thereof
|
6.
2.
4.
|
|
Whereof
the
vncanselled
facit
|
152.
18.
4.d
.
|
For
proofe
at
2
.
s
.
1.d
.
what
1468.
Take
½
of
⅕
and
⅓
of
⅛
thereof
.
The
giuen
number
at
2
.
s
.
1.d
.
1468.
|
|
|
|
|
146.16.0
.
|
|
|
|
|
|
6.
2.4
.
|
|
|
152.18.4
.
|
Or
for
the
same
proofe
.
Take
1
/
30
treble
and
⅛
of
1
/
30
,
or
1
/
40
quadruple
and
⅙
of
1
/
40
&c.
|
At
3
s
.
2
d
.
what
|
1248.
elles
.
|
|
Take
⅛
and
1
/
30.
|
|
|
At
3.
s
.
2.
d
.
what
|
1248.
elles
.
|
|
For
1
/
●
|
156.
|
|
For
●
/
30
|
41.
12.0
|
|
facit
|
197.
12.0
|
And
for
proofe
.
Take
1
/
10
and
½
thereof
,
and
⅙
thereof
as
by
example
.
|
At
3
s
.
2
d
.
what
|
1248.
|
|
for
1
/
10
|
124.
16.
|
|
for
½
thereof
|
62.
8.
|
|
for
⅙
thereof
|
10.
8.
|
|
facit
|
197.
12.
|
Or
for
the
same
proofe
.
Take
⅙
lackyng
1
/
12
of
1
/
10
or
½
lacke
⅙
of
1
/
10.
&c.
|
Euery
of
whiche
facit
|
197
li.
12
s
.
0
|
|
At
4
s
.
3
d
.
what
|
1234.
Take
⅕
and
1
/
10.
|
|
for
⅕
|
246.
16
s
.
0
d
.
|
|
for
1
/
50
|
15.
8.
6
|
|
facit
|
262.
4.
6
d
.
|
For
proofe
at
4
s
.
3
d
.
what
1234.
Take
2
/
10
double
,
and
¼
of
1
/
20
|
for
1
/
10
double
|
246.
16.
0
|
|
for
—
1
/
20
|
|
|
for
¼
thereof
|
15.
8.
6
|
|
facit
|
262.
4.
6
|
Or
for
the
same
proofe
.
Take
⅕
&
⅛
of
1
/
10.
&c.
And
all
makes
262
li.
4
s
.
6
d
.
At
5.
s
.
4.
d
.
the
ounze
.
what
1111
ounze
.
Take
¼
and
⅙
of
1
/
10.
|
|
277.
15.
0
|
|
|
|
|
|
18.
10.
4
|
|
Facit
.
|
296.
5.
4
|
And
for
proofe
,
at
5
s
4.
what
1111.
Take
¼
and
1
/
60.
|
For
¼
|
277.
15.
0
|
|
For
1
/
60
|
18.
10.
4
|
|
facit
|
296.
5.
4
|
Or
for
the
same
proofe
,
¼
and
⅓
of
1
/
20
,
or
¼
and
½
of
1
/
30
or
⅕
and
⅕
thereof
,
and
⅓
thereof
.
Euery
of
whiche
facit
—
296.
li.
5.
s
.
4.
d
.
At
6.
s
.
5.
d
.
—
1231.
Take
¼
and
⅕
therof
,
and
⅓
thereof
and
¼
thereof
.
|
For
¼
|
307.
15.
0
|
|
For
—
⅕
thereof
|
61.
11.
0
|
|
For
⅓
thereof
|
20.
10.
4
|
|
For
—
¼
thereof
|
5.
2.
7
|
|
Whiche
together
facit
|
394.
18.
11
|
And
for
profe
at
6.
s
.
5.
d
.
what
1231.
Take
⅕
add
½
thereof
and
⅙
thereof
and
¼
thereof
.
|
The
giuen
number
|
1231.
at
6.
s
.
5.
d
.
|
|
For
⅕
|
246.
4.
0
|
|
For
½
thereof
|
123.
2.
0
|
|
For
⅙
thereof
|
20.
10.
4
|
|
For
¼
thereof
|
5.
2.
7
|
|
facit
|
394.
18.
11
|
Or
for
the
same
proofe
⅓
lacke
1
/
20
,
or
¼
&
⅓
therof
lacke
1
/
80
or
⅕
and
½
thereof
,
and
1
/
40
lacke
1
/
●
thereof
.
Euery
of
whiche
facit
394
li.
18.
s
.
11
d
.
At
7
.
s
6.d
what
9867.
peeces
.
Take
¼
and
½
thereof
.
|
At
7
.
s
6.d
.
what
|
9867.
peeces
.
|
|
For
¼
|
2466.
15.
0.d
|
|
For
—
½
thereof
|
1233.
7.
6.
|
|
facit
|
3700.
2.
6.
|
And
for
proofe
at
7
s
.
6.
what
9867.
Take
½
lacke
¼
thereof
.
The
giuen
number
at
7.6
.
d
.
9867.
|
For
½
|
4933.
10.
0.
|
|
From
whiche
¼
|
1233.
7.
6.
|
|
Par
reste
facit
|
3700.
2.
6.
|
Or
for
the
same
proofe
.
Take
⅓
and
1
/
10
thereof
and
¼
therof
or
⅕
and
½
thereof
,
and
½
therof
,
and
½
thereof
or
⅕
double
lacke
⅛
of
⅕
.
Euery
of
whiche
facit
—
3700.
li.
2.
s
.
6.
d
.
At
8
.
s
.
7.d
.
what
—
8976.
Take
⅓
and
¼
thereof
,
and
1
/
80.
The
giuen
number
at
8
s
.
7.d
.
8976.
|
For
⅓
|
2992.
0.
0.
|
|
For
¼
thereof
|
748.
|
|
For
—
1
/
80
|
112.
4.
0.
|
|
Whiche
together
facit
|
3852.
4.
0.
|
And
for
proofe
,
at
8
.
s
.
7.d
.
what
8976.
Take
⅕
double
,
and
⅛
of
⅕
,
and
⅙
thereof
.
The
giuen
nomber
at
8
s
.
7
d
.
8976.
|
For
⅕
|
1795.
4.
0.
|
|
Also
for
⅕
|
1795.
4.
0.
|
|
For
⅛
thereof
|
234.
8.
0.
|
|
For
—
⅙
thereof
|
37.
8.
0.
|
|
Whiche
together
facit
|
3852.
4.
0.
|
Or
for
the
same
proofe
.
Take
¼
and
½
thereof
,
and
1
/
20
and
1
/
12
thereof
,
or
¼
and
1
/
10
and
½
thereof
,
and
½
thereof
,
and
⅙
thereof
.
Euery
of
whiche
facit
—
3852
li.
4.
s
.
0.
d
.
|
At
9
.
s.8.d
.
what
|
8572.
Barrelles
.
|
|
Take
½
lacke
1
/
60.
|
|
|
For
½
|
4286.
0.
0.
|
|
From
whiche
1
/
60
|
142.
17
s.4.d.
|
|
Reste
facit
|
4143.
2.
8.
|
And
for
proofe
.
Take
¼
and
⅕
and
⅙
thereof
.
|
At
9.
s
.
8.
d
.
what
|
8572.
|
|
For
¼
|
2143.
0.
0.
|
|
For
—
⅕
|
1714.
8.
0.
|
|
For
⅙
thereof
|
285.
14.
8.
|
|
Whiche
together
facit
|
4143.
2.
8.
|
Or
for
the
same
proofe
.
Take
⅕
double
and
½
of
⅙
,
or
¼
and
⅕
and
1
/
30
,
or
⅕
double
,
and
1
/
●0
double
.
Euery
of
the
whiche
facit
4143.
li
2
s
.
8.
d
.
At
10
s.9.d.
what
7864.
Take
½
&
1
/
40
&
½
thereof
.
For
—
½
3932.
|
For
1
/
40
|
196.
12.
0.
|
|
For
½
thereof
|
98.
6.
0.
|
|
Whiche
facit
|
4226.
18
.
s
.
0.
|
And
for
proofe
.
Take
¼
double
and
1
/
30
and
⅛
thereof
,
or
⅕
double
,
and
1
/
1●
and
¼
thereof
,
and
½
thereof
,
or
½
and
1
/
08
treble
.
Euery
of
which
facit
4226.
18.
At
11
.
s.10.d
.
what
—
864.
Hogsheades
.
Take
½
and
½
of
⅙
,
and
1
/
10
thereof
.
|
The
giuen
number
|
864
At
11
.
s.10
.
|
|
For
½
|
432.
|
|
For
⅙
|
|
|
For
½
thereof
|
72.
|
|
For
1
/
10
thereof
|
7.
4.
s
.
0.
d
.
|
|
The
which
vncanselled
is
|
511.
4.
0
|
For
profe
at
11s
.
10
d
.
what
864.
hogsheds
.
Take
,
and
1
/
30
double
and
1
/
40.
|
For
½
|
432.
0.
0
|
|
For
1
/
30
|
28.
16.
0
|
|
For
1
/
30
againe
|
28.
16.
0
|
|
For
1
/
40
|
21.
12.
0
|
|
Whiche
together
facit
|
511.
4.
0
d
.
|
Or
for
the
same
proofe
.
Take
½
and
⅕
therof
,
lackyng
1
/
12
thereof
,
or
½
and
1
/
20
,
and
1
/
30
and
¼
thereof
,
or
½
and
1
/
20
and
1
/
40
and
1
/
60.
Euery
of
whiche
facit
511.
li.
4.
s
.
0.
d
.
At
12.
s
.
11.
d
.
what
7853.
Take
½
and
1
/
10
and
1
/
30
and
1
/
80.
|
for
½
|
3926.
10.
0
|
|
for
1
/
10
|
785.
6.0
|
|
for
1
/
30
|
261.
15.
4
|
|
for
1
/
80
|
98.
3.
3
|
|
Whiche
together
facit
|
5071.
14.
7
|
For
profe
at
12
s
.
11
d
.
what
7854.
Take
½
and
¼
thereof
,
and
1
/
60
and
¼
thereof
.
|
The
giuen
nomber
|
7853.
at
12
s
.
11
d
|
|
for
½
|
3926.
10.
0
|
|
for
¼
thereof
|
981.
12.
6
|
|
for
1
/
60
|
130.
17.
8
|
|
for
¼
thereof
|
32.
14.
5
|
|
Whiche
together
facit
|
5071.
14.
7
|
Or
for
more
proofe
.
Take
½
and
¼
thereof
,
and
1
/
40
lacke
⅙
therof
,
or
¼
&
⅕
and
⅙
and
1
/
60
and
●
/
●●
.
Euery
of
whiche
facit
5071
li.
14.7
At
13
.
s
1.d
.
the
quarter
,
what
5938.
Take
½
and
1
/
10
&
½
therof
&
1
/
12
thereof
.
|
for
½
|
1969.
|
|
for
1
/
10
|
593.
16s
.
0
d
|
|
for
½
thereof
.
|
296.18.0
|
|
for
1
/
12
thereof
|
24.14.10
|
|
Whiche
together
facit
|
3884.
8.
10
|
And
for
profe
at
13
s
.
1
d
.
what
5938.
Take
½
and
⅛
and
1
/
60
and
1
/
80.
|
for
½
|
2969.
|
|
for
⅛
|
742.05.0
|
|
for
1
/
60
|
98.19.4
|
|
for
1
/
80
|
74.
4.
6
|
|
Whiche
together
facit
|
3884.
8.
10
|
Or
for
more
proofe
.
Take
½
and
⅙
lacking
1
/
80
or
¼
and
⅕
and
⅙
and
1
/
40
and
½
thereof
,
or
⅓
and
¼
and
1
/
20
and
⅓
thereof
,
a
and
¼
therof
.
Euery
of
which
facit
3884
.
li
.
8
.
s
10
d
.
|
At
16
s
.
4
d
.
what
|
2531.
|
|
For
—
½
|
1265.
10.
0.
|
|
For
½
thereof
|
632.
15.
0.
|
|
For
⅙
thereof
|
126.
11.
0.
|
|
For
⅓
thereof
|
42.
3.
0.
|
|
Whiche
together
facit
|
2066.
19.
8.
|
For
proofe
at
16
s
.
4.
d
.
what
2531.
Take
½
and
⅓
lacke
1
/
60.
|
At
16
.
s
.
4.
what
|
2531.
|
|
For
—
½
|
1265.
10.
0.
|
|
For
⅓
|
843.
13.
4.
|
|
From
whiche
1
/
60
|
42.
3.
8.
|
|
Per
reste
facit
|
2066.
19.
8.
|
Or
for
more
proofe
.
Take
⅓
double
,
and
1
/
10
and
1
/
20
thereof
,
or
¼
treble
,
and
,
1
/
20
and
⅓
thereof
,
or
1
/
60.
Euery
of
whiche
—
2066.l
'
19
.
s
.
8.d
.
At
17
.
s
.
5.d
.
what
—
9856.
yardes
.
Take
½
and
½
thereof
,
and
1
/
10
and
⅙
thereof
,
and
¼
thereof
.
At
17
.
s
.
5.d
.
what
—
9856.
yardes
.
|
for
—
½
|
4928.
0.
0.d
.
|
|
for
½
thereof
|
2464.
0.
0.
|
|
for
—
1
/
10
|
985.
12.
0.
|
|
for
⅙
thereof
|
164.
5.
4.
|
|
for
—
¼
thereof
|
41.
1.
4.
|
|
Whiche
together
is
|
8582.
18
,
8.
|
For
proofe
at
17
s
.
5.d
.
what
9856.
Take
½
and
⅓
and
1
/
40
,
and
½
thereof
.
At
17
.
s
.
5.d
what
—
9856.
|
for
—
½
|
4928.
|
|
for
1
/
●
|
3285.6
.
8.
|
|
for
—
1
/
40
|
246.8
.
0.
|
|
for
½
thereof
.
|
123.4
.
0.
|
|
Whiche
together
facit
|
8582.
18.
8.
|
Or
for
the
same
proofe
.
Take
⅓
double
,
and
⅕
and
¼
of
1
/
60
,
or
⅕
double
and
⅓
and
⅛
and
⅓
of
1
/
40.
Euery
of
whiche
facit
—
8582.
18.
8.
At
18.
s
.
6.
d
.
what
—
896.
Take
the
whole
lacke
1
/
20
and
½
thereof
.
At
18
.
s
.
6.d
.
what
—
896.
|
|
44.
16.
0.
|
|
|
22.
8.
0.
|
|
Per
reste
facit
|
828.
16.
0.
|
For
proofe
at
18
.
s
.
6.d
.
what
—
896.
Take
½
and
½
thereof
,
and
½
thereof
and
1
/
20.
|
At
18.
s
.
6.
d
.
|
896.
|
|
for
—
½
|
448.
|
|
for
½
thereof
.
|
224.
|
|
for
—
½
thereof
|
112.
|
|
for
1
/
●0
|
44.
16.
0.
|
|
Whiche
together
facit
|
828.
16.
0.
|
Or
for
more
proofe
.
Take
½
and
⅖
and
1
/
40
,
or
½
and
⅓
and
1
/
10
lacke
1
/
12
thereof
,
or
⅔
and
⅕
and
1
/
20
,
and
1
/
40
and
1
/
60
,
or
⅔
and
¼
lacke
½
of
1
/
60.
Euery
of
whiche
facit
—
828
li.
16.
0.
At
19.
s
.
7.
d
.
the
péece
.
what
—
746.
Take
the
whole
lackyng
1
/
60
and
¼
thereof
.
At
19.
s
.
7.d
.
the
péece
.
what
746.
From
|
whiche
1
/
60
|
12.
8.
8.d
.
|
|
and
¼
thereof
|
3.
2.
2
|
|
per
rest
facit
|
730.
9.
2.d
.
|
For
proofe
at
19.
s
.
7.
d
.
what
746.
Take
½
and
¼
⅕
&
1
/
60
and
1
/
80.
|
for
½
|
373.
0.
0.
|
|
for
¼
|
186.
10.
0.
|
|
for
⅕
|
149.
4.
0.
|
|
for
1
/
60
|
12.
8.
8.
|
|
for
1
/
80
|
9.
6.
6.
|
|
Whiche
together
facit
|
730.
9.
2.
|
Or
for
more
proofe
.
Take
½
and
⅓
and
⅛
and
1
/
60
and
¼
thereof
,
or
½
and
⅖
and
1
/
20
and
½
thereof
,
and
⅙
thereof
,
or
⅔
and
¼
and
1
/
20
and
¼
thereof
.
Euery
of
whiche
facit
730
.
li
.
9
.
s
.
2.d
.
|
At
20.
s
.
and
8.
d
.
what
|
694.
|
|
Take
the
whole
and
1
/
30
|
|
|
At
20
s
.
and
8.
d
.
what
|
694.
|
|
for
the
whole
|
694.
|
|
for
1
/
30
thereof
|
23.2.7
.
|
|
facit
|
717.
2.8
.
|
For
proofe
.
At
20
.
s
.
8.d
.
what
694.
Take
the
whole
and
1
/
40
and
⅓
therof
|
694.
|
|
17.
7
|
|
5.
15.8
|
|
717.
2.8
|
Thus
muche
may
séeme
sufficient
for
the
summyng
of
any
number
,
whereof
the
price
of
the
vnitie
is
vnder
20.
s
.
and
when
in
any
number
the
price
of
the
vnitie
is
20.
s
.
with
some
parte
of
a
pounde
more
,
then
the
whole
giuen
number
is
to
be
taken
,
and
the
partes
ouer
and
aboue
the
same
to
be
taken
,
and
added
thereunto
in
former
order
.
Whereof
to
giue
example
,
were
superfluous
,
the
effect
easie
to
vnderstande
,
and
appearyng
in
the
last
example
.
&c.
As
in
the
former
examples
,
the
price
of
an
vnitie
in
euery
giuen
noumber
beyng
vnder
20.
s
.
Diuision
hath
béene
practized
memoratiuely
,
so
in
some
other
folowyng
,
wherein
the
price
of
an
vnitie
beyng
40
s
.
or
aboue
,
shall
Multiplication
bee
furthered
,
as
néede
shall
require
,
accordyngly
sometime
alone
,
&
sometyme
with
the
like
Diuision
also
,
where
the
partes
of
a
pounde
the
same
may
require
,
as
in
examples
more
at
large
you
may
perceiue
.
At
40.
the
péece
,
what
568.
Carseis
Memoratiuely
by
2
and
take
the
product
.
At
40
.
s
.
the
péece
what
568.
Carseis
.
At
41
s
.
8.
d
.
what
—
546.
By
2.
and
take
½
of
⅙
to
be
added
with
the
product
.
|
At
41.
s
.
8.
d
.
what
|
546.
|
|
The
product
|
1092.
|
|
For
●
/
●
|
|
|
Where
½
|
45.
10.
|
|
Together
facit
|
1137.
10.
|
For
proofe
at
41
.
s
.
8.d
.
what
546.
Take
the
product
by
2.
and
1
/
12
li.
|
The
product
|
1092.
0.
0.
|
|
for
1
/
12
li.
|
45.
10.
0.
|
|
facit
|
1137.
10.
0.
|
At
3
li.
what
642.
Take
the
product
by
3.
At
3.
li.
2.
s
.
4.
d
.
what
465.
Take
the
product
by
3.
and
1
/
10
li.
and
⅙
thereof
.
At
3.
li.
2.
s
.
4.
d
.
what
465.
|
The
product
|
1395.
|
|
for
—
1
/
10
|
46.
100.
|
|
for
⅙
thereof
|
7.
15.0
.
|
|
facit
|
1449.
5.
0.
|
At
4.
li.
3
.
s
.
6.
d
.
—
what
572.
Take
the
product
by
4
&
½
li.
and
1
/
20
li.
|
At
4.
li
3.
s
.
6.
d
.
what
|
572.
|
|
By
4
the
product
|
2288.
0.
0.
|
|
for
⅛
li.
|
71.
10.
0.
|
|
for
—
1
/
20
|
28.
12.
0.
|
|
facit
|
2388.
2.
0.
|
At
5.
li.
4.
s
.
7.
d
.
what
—
346.
Take
the
producte
by
5.
and
⅕
li.
and
1
/
40
and
⅙
thereof
.
|
At
5.
li.
4.
s
.
7.
d
.
|
346.
|
|
The
producte
|
1730.
0.
0.
|
|
for
⅕
li.
|
69.
4.
0.
|
|
for
—
1
/
40
|
8.
13.
10.
|
|
for
●
/
6
thereof
|
1.
8.
10.
|
|
facit
|
1809.
5.
10.
|
At
6.
li.
5.
s
.
8.
what
—
293.
Take
the
producte
by
6.
and
¼
li.
and
1
/
30.
|
At
6.
li.
5.
s
.
8.
d
.
what
|
293.
|
|
The
producte
|
1758.
|
|
for
¼
li.
|
73.
5.
0.
|
|
for
1
/
30
|
9.
15.
3.
|
|
facit
|
1841.
0.
4.
|
At
7.
li.
6.
s
.
9.
d
.
what
278.
Take
the
producte
by
7.
and
⅓
li.
and
¼
of
1
/
60.
|
At
7.
li.
6.
s
.
9.
d
.
what
|
278.
|
|
The
producte
|
1946.
|
|
for
⅓
li.
|
92.
13.
4.
|
|
for
1
/
60
|
|
|
for
¼
thereof
.
|
1.
3.
2.
|
|
Whiche
vncanselled
facit
|
2039.
16.
6.
|
At
8.
li.
7.
s
.
10.
d
.
what
—
244.
Take
the
producte
by
8.
and
⅓
li.
and
1
/
20
,
and
2
/
6
thereof
.
|
The
giuen
nomber
|
243.
|
|
By
8.
the
producte
|
1944.
0.
0.
|
|
for
⅓
|
81.
0.
0.
|
|
for
—
1
/
20
|
12.
3.
0.
|
|
for
⅙
thereof
.
|
2.
0.
6.
d
.
|
|
facit
|
1944.
0.
0.
|
At
9.
li.
what
—
231.
Take
the
producte
by
9.
|
The
giuen
nomber
|
231.
|
|
facit
|
2079.
|
When
the
value
of
an
vnitie
is
more
then
with
a
diget
to
bee
expressed
:
Then
the
saied
value
expressed
by
mixed
figures
,
is
vrged
by
necessitie
,
to
bee
set
doune
for
multiplicatour
,
vnder
the
giuen
nomber
,
and
no
parte
thereof
referred
to
memorie
,
as
in
the
former
examples
,
and
the
partes
taken
by
former
order
,
as
in
some
examples
followyng
,
the
effecte
also
appearyng
.
At
11.
li.
12.
s
.
4.
d
.
what
524.
Take
the
producte
of
11.
and
½
l.
and
⅕
therof
,
and
⅙
thereof
.
|
The
giuen
nomber
|
524.
|
|
|
11.
|
|
|
524.
|
|
|
524.
|
|
|
262.
0.
0.
|
|
|
52.
8.
0.
|
|
|
8.
14.
8.
|
|
facit
|
6087.
2.
8.
|
At
23.
li.
13.
s
.
6.
d
.
what
234.
Take
the
producte
of
23.
and
½
li.
and
⅓
thereof
,
and
1
/
20
thereof
.
|
The
giuen
nomber
|
234.
|
|
|
23.
|
|
|
702.
|
|
|
468.
|
|
|
117.
|
|
|
39.
|
|
|
1.
19.
0.
|
|
facit
.
|
5539.
19.
0.
|
At
34.
li.
14
s
.
8
d
.
what
142.
Take
the
producte
of
34
,
and
½
li.
and
⅕
and
⅙
thereof
.
|
The
giuen
nomber
|
142.
|
|
|
34.
|
|
|
568.
|
|
|
426.
|
|
|
71.
0
0.
|
|
|
28.
8
0.
|
|
|
4.
14.
8.
|
|
facit
.
|
4932.
28.
|
And
accordyng
to
the
same
order
,
euery
mannes
occasion
maie
bée
furnished
infinitely
,
wherefore
to
giue
more
examples
of
former
effecte
,
might
seme
superfluous
.
Howbeit
to
giue
the
valuation
accordyngly
,
of
the
Quintall
and
seuerall
C.
waightes
and
partes
of
euery
of
the
same
:
sondrie
examples
hereafter
followe
.
The
Quintall
containing
100
lib
.
subtill
.
The
quintall
at
34.
li.
13.
s
.
4.
d
.
what
95
lib
.
Take
the
price
of
the
100.
lacking
1
/
20
therof
At
34.
li.
13.
s
.
4.
d
.
what
.
95.
lib
.
|
for
the
whole
100.
|
34.
13.
4.
d
.
|
|
whereof
1
/
20
rebated
|
1.
14.
8.
|
|
Per
rest
facit
|
32.
18.
8.
|
The
100
lib
.
at
29.
li.
10.
s
.
what
90.
lib
.
Take
the
whole
lacke
1
/
10.
|
the
whole
.
|
29.
10.
0
d
|
|
from
whiche
1
/
10
|
2.
19.
0
|
|
per
rest
facit
|
26.
11.
0
|
The
100
lib
.
at
26
li.
3.
8.
d
.
what
86.
lib
.
Take
¾
of
the
whole
,
and
1
/
10
and
1
/
10
thereof
.
At
12
li.
16
s
.
what
37.
lib
.
|
|
3.
4.
0
|
|
|
1.
05.
7.
⅕
|
|
|
05.
1.
⅖
&
⅕
of
⅕
|
|
facit
|
4.
14.
8.
16
/
21
|
The
100
lib
.
at
8
li.
2
s
.
6
d
.
what
14.
lib
.
Take
1
/
10
and
⅖
thereof
|
|
0.
16.
3
|
|
|
06.
6
|
|
Facit
.
|
1.
2.
9
d
.
|
The
100
lib
.
at
5.
13.
4.
what
9.
lib
.
Take
1
/
10
lacke
1
/
10
thereof
.
|
for
1
/
10
|
0.
11.
4
|
|
from
whiche
1
/
10
|
1.
1.
⅕
|
|
Per
rest
facit
|
10.
2.
⅖
|
The
100
lib
.
at
3
li.
6
s
.
8
d
.
what
6.
lib
.
Take
½
of
1
/
10
and
⅕
thereof
|
|
0.
6.
8
|
|
|
3.
4
|
|
facit
.
|
0.
4.
0
d
.
|
|
The
100
lib
.
at
2.
li.
10.
s
.
what
|
4
lib
.
|
|
Take
⅖
of
1
/
10.
For
1
/
10.
|
0.
5.
0.
d
.
|
|
Whereof
⅖
facit
|
0.
2.
0.
d
.
|
|
The
100
lib
.
at
16
s
.
8.
d
.
what
3.
lib
.
Take
⅕
of
1
/
10
&
½
thereof
.
For
1
/
10
|
|
|
For
⅕
thereof
|
0.
0.
4.
|
|
For
½
thereof
.
|
0.
0.
2.
|
|
facit
|
0.
0.
6.
d
.
|
|
The
100
lib
.
at
13
s
.
4.
d
.
what
2.
lib
.
Take
⅕
of
1
/
10.
|
|
|
|
0.
0.
3.d
.
⅕
|
|
The
100
lib
.
at
10
s
.
what
1.
lib
.
Take
1
/
10
of
1
/
10.
|
|
|
facit
|
0.
0.
1.
⅕
|
|
The
100
lib
.
at
8
s
.
4.
d
.
what
4.
onzes
.
Take
¼
of
1
/
10
of
1
/
10.
For
1
/
10.
|
0.
0
10
d
.
|
|
For
1
/
10
thereof
|
|
|
Whereof
¼
facit
|
0.
0.
0
6.
mits
|
As
euery
of
former
examples
are
profitable
,
and
of
many
the
vnderstandyng
maie
bee
desired
to
finde
the
sonderie
partes
of
the
100
lib
the
same
to
value
after
the
rate
of
the
C.
so
of
all
the
other
it
maie
seme
moste
necessary
to
vnderstande
,
how
by
the
price
of
the
C.
to
finde
the
value
of
the
pounde
waight
,
&
the
onze
with
moste
facilitie
:
wherefore
for
a
generall
rule
,
to
finde
the
value
of
1.
pounde
waight
by
the
price
of
the
C.
take
euer
1
/
10
of
1
/
10
of
the
price
that
the
C.
lib
.
is
valued
at
,
and
that
is
the
true
value
of
the
pounde
waight
,
as
before
appeareth
,
and
by
an
other
example
folowyng
,
the
effecte
is
manifeste
.
|
The
C.
at
45.
li.
17
s
.
6.
d
.
what
1
li.
Take
1
/
10
of
1
/
10.
For
1
/
10
|
4.
11.
9
d
.
|
|
Whereof
1
/
10
facit
|
09
2.
d
1
/
10.
|
Likewise
to
finde
the
value
of
the
vnze
beyng
16.
as
in
the
haberdepoise
.
Take
1
/
10
of
1
/
10.
of
1
/
10
and
haue
your
desire
.
How
be
it
,
if
the
vnze
bee
of
12
in
the
lib
.
waight
Troye
,
then
take
1
/
12
of
1
/
10
of
1
/
10
and
accordyngly
haue
your
desire
.
Of
the
C.
waight
containyng
112
li.
The
C.
waight
at
36.
li.
what
96
lib
.
Take
the
whole
price
of
the
C.
lackyng
⅛
and
1
/
7
therof
.
|
The
whole
|
36.
0.
0.
d
.
|
|
From
whiche
⅛
|
4.
10.
0.
|
|
And
1
/
7
of
it
|
0.
12.
10.
2
/
7.
|
|
Per
rest
facit
|
30.
17.
1.
5
/
●
.
|
For
proofe
,
the
C.
at
36.
l.
what
¾
&
12
lib
.
Take
½
and
½
thereof
,
and
½
thereof
,
lacke
7
/
2
|
For
—
½
|
18.
0.
0.
|
|
For
½
thereof
|
9.
0.
0.
|
|
For
—
½
thereof
|
4.
10.
0.
|
|
From
whiche
1
/
7
|
0.
12.
10.
2
/
7.
|
|
Per
reste
facit
.
|
30.
17.
1.
5
/
7.
|
|
The
C.
at
32.
li.
what
|
8
4.
lib
.
Take
¾
|
|
of
the
whole
price
.
For
½
|
16.
li.
5.
s
.
0.
d
.
|
|
For
½
thereof
|
8.
2.
6.
|
|
Together
facit
|
24.
li
7.
s
.
6.
d
.
|
For
profe
the
C.
at
32.
li.
10.
s
.
what
84.
lib
.
Take
the
whole
lacke
¼
thereof
.
|
At
32
li.
10
s
.
what
|
84.
li.
|
|
For
the
whole
|
32.
10.
|
|
From
whiche
¼
|
8.
2.
6.
|
|
Per
reste
facit
|
24.
7.
6.
|
The
C.
at
28.
li.
5.
s
.
what
—
72.
li.
Take
½
and
¼
thereof
,
and
1
/
7
thereof
.
|
At
28
li.
5
s
.
what
|
72.
li.
|
|
For
—
½
|
14.
2.
6.
d
.
|
|
For
—
¼
thereof
|
3.
10.
7.
½
.
|
|
For
—
1
/
7
thereof
|
0.
10.
1.
1
/
14
|
|
Together
facit
|
18.
3.
2.
4
/
7.
|
The
C.
at
25.
li.
13.
s
.
4.
d
.
what
6
6.
li.
Take
½
and
⅛
thereof
,
and
3
/
7
thereof
.
|
At
25
li.
13
s
.
4
d
.
what
|
66.
li.
|
|
For
—
½
|
12.
16.
8.
d
.
|
|
For
⅛
thereof
|
1.
12.
1.
|
|
For
—
1
/
7
thereof
|
4.
7.
|
|
For
the
double
therof
|
9.
2.
|
|
Together
facit
|
15.
2.
6.
|
The
C.
at
22
li.
12
s
.
what
—
60.
Take
½
and
1
/
7
of
½
thereof
.
|
At
22
li.
12
s
.
what
|
60.
|
|
For
—
½
|
11.6
.
0.
d
.
|
|
For
½
thereof
|
|
|
For
—
1
/
7
thereof
|
16.
1.
5
/
7
|
|
Vncanselled
facit
|
12.
2.
1.
5
/
7
|
|
The
C.
at
18.
li.
6.
s
.
8.
d
.
what
|
50.
li.
|
|
Take
¼
and
½
thereof
,
&
½
therof
,
&
1
/
7
thereof
.
|
|
At
18
li.
6
s
.
8
d
.
what
|
50.
li.
|
|
For
—
¼
|
4.
11.
8.
|
|
For
½
thereof
|
2.
5.
10.
|
|
For
½
thereof
|
1.
2.
11.
|
|
For
1
/
7
thereof
|
3.
3.
2
/
7.
|
|
Together
facit
|
8.
3.
8.
2
/
7.
|
|
The
C.
at
16.
li.
13.
s
.
4.
d
.
what
|
42.
li.
|
|
Take
¼
and
½
therof
.
|
|
|
At
16
li.
13
s
.
4
d
.
what
|
42.
li.
|
|
For
—
¼
|
4.
3.
4.
d
.
|
|
For
½
thereof
|
2.
1.
8.
|
|
Together
facit
|
6.
5.
0.
d
.
|
|
The
C.
at
12
li.
10.
s
.
what
|
35.
li.
|
|
Take
¼
and
¼
thereof
.
|
|
|
At
12
li.
10.
s
.
|
what
35.
li.
|
|
For
—
¼
|
3.
2.
6.
d
.
|
|
For
¼
thereof
|
15.
7.
½
.
|
|
Together
facit
|
3.
18.
1.
½
.
|
|
The
C.
at
10.
li.
15.
s
.
what
|
30.
lib
.
|
|
Take
¼
and
1
/
14
thereof
.
|
|
|
At
10.
li.
15.
s
.
what
|
30.
li.
|
|
For
—
¼
|
2.
13.
9.
|
|
For
1
/
14
thereof
|
3.
10.
¼
|
|
facit
|
2.
17.
7.
1
/
14.
|
|
The
C.
at
8.
li.
16
.
s
.
what
|
24.
|
|
Take
¼
lacke
1
/
7
thereof
.
|
|
|
At
8.
li.
16
s
.
|
what
24.
li.
|
|
For
—
¼
|
2.
4.
0.
d
.
|
|
From
whiche
1
/
7
|
6.
3
,
3
/
7.
|
|
Per
reste
facit
|
1.
17.
8.
4
/
7.
|
|
The
C.
at
6.
li.
13
.
s
.
4.
what
|
20
.
li
.
|
|
Take
⅛
and
½
thereof
lacke
1
/
7
thereof
.
|
|
The
C.
at
6
li.
13
s
.
4
d
.
what
20.
li
,
|
For
—
⅛
|
0.
16.
8.
d
.
|
|
For
—
½
thereof
.
|
8.
4.
|
|
From
whiche
—
1
/
7
|
1.
2.
2
/
7.
|
|
Per
reste
facit
|
1.
3.
9.
5
/
7.
|
|
The
C.
at
5.
s
.
4.
what
|
16
li.
Take
⅛
and
|
|
and
1
/
7
thereof
.
For
⅛
|
0.
13
0.
d
.
|
|
For
1
/
7
thereof
|
1.
10.
2
/
7.
|
|
facit
|
0.
14.
10.
2
/
7.
|
The
C.
at
3.
li.
6
s
.
8
d
.
what
10.
lib
.
Take
¼
of
¼
and
3
/
7
thereof
.
|
for
¼
|
|
|
for
—
¼
thereof
|
0.
4.
2
|
|
for
1
/
7
thereof
|
0.
0.
7.
1
/
7
|
|
for
the
double
therof
|
0.
1.
2.
d
.
2
/
7
|
|
facit
|
0.
5.
11
d
.
2
/
7
|
|
The
C.
at
40
s
.
what
|
7.
lib
.
Take
¼
of
¼
|
|
for
¼
|
|
|
whereof
¼
facit
|
0.
2.
6
d
.
|
|
The
C.
at
33
s
.
4
d
.
what
|
6.
lib
.
Take
1
/
7
|
|
of
¼
and
½
thereof
|
|
|
for
¼
|
|
|
whereof
1
/
7
|
0.
1.
2.
2
/
7
|
|
and
½
therereof
|
0.
0.
7.
1
/
7
|
|
facit
|
0.
1.
9.
3
/
7
|
The
C.
at
30
s
.
6
d
.
what
4
lib
.
Take
1
/
7
of
¼
|
for
¼
|
|
|
whstrof
1
/
7
facit
|
0.
1
s
.
6
/
7
d
.
|
The
C.
at
26
s
.
8
d
.
what
2.
lib
.
take
½
of
1
/
7
of
¼
|
for
¼
|
0.
06.
s
.
8
d
.
|
|
for
—
1
/
7
thereof
0.
|
0.
11
d
.
3
/
7
|
|
whereof
½
facit
|
0.
5
d
.
5
/
7
|
The
C.
at
20
s
.
what
1.
lib
.
Take
¼
of
1
/
7
of
¼
or
1
/
7
of
1
/
16
|
for
¼
|
0.
5.
0
|
|
for
—
1
/
7
therenf
|
8.
4
/
7
|
|
whereof
¼
facit
|
0.
0.
2.
1
/
7
|
To
find
the
value
of
the
ounze
by
the
price
of
the
C.
waight
,
you
must
first
finde
the
value
of
the
pound
waight
,
as
before
,
and
then
take
1
/
16
thereof
,
and
that
is
the
value
of
the
ounze
,
as
by
example
.
The
C.
at
24.
li.
what
1.
onz
.
Take
1
/
16
of
1
/
7
of
1
/
16
|
for
—
1
/
16
|
|
|
for
1
/
7
thereof
|
|
|
whereof
1
/
16
facit
|
0.
0.
3
3
/
14
|
For
profe
,
the
C.
at
24
lib
.
what
1.
ounze
.
Take
1
/
16
of
¼
of
1
/
7
of
¼
|
for
—
¼
|
6.
0.
0
d
.
|
|
for
1
/
7
thereof
|
0.
17.
1
5
/
7
|
|
for
—
¼
thereof
|
0.
4.
3.
3
/
7
|
|
whereof
1
/
16
facit
|
0.
0.
3.
3
/
14
|
In
like
maner
may
bée
taken
any
parte
of
the
pounde
waight
,
accordyng
to
the
proportion
it
beareth
to
the
whole
.
Of
the
C.
containyng
120.
for
the
C.
The
C.
of
Canuas
at
7.
li.
what
90.
elles
.
Take
½
and
½
thereof
.
|
At
7
li.
what
|
90.
elles
.
|
|
For
—
½
|
3
li.
10
s
.
0
d
.
|
|
For
½
thereof
|
1.
15.
0
|
|
Together
facit
|
5.
5.
0
|
|
The
C.
at
8
li.
what
|
85.
Take
⅔
and
|
|
1
/
16
thereof
.
|
|
|
For
—
⅔
|
5.
6.
8
d
.
|
|
For
1
/
16
—
thereof
|
0.
6.
8
|
|
Together
is
|
5.
13.
4
|
|
The
C.
at
9
li.
what
|
74.
Take
½
and
⅙
|
|
thereof
,
and
⅖
thereof
|
|
|
Fer
½
|
4.
10.
0
d
.
|
|
For
—
⅙
thereof
|
0.
15.
0
|
|
For
⅖
—
thereof
|
0.
6.
0
|
|
|
5.
11.
0
|
The
C.
16
s
.
8
d
.
what
—
68.
Take
½
and
⅕
of
⅓
.
|
For
—
½
|
0.
8.
4
d
.
|
|
For
⅓
|
|
|
For
—
⅕
|
0.
1.
1.
⅓
|
|
The
vncanselled
is
|
0.
9.
5
d
.
⅓
|
The
C.
at
13
s
8
d
.
what
51.
l.
Take
⅓
and
¼
thereof
ond
1
/
10
thereof
|
For
—
⅓
|
0.
4
s
.
6
⅔
|
|
For
¼
thereof
.
|
0.
1.
1
⅔
|
|
For
—
1
/
10
thereof
|
0.
0.
1
⅓
&
1
/
10
of
⅓
|
|
Together
facit
|
0.
—
5.
9.
7
/
10
|
The
C.
at
12
s
.
6
d
.
what
—
45.
—
Take
—
½
and
⅛
thereof
.
|
For
—
⅓
|
0.
4.
2
d
.
|
|
for
⅛
thereof
|
0.
0.
6.
¼
|
|
facit
|
0.
4.
8.
¼
|
The
C.
at
11
s
.
what
—
36.
—
Take
¼
and
⅕
thereof
|
For
—
¼
|
0.
2.
9.
|
|
For
1
/
5
thereof
|
0.
0.
6.
3
/
5
|
|
facit
|
0.
3.
3.
⅗
|
|
The
C.
at
10
s
.
what
|
30.
—
Take
¼
|
|
for
¼
facit
|
9.
2.
6
|
The
C.
at
8
s
.
what
—
25.
Take
⅙
and
¼
therof
,
or
¼
lacke
⅙
thereof
|
For
—
⅙
|
0.
1.
4.
|
|
For
¼
therof
|
0.
0.
4.
|
|
facit
|
0.
1.
8
d
.
|
The
C.
at
6
s
.
8
d
.
what
—
16.
—
Take
3
/
6
lacke
⅕
therof
or
1
/
10
&
⅓
thereof
|
For
—
1
/
10
|
0.
0.
8
d
.
|
|
For
⅓
thereof
|
0.
0.
2.
⅔
|
|
facit
|
0.
0.
10.
⅔
|
The
C.
at
5
s
.
what
—
10.
Take
1
/
12
,
or
½
of
⅙
,
or
¼
of
⅓
|
For
1
/
12
facit
|
0.
0.
5.
d
.
|
The
C.
at
4
.
s
.
what
—
6.
—
Take
½
of
1
/
10
,
or
⅕
of
¼
.
|
At
4
s
.
what
|
6.
—
|
|
For
—
1
/
10
|
|
|
Whereof
½
is
|
0.
0.
2.
⅖
.
|
The
C.
at
3
s
.
4
d
.
what
—
2.
—
Take
⅙
of
1
/
10
,
or
⅓
of
⅕
of
¼
or
⅕
of
½
of
,
⅙
or
⅕
of
⅓
of
¼
.
|
The
giuen
nomber
what
|
2
—
|
|
For
—
1
/
10
|
|
|
For
⅙
thereof
is
|
0.
0.
0.
⅔
d
.
|
The
C.
at
3
.
li
.
6
.
s
.
8.
what
—
1.
—
Take
1
/
22
of
1
/
10
,
or
⅙
of
⅕
of
¼
.
|
The
C.
at
3
li.
6
s
.
8
d
.
|
1.
—
|
|
For
—
1
/
10
|
|
|
Whereof
—
1
/
12
is
|
0.
0.
6.
⅔
.
|
For
proofe
the
C.
at
3.
li.
6.
8.
what
—
1
—
Take
⅙
of
⅕
of
¼
.
|
At
3
li.
6
s
.
8
d
.
what
|
1.
—
|
|
For
—
¼
|
|
|
For
⅕
thereof
|
|
|
Whereof
⅙
facit
|
0.
0.
6.
⅔
.
|
Here
note
for
a
generall
rule
,
that
suche
proportion
as
the
giuen
nomber
beareth
to
the
C.
the
same
proportion
beareth
the
price
of
the
giuen
nomber
,
to
the
price
of
the
C.
and
therein
consisteth
the
difficultie
,
that
to
any
learner
maie
appeare
.
Thus
is
brought
to
ende
gentle
reader
,
the
effecte
by
my
trauaile
pretended
herein
.
The
whiche
beyng
so
well
accepted
of
thee
,
as
it
hath
been
willyngly
furthered
,
to
procure
contentation
to
all
suche
,
as
maie
take
profite
or
delectation
by
the
same
:
so
I
maie
bee
incouraged
to
augmente
my
good
will
,
in
furtheryng
of
other
workes
of
greater
consequence
,
therin
assisted
by
the
fauour
of
the
almightie
,
into
whose
handes
I
committe
thee
farewell
.