The
Appendix
.
The
Preface
.
SEing
that
we
haue
already
described
the
Disme
,
we
will
now
come
to
the
vse
thereof
,
shewing
by
vi
.
Articles
,
how
all
computations
which
can
happen
in
any
mans
busines
,
may
be
easily
performed
thereby
:
beginning
first
to
shew
how
they
are
to
be
put
in
practize
,
in
the
casting
vp
of
the
content
or
quantity
of
Land
measured
as
followeth
.
The
first
Article
,
of
the
Computations
of
Land-meating
.
CAll
the
Pearch
or
Rood
also
Comencement
,
which
is
1
(
0
)
,
diuiding
that
into
10
equall
parts
,
whereof
each
one
shal
be
1
(
1
)
;
them
diuide
each
prime
againe
into
10
equall
parts
,
each
of
which
shal
be
1
(
2
)
;
and
againe
each
of
them
into
10
equall
parts
,
and
each
of
them
shal
be
1
(
3
)
;
proceeding
further
so
,
if
neede
be
;
but
in
Land-meating
,
diuisions
of
seconde
wil
be
small
enough
:
yet
for
such
things
as
require
more
exactnes
,
as
Fathome
of
the
Lead
,
Bodyes
&c.
there
may
be
thirds
vsed
:
and
for
as
much
as
the
greater
number
of
Land-meaters
vse
not
the
Pole
,
but
a
chayne
line
of
three
,
foure
or
fiue
Perch
long
marking
vpon
the
yard
of
their
crosse
staffe
certaine
feete
5
or
6
with
fingers
,
palmes
&c.
the
like
may
be
done
here
:
for
in
the
place
of
their
fiue
or
sixe
feete
with
their
fingers
,
they
may
put
5
or
6
primes
with
their
seconds
.
THis
being
so
prepared
,
these
shal
be
vsed
in
measuring
,
without
regarding
the
feete
and
fingers
of
the
Pole
,
according
to
the
Custome
of
the
place
:
&
that
which
must
be
added
,
substracted
,
multiplied
or
diuided
according
to
this
measure
,
shal
be
performed
according
to
the
doctrine
of
the
precedent
examples
.
AS
for
example
,
we
are
to
adde
4.
tryangles
or
surfaces
of
Land
,
whereof
the
first
345
(
0
)
7
(
1
)
2
(
2
)
,
the
second
872
(
0
)
5
(
1
)
3
(
2
)
,
the
third
615
(
0
)
4
(
1
)
8
(
2
)
the
fourth
956
(
0
)
8
(
1
)
6
(
2
)
;
THese
being
added
according
to
the
manner
declared
in
the
first
Proposition
of
this
Disme
in
this
sort
,
their
summe
wil
be
2790
(
0
)
or
Perches
5
(
1
)
9
(
2
)
,
the
sayd
Roods
or
Perches
,
diuided
according
to
the
custome
of
the
place
;
(
for
euery
Acre
contayneth
certaine
Perches
)
by
the
number
of
perches
you
shall
haue
the
Acres
sought
.
BVt
if
one
would
know
how
many
feete
and
fingers
are
in
the
5
(
1
)
9
(
2
)
(
that
which
Land-meater
shall
need
to
doe
but
once
,
and
that
at
the
end
of
the
casting
vp
of
the
proprietaries
,
although
most
men
esteeme
it
vnnecessary
to
make
any
mention
of
feete
and
fingers
)
it
will
appeare
vpon
the
Pole
how
many
feete
and
fingers
(
which
are
marked
,
ioyning
the
tenth
part
vpon
another
side
of
the
Rood
)
accord
with
themselues
.
In
the
second
,
out
of
57
(
0
)
3
(
1
)
2
(
2
)
substracted
32
(
0
)
5
(
1
)
7
(
2
)
it
may
be
effected
according
to
the
second
proposition
of
this
Disme
,
in
this
maner
:
In
the
third
(
for
multiplication
of
the
sides
of
certaine
Triangles
and
Quadrangles
)
multiply
8
(
0
)
7
(
1
)
3
(
2
)
,
by
7
(
0
)
5
(
1
)
4
(
2
)
2
this
may
be
performed
according
to
the
third
proposition
of
this
Disme
,
in
this
manner
:
And
giueth
for
the
product
or
superfices
65
(
0
)
8
(
1
)
&c.
Deuide
367
(
0
)
6
(
1
)
by
26
(
0
)
3
(
1
)
according
to
the
fourth
proposition
of
this
Disme
:
so
the
Quotient
giueth
from
A
,
towards
B
,
13
(
0
)
9
(
1
)
7
(
2
)
,
which
is
A
E.
And
if
wee
will
,
wee
may
come
neerer
(
although
it
bée
needles
)
by
the
second
note
of
the
fourth
Proposition
,
the
demonstrations
of
all
these
examples
are
alreadie
made
in
their
propositions
.
The
II.
Article
:
of
the
Computations
of
the
measures
of
Tapistry
,
or
Cloth
.
THe
Ell
of
the
Measurer
of
Tapistrie
or
cloth
,
shall
be
to
him
1
(
0
)
,
the
which
he
shall
deuide
(
vpon
the
side
whereon
the
partitions
,
which
are
according
to
the
ordinance
of
the
Towne
,
is
not
set
out
)
as
is
done
aboue
on
the
Pole
of
the
Land
meater
,
namely
into
10
equall
parts
,
whereof
each
shall
be
1
(
0
)
,
then
each
1
(
1
)
into
10
equall
partes
,
of
which
each
shall
be
1
(
2
)
&c.
And
for
the
practise
seeing
that
these
examples
doe
altogether
accord
with
those
of
the
first
Article
of
Landmeating
,
it
is
thereby
sufficiently
manifest
,
so
as
we
need
not
here
make
any
mention
againe
of
them
.
The
III.
Article
:
of
the
Computations
,
seruing
to
Gaudging
,
and
the
measures
of
all
Liquor
vessels
.
ONe
Ame
(
which
maketh
100
pots
Antwerp
)
shal
be
1
(
0
)
,
the
same
shall
be
deuided
in
length
and
deepnes
,
into
10
equall
parts
(
namely
,
equall
to
respect
of
the
wine
,
not
of
the
Rod
;
of
which
the
parts
of
the
pro●…ditie
shal
be
vnequall
)
&
each
part
shal
be
1
(
1
)
containing
10
pots
,
then
again
each
1
(
1
)
into
10
,
parts
equal
as
afore
,
and
each
will
make
1
(
2
)
worth
1
pot
,
then
each
1
(
2
)
into
10.
equal
parts
making
each
1
(
3
)
.
Now
the
Ro●
being
so
deuided
,
to
know
the
content
of
the
Tunne
,
multiply
and
worke
as
in
the
precedent
first
Article
,
of
which
(
being
sufficiently
manifest
)
we
will
not
speake
here
any
farther
.
It
remaineth
yet
to
deuide
each
length
as
B
O
&
O
C
,
&c.
into
fiue
,
thus
:
Seeke
the
meane
proportionall
betweene
B
M
:
&
his
10
part
which
shal
be
B
R
:
cutting
B
S
:
equal
to
B
R
:
Then
the
length
S
R.
noted
from
B
towards
A
:
as
B
T
:
and
likewise
the
length
T
R
:
from
B
to
V
:
&
so
of
the
others
:
&
in
like
sort
proceeding
to
deuide
B
S
:
and
S
T
:
&c.
into
(
3
)
,
I
say
that
B
S
:
S
T
:
and
T
V
:
&c.
are
the
desired
(
2
)
which
is
thus
to
bee
demonstrated
.
For
that
B
N
:
is
the
meane
proportionall
line
(
by
the
Hipothesis
betwéene
B
M
:
and
his
moytie
,
the
square
of
B
N
:
(
by
the
17.
proposition
of
the
sixt
booke
of
Euclide
)
shal
be
equall
to
the
Rectangle
of
B
M
:
&
his
moytie
:
But
the
same
Rectangle
is
the
moytie
of
the
square
of
B
M
:
the
square
then
of
B
N
:
is
equall
to
the
moytie
of
the
square
of
B
M
:
But
B
O
is
(
by
Hipothesis
)
equall
to
B
N
:
and
B
C
:
to
B
M
:
the
square
then
of
B
O
:
is
equall
to
the
moitie
of
the
square
of
B
C.
And
in
like
sort
it
is
to
be
demonstrated
,
that
the
square
of
B
S
is
equall
to
the
tenth
part
of
the
square
of
B
M.
Wherefore
&c.
we
haue
made
the
demonstration
briefe
,
because
wee
write
not
this
to
learners
,
but
vnto
masters
in
their
science
.
The
IIII.
Article
:
of
Computations
of
Stereometrie
in
generall
.
TRue
it
is
,
that
Gaudgerie
which
we
haue
before
declared
,
is
Stereometrie
(
that
is
to
say
,
the
Art
of
measuring
of
bodies
)
but
considering
the
diuers
diuisions
of
the
Rod
,
Yard
,
or
Measure
of
the
one
and
other
,
and
that
and
this
doe
so
much
differ
,
as
the
Genus
and
the
Species
:
they
ought
by
good
reason
to
be
distinguished
.
For
all
Stereometrie
is
not
Gaudgerie
.
To
come
to
the
point
,
the
Stereometrian
shall
vse
the
measure
of
the
towne
or
place
,
as
the
Yard
,
Ell
&c.
with
his
tenne
partitions
,
as
is
described
in
the
first
and
second
Articles
,
the
vse
and
practise
thereof
,
(
as
is
before
shewed
)
is
thus
:
Put
case
wee
haue
a
Quadrangular
,
Rectangular
Columne
to
bee
measured
,
the
length
whereof
is
3
(
1
)
2
(
2
)
,
the
breadth
2
(
1
)
4
(
2
)
,
the
height
2
(
0
)
3
(
1
)
5
(
2
)
,
The
question
is
,
how
much
the
substance
or
matter
of
that
Piller
is
:
Multiply
(
according
to
the
doctrine
of
the
4.
proposition
of
this
Disme
)
the
length
by
the
bredth
,
&
the
product
again
by
the
height
in
this
manner
,
And
the
product
appeareth
to
be
1
(
1
)
8
(
2
)
4
(
4
)
8
(
5
)
.
NOte
,
some
ignorant
(
and
vnderstanding
not
that
wee
speake
here
)
of
the
Principles
of
Stereometry
,
may
maruayle
wherefore
it
is
sayd
,
that
the
greatnes
of
the
abouesaid
colūn
is
but
1
(
1
)
&c.
seing
that
it
contayneth
more
then
180
cubes
,
of
which
the
length
of
each
side
is
1
(
1
)
,
he
must
know
that
the
body
of
one
yard
is
not
a
body
of
10
(
1
)
as
a
yard
in
length
,
but
1000
(
1
)
in
respect
whereof
1
(
1
)
maketh
100
Cubes
,
each
of
1
(
1
)
as
the
like
is
sufficiently
manifest
amongst
Land-meats
in
surfaces
:
for
when
they
say
2
Roodes
,
3
Feete
of
Land
,
it
is
not
barelymeant
2
square
Roods
,
and
three
square
feete
,
but
two
Roods
(
and
counting
but
12
feete
to
the
Rood
)
36
feete
square
:
therefore
if
the
sayd
Question
had
beene
how
many
Cubes
each
being
1
(
1
)
was
in
the
greatnes
of
the
sayd
Piller
,
the
solution
should
haue
bene
fitted
accordingly
,
considering
that
each
of
these
1
(
1
)
doth
make
100
(
1
)
of
those
;
and
each
1
(
2
)
of
these
maketh
10
(
1
)
of
those
&c.
or
otherwise
,
if
the
tenth
part
of
the
yard
be
the
greatest
measure
that
the
Stereometrian
proposeth
,
he
may
call
it
1
(
0
)
,
and
so
as
abouesayd
.
The
fift
Article
;
of
Astronomicall
Computations
.
THe
ancient
Astronomers
hauing
diuided
their
Circles
each
into
360
degrees
,
they
saw
,
that
the
Astronomicall
Computations
of
them
with
their
parts
was
too
laborious
:
and
therefore
they
diuided
also
each
degree
into
certaine
parts
,
and
those
againe
into
as
many
,
&c.
to
the
end
thereby
to
worke
alwayes
by
whole
numbers
,
chusing
the
60th
progression
,
because
that
60
is
a
number
measurable
by
many
whole
measures
,
namely
,
1
,
2
,
3
,
4
,
5
,
6
10
,
12
,
15
,
20
,
30
:
but
if
experience
may
be
credited
(
we
say
with
reuerence
to
the
venerable
antiquity
,
and
moued
with
the
common
vtility
)
the
60th
progression
was
not
the
most
conuenient
,
(
at
least
)
amongst
those
that
in
nature
consist
potentially
,
but
the
tenth
which
is
thus
:
we
call
the
360
degrees
also
Comencements
,
expressing
them
so
360
(
0
)
,
and
each
of
them
a
degree
12
1
(
0
)
to
be
diuided
into
10
equall
parts
,
of
which
each
shall
make
1
(
1
)
,
and
againe
each
1
(
1
)
into
10
(
2
)
and
so
of
the
rest
,
as
the
like
hath
already
bene
often
done
.
Now
this
diuision
being
vnderstood
,
we
may
describe
more
easily
that
we
promised
in
Addition
,
Substraction
,
Multiplication
,
and
Diuision
;
but
because
there
is
no
difference
betweene
the
operation
of
these
,
and
the
foure
former
propositions
of
this
booke
,
it
would
but
be
losse
of
time
,
and
therefore
they
shall
serue
for
examples
of
this
Article
:
yet
adding
thus
much
,
that
we
will
vse
this
maner
of
partition
in
all
the
Tables
&
computations
which
happen
in
Astronomy
,
such
as
we
kepe
to
diuulge
in
our
vulgar
Germane
Language
,
which
to
the
most
rich
adorned
and
perfect
Tongue
of
all
other
,
&
of
the
most
singularity
,
of
which
we
attend
a
more
abundant
demonstration
,
then
Peter
and
Iohn
haue
made
thereof
in
the
Bewysconst
and
Dialectique
,
lately
diuulged
,
and
haue
in
the
lease
following
placed
a
necessary
Table
,
for
the
reducing
of
the
minutes
,
seconds
,
&c.
of
the
60
,
progression
,
into
primes
,
seconds
,
&c.
of
the
tenth
progression
:
the
vse
whereof
followeth
.
The
vse
of
this
Table
.
WHen
any
number
of
minutes
,
seconds
,
thirds
,
fourths
&c.
of
the
60th
progression
,
are
giuen
to
be
reduced
into
the
primes
,
seconds
,
thirds
,
&c.
of
the
tenth
progression
,
seeke
the
giuen
number
in
this
Table
,
or
if
the
number
be
not
there
to
be
found
,
take
the
neerest
:
if
none
be
there
great
enough
,
take
halfe
or
one
quarter
of
the
giuen
:
if
there
be
none
small
enough
,
double
,
treble
,
or
quadruple
,
the
giuen
,
and
then
as
aforesayd
seeke
the
neerest
number
thereunto
in
the
Table
,
and
the
two
numbers
in
whose
common
Angle
the
giuen
number
is
found
,
or
neerest
found
,
shall
shew
you
the
quantity
and
quality
of
the
subdiuisions
of
the
ten
progressions
proper
to
that
giuen
number
,
namely
,
the
number
standing
in
the
toppe
or
front
of
the
table
directly
ouer
it
,
shall
shew
the
quantity
,
and
the
number
directly
against
it
in
the
first
Columne
toward
the
left
hand
,
shall
denote
the
quality
;
as
for
example
,
be
the
pronumber
giuen
,
seeke
it
in
the
Table
,
and
you
shall
find
to
stand
in
the
front
directly
ouer
it
the
figure
7
,
and
in
the
first
Columne
directly
against
it
toward
the
left
hand
(
5
)
:
therefore
according
to
the
rule
aboue
mentioned
,
I
conclude
,
that
of
the
60
progression
valueth
iust
7
(
5
)
of
the
tenth
progression
&c.
This
example
I
thinke
sufficient
to
enlighten
the
ingenious
practizer
:
onely
this
,
that
if
there
be
no
number
to
be
found
in
the
Table
,
iust
or
neere
the
number
giuen
,
you
may
take
two
,
three
or
more
of
those
that
will
come
neerest
,
and
so
worke
as
before
:
as
for
example
also
,
be
the
number
giuen
of
the
60
progression
;
you
shall
find
them
all
by
taking
4
of
the
numbers
of
the
colūne
vnder
3
,
to
be
of
the
tenth
progression
:
and
so
with
a
small
diligence
may
any
other
number
of
the
one
progression
be
reduced
into
the
other
,
which
I
omit
to
speake
any
further
of
at
this
time
.
The
sixt
Article
;
of
the
Computations
of
Money-masters
,
Marchants
,
and
of
all
estates
in
generall
.
TO
the
end
we
speake
in
generall
and
briefly
of
the
summe
and
contents
of
this
Article
,
it
must
be
alwayes
vnderstood
,
that
all
measures
(
be
they
of
length
,
liquors
,
of
mony
&c.
)
be
parted
by
the
tenth
progression
,
and
each
notable
species
of
them
,
shal
be
called
Comencement
:
as
a
Marke
,
comencement
of
weight
,
by
the
which
Siluer
and
Gold
are
wayed
,
Pound
of
other
common
weights
,
Liuers-degros
in
Flanders
,
Pound
sterling
in
England
,
Ducat
in
Spaine
&c.
Comencement
of
Money
:
the
highest
signe
of
the
Marke
shal
be
(
4
)
,
for
1
(
4
)
shall
weigh
about
the
halfe
of
one
Es
of
Antwerp
,
the
(
3
)
shall
serue
for
the
highest
signe
of
the
Liure
de
gros
,
seing
that
1
(
3
)
maketh
lesse
then
the
quarter
of
one
DS.
The
subdiuisions
of
weight
to
weigh
al
things
,
shal
be
(
in
place
of
the
halfe
pound
,
quarter
,
halfe
quarter
,
ounce
,
halfe
ounce
,
esterlin
,
graine
,
Es
,
&c.
of
each
signe
,
5
,
3
,
2
,
1
,
that
is
to
say
,
that
after
the
pound
or
1
(
0
)
shall
follow
the
halfe
pound
or
5
(
1
)
,
then
the
3
(
1
)
then
the
2
(
1
)
then
the
1
(
1
)
,
and
the
like
subdiuisions
haue
also
the
1
(
1
)
and
the
other
following
.
WE
thinke
it
necessary
,
that
each
subdiuision
,
what
matter
soeuer
the
subiect
be
of
,
be
called
Prime
,
Second
,
Third
,
&c.
and
that
because
it
is
notable
vnto
vs
,
that
the
Second
,
being
multiplied
by
the
Third
,
giueth
in
the
product
the
Fifth
(
because
two
and
three
make
fiue
,
as
is
sayd
before
)
also
the
Third
diuided
by
the
Second
,
giueth
the
Quotient
Prime
&c.
that
which
so
properly
cannot
be
done
by
any
other
names
:
but
when
it
shal
be
named
for
distinction
of
the
matters
(
as
to
say
,
halfe
an
Ell
,
half
a
pound
,
halfe
a
pynte
&c.
)
we
may
call
them
Prime
of
Marc
,
Second
of
Marc
,
Second
of
Pound
,
Second
of
Ell
,
&c.
But
to
the'nd
wee
may
giue
example
,
suppose
1
Mark
of
Gold
value
36
lib.
5
(
1
)
3
(
2
)
the
Question
what
valueth
8
Marks
3
(
1
)
5
(
2
)
4
(
3
)
:
multiply
3653
by
8354
giuing
the
product
by
the
fourth
Proposition
(
which
is
also
the
solution
required
)
395
lib.
1
(
1
)
7
(
2
)
1
(
3
)
;
as
for
the
6
(
4
)
and
2
(
5
)
they
are
here
of
no
estimation
.
SVppose
againe
,
that
2
Ells
and
3
(
1
)
cost
3
lib.
2
(
1
)
5
(
2
)
the
question
is
,
what
shall
7
Ells
5
(
1
)
3
(
2
)
cost
:
multiply
according
to
the
custome
the
last
terme
giuen
by
the
second
,
and
diuide
the
product
by
the
first
,
that
is
to
say
,
753
by
325
maketh
244725
,
which
diuided
by
23
,
giueth
the
Quotient
and
Solution
10
lib.
6
(
1
)
4
(
2
)
.
WE
could
also
more
amply
demonstrate
by
easie
examples
of
broken
numbers
,
the
comparison
and
great
difference
of
the
facility
of
this
more
then
that
,
but
we
will
passe
them
ouer
for
breuity
sake
.
LAstly
,
it
may
be
sayd
,
that
there
is
some
difference
betweene
this
last
sixt
Article
,
and
the
5
precedent
Articles
,
which
is
,
that
each
one
may
exercise
for
them selues
the
tenth
partition
of
the
said
precedent
5
Articles
,
thoughst
be
not
giuen
by
the
Magistrate
of
the
place
as
a
generall
order
,
but
it
is
not
so
in
this
latter
:
for
the
examples
hereof
,
are
vulgar
computations
,
which
do
almost
continually
happen
to
euery
man
,
to
whom
it
were
necessary
that
the
solution
so
found
,
were
of
each
accepted
for
good
and
lawfull
:
Therefore
considering
the
so
great
vse
,
it
would
be
a
commendable
thing
,
if
some
of
those
who
expect
the
greatest
commodity
,
would
solicit
to
put
the
same
in
execution
to
effect
,
namely
,
that
ioyning
the
vulgar
partitions
that
are
now
in
weight
,
measures
,
and
moneyes
(
continuing
still
each
Capitall
measure
,
waight
and
Coyne
in
all
places
vnaltred
)
that
the
same
tenth
progression
might
be
lawfully
ordained
by
the
superiors
,
for
euery
one
that
would
vse
the
same
it
might
also
do
well
,
if
the
values
of
Moneys
,
principally
the
new
Coynes
,
might
be
valued
and
reckned
vpon
certayne
Primes
,
Seconds
,
Thirds
&c
But
if
all
this
be
not
put
in
practize
so
soone
as
we
could
wish
,
yet
it
will
first
content
vs
,
that
it
wil
be
beneficiall
to
our
successors
,
if
future
men
shal
hereafter
be
of
such
nature
as
our
predecessors
,
who
were
neuer
negligent
of
so
great
aduantage
.
Secondly
,
that
it
is
not
vnnecessary
for
each
in
particular
,
for
so
much
as
concerneth
him
,
for
that
they
may
all
deliuer
them selues
when
they
will
,
from
so
much
and
so
great
labour
.
And
lastly
,
although
the
effects
of
the
sixt
Article
appeare
not
immediatly
,
yet
it
may
be
;
and
in
the
meane
time
may
each
one
exercise
himselfe
in
the
fiue
precedent
,
such
as
shal
be
most
conuenient
for
them
;
as
some
of
them
haue
already
practized
.
The
end
of
the
Appendix
.