SOME
DEFINITIONS
AND
PRINCIPLES
OF
PERSPECTIVE
.
The
Definitions
,
Names
and
Terms
of
the
Points
,
Lines
and
Figures
which
we
shall
use
.
THe
point
hath
not
any
parts
,
as
we
see
A
,
in
figure
.
1.
In
Perspective
,
there
are
three
sorts
thereof
,
which
are
called
,
points
of
sight
,
points
of
distance
,
and
points
contingent
or
accidental
.
The
line
,
is
a
length
without
breadth
,
as
A
B
in
figure
2.
The
Perspective
hath
five
principle
ones
,
the
which
it
always
useth
.
The
1.
The
line
of
the
base
or
plane
,
as
C
D
may
be
in
figure
3.
The
2.
The
line
Perpendicular
,
or
Plomb-line
,
which
falling
upon
another
,
maketh
the
Angles
on
the
one
part
and
another
equal
,
and
these
Angles
are
called
Right
Angles
,
and
the
line
is
Perpendicular
to
that
upon
the
which
it
falleth
as
in
the
figure
3.
A
B
and
E
F
,
falling
upon
C
D
,
do
make
the
Angle
right
in
G.
The
3.
are
lines
parallel
;
These
are
lines
the
wh●ch
being
continued
upon
the
same
plane
,
and
prolonged
on
the
one
part
and
other
infinitely
,
will
never
meet
together
,
as
N
O
,
in
the
figure
6.
The
Horizontal
line
,
is
no
other
thing
,
then
a
parallel
to
the
base
;
We
shall
speak
of
it
more
largely
in
its
place
.
The
4.
is
the
line
Diagonal
,
this
is
a
line
drawn
from
one
Angle
to
another
,
as
K
L
in
the
figure
10.
And
the
5.
The
line
occult
or
pointed
,
is
a
line
which
ought
to
be
made
in
white
,
or
with
points
,
as
O
N
in
figure
2.
and
these
lines
never
ought
to
appear
,
when
the
work
is
finished
.
The
right
Angle
,
is
that
which
we
speak
of
treating
of
Perpendiculars
,
I
have
set
it
apart
by
it self
,
that
it
may
be
better
known
what
it
is
,
by
E
F
G
,
in
Figure
4.
There
are
two
other
Angles
,
under
which
are
comprized
all
the
Angles
which
are
not
right
,
the
one
is
called
the
Obtuse
which
is
more
then
right
,
as
H
L
M
,
in
figure
5.
And
the
other
sharp
,
which
is
less
then
right
,
as
is
H
I
K
,
in
the
same
figure
.
A
term
,
is
the
end
of
any
thing
,
as
in
the
2.
A
and
B
are
terms
or
the
ends
of
the
line
.
A
figure
,
is
comprized
by
one
or
by
more
terms
,
as
in
7.
8.
9.
13.
14
,
&c.
are
figures
.
The
square
,
hath
the
four
sides
equal
,
and
the
four
Angles
right
,
A
B
C
D
,
in
fig.
7.
The
Parallelogram
,
or
long
square
,
hath
the
four
Angles
right
,
but
not
the
sides
equal
as
C
D
E
F
,
in
fig.
8.
The
Triangle
Equilateral
,
hath
the
three
sides
equal
,
as
G
H
I
in
fig.
9.
Section
and
Intersection
of
lines
,
are
two
lines
which
do
cross
and
divide
themselves
in
one
point
,
as
in
the
figure
11
,
the
lines
A
B
and
C
D
,
divide
themselves
in
E.
The
bowed
or
crooked
line
;
is
that
which
is
drawn
by
a
Circuit
from
one
point
to
another
,
as
L
M
,
in
fig.
12
A
Circle
or
Round
,
is
a
plane
figure
,
comprized
in
one
line
only
,
called
a
circumference
,
towards
which
all
the
lines
coming
from
the
Center
are
equal
between
themselves
,
as
B
C
D
of
the
figure
13
,
the
point
of
the
midst
of
the
Circle
A
,
is
called
the
Center
The
Diameter
,
is
the
right
line
B
C
of
the
Circle
,
the
which
passing
by
the
Center
of
the
Circle
A
,
divideth
it
into
two
equally
.
The
Oval
is
a
long
figure
,
comprized
within
one
line
only
,
not
Circular
but
bowed
and
Regular
as
E
in
fig.
14.
The
Spiral
or
Volute
,
is
a
line
,
that
is
framed
by
two
Centers
,
or
by
one
only
by
Revolution
or
Diminution
F
,
in
fig.
15.
The
Rest
of
the
Definiti●ns
,
Names
and
Termes
.
TAngents
are
one
or
more
lines
,
which
being
drawn
forth
,
do
but
only
touch
or
graze
upon
some
Object
,
figures
or
lines
,
without
dividing
them
in
any
manner
,
as
A
B
touch
the
Circle
C
,
at
the
points
D
D.
I
have
placed
here
two
sorts
of
lines
,
which
bear
the
same
name
with
the
Precedent
,
and
which
nevertheless
produce
another
effect
,
by
reason
of
the
point
of
sight
,
and
of
the
Perspective
,
for
the
Angle
E
A
B
ought
to
be
held
for
a
right
Angle
,
and
all
the
lines
C
ought
to
be
held
for
Perpendiculars
upon
the
Plane
in
Perspective
,
as
is
D
F
,
and
the
lines
A
B
,
G
I
,
and
H
K
,
are
accounted
Perpendiculars
upon
the
base
,
and
all
the
lines
which
go
to
the
point
of
sight
,
either
from
above
or
from
below
,
or
on
the
side
,
are
called
Rays
,
and
lines
visual
or
Radial
.
The
Plane
or
Ichnography
,
is
a
description
or
first
design
,
the
which
representeth
by
single
lineaments
the
Prints
or
foot-steps
,
which
the
foundation
of
the
thing
which
one
would
describe
,
would
make
upon
the
Ground
,
to
the
end
that
by
one
view
only
,
one
may
behold
the
correspondence
,
scituation
and
interval
of
the
parts
between
themselves
,
as
one
may
see
in
L
and
M.
A
Polygone
is
a
figure
which
hath
many
Angles
as
is
L
A
Degree
is
one
little
part
,
whereby
the
Circle
is
divided
into
360
,
and
every
degree
is
further
divided
by
the
Astronomers
into
60
Minutes
,
and
these
Minutes
into
60
others
which
they
call
Seconds
,
&c.
the
which
is
not
useful
for
us
here
.
It
sufficeth
that
we
know
,
that
the
degrees
are
those
little
divisions
which
are
in
the
Circle
N
O
P
Q
,
for
to
have
the
knowledge
of
the
Angles
.
This
knowledge
will
enable
easily
to
make
all
sorts
of
Polygones
,
by
dividing
360
by
the
number
of
Angles
,
which
one
would
have
in
the
figure
:
for
example
,
if
I
would
make
a
square
,
I
divide
360
by
4
,
and
the
Quotient
will
give
90
,
which
is
the
right
Angle
N
M
O
,
and
so
of
others
:
for
those
which
have
not
the
use
of
Arithmetick
,
they
shall
finde
at
the
fourth
side
of
the
Geometrical
Orders
to
make
such
,
whatsoever
may
please
them
.
Some
Orders
of
Geometry
,
for
to
make
the
Lines
and
Figures
,
which
we
are
about
to
define
.
1.
FOr
to
make
the
Perpendiculars
,
or
as
the
Workmen
say
,
the
square
Draught
,
which
is
necessary
in
all
our
operations
.
If
that
you
would
have
it
in
the
midst
of
a
line
,
as
A
E
,
you
must
open
the
Compass
more
then
the
half
of
the
line
,
and
place
one
leg
of
it
at
the
point
A
,
and
with
the
other
frame
two
little
Arches
or
Bows
above
and
below
,
as
F
and
to
do
the
same
from
the
point
E
,
and
the
sections
of
these
little
Arches
,
will
give
the
Perpendicular
upon
A
E
,
1
figure
.
2.
If
the
line
be
at
the
bottom
of
the
table
or
paper
,
and
that
one
cannot
make
the
Arches
above
and
below
.
You
must
divide
this
line
into
two
,
for
to
have
the
point
G
,
then
from
the
ends
of
this
line
to
make
the
Arches
,
which
shall
divide
themselves
in
H
,
then
to
draw
a
line
from
H
,
to
G
,
as
in
the
second
figure
.
3.
To
elevate
a
Perpendicular
from
the
end
of
a
line
,
as
from
the
point
I
of
the
line
I
K.
This
may
be
done
divers
ways
,
first
as
we
have
said
,
but
when
place
is
wanting
you
must
place
one
leg
of
the
Compass
at
the
point
I
,
and
with
the
other
leg
to
make
a
great
portion
of
the
Circle
L
M
,
then
to
set
the
Compass
so
opened
upon
the
point
M
,
and
with
the
other
to
make
it
to
divide
the
Circle
at
the
point
N
,
then
to
take
the
half
towards
the
point
O
,
for
to
have
the
right
Angle
O
I
K
,
or
without
busying
ones
self
to
seek
this
half
of
the
Arch
M
N
,
you
must
with
the
same
,
opening
of
the
Compass
make
yet
upon
the
N
,
and
from
the
same
point
N
,
an
Arch
P
Q
,
then
having
laid
the
Ruler
at
the
points
M
and
N
,
you
must
draw
a
line
which
shall
divide
this
Arch
P
Q
,
at
the
point
P
,
and
elevate
a
line
from
I
to
P
,
for
to
have
the
Perpendicular
and
the
right
Angle
P
I
K
,
figure
3.
4
Otherwise
.
If
from
the
point
P
,
you
would
raise
a
Perpendicular
,
take
a
point
at
pleasure
upon
the
line
P
R
,
as
Q
,
and
from
the
point
Q
make
a
Circle
which
toucheth
the
point
P
,
and
shall
divide
the
line
P
S
,
in
some
part
,
as
S
,
then
to
draw
from
S
,
by
the
point
Q
,
unto
the
circumference
of
the
Circle
T
,
and
T
P
,
shall
be
the
Perpendicular
.
fig
4.
For
to
abreviate
all
the
orders
,
you
must
have
an
equaller
very
just
.
5.
From
a
point
given
upon
a
line
to
make
a
Perpendicular
to
fall
From
the
point
given
A
;
you
must
make
the
Arch
B
C
,
which
divideth
the
line
given
E
F
,
at
the
points
G
H
,
from
these
points
G
H
,
make
two
little
Arches
above
and
below
,
which
shall
divide
themselves
as
at
the
point
I
,
then
from
the
point
A
,
cause
a
line
to
fall
passing
by
I
,
upon
the
line
E
F
,
and
that
shall
be
the
Perpendicular
of
the
point
given
.
6.
From
a
point
given
at
the
end
of
a
line
to
make
a
Perpendicular
fall
.
Let
the
point
given
be
K
,
and
the
line
L
M
,
from
the
point
K
,
you
must
draw
a
line
traversing
at
pleasure
,
which
divideth
in
some
place
the
line
L
M
,
as
N
:
after
divide
this
line
K
N
,
into
two
equal
parts
,
and
from
the
midst
O
,
make
the
Arch
that
passeth
by
the
point
K
,
and
at
the
section
which
it
will
make
upon
the
line
L
M
,
as
P
,
and
the
point
P
,
shall
be
to
make
the
Perpendicular
to
fall
K
P.
7.
The
parallels
.
For
to
be
well
made
ought
to
be
over
half-Rounds
,
which
they
ought
to
touch
as
F
G
,
which
is
parallel
to
H
I
,
it
is
made
over
the
half
,
Round
which
it
toucheth
at
the
points
K
L.
8.
To
divide
a
line
into
many
equal
parts
.
Let
the
line
to
be
divided
be
A
B.
You
must
draw
another
above
or
below
,
which
may
be
parallel
to
it
,
as
C
D
,
and
upon
this
latter
,
which
must
be
greater
or
lesser
,
then
that
which
is
to
be
divided
:
You
must
make
as
many
parts
,
as
you
would
divide
that
of
A
B
into
,
as
in
our
example
seven
,
then
from
the
first
and
last
point
of
these
divisions
,
to
draw
lines
which
pass
by
the
ends
of
that
which
is
to
be
divided
,
which
shall
divide
themselves
in
a
certain
point
as
here
,
having
drawn
from
C
by
A
,
and
from
D
,
by
B
,
the
section
E
is
made
,
at
which
point
F
,
you
must
draw
all
the
divisions
of
the
line
C
D
,
and
the
line
A
B
,
shall
be
divided
as
one
desireth
.
For
to
frame
the
Figures
.
1.
IF
the
line
A
B
,
be
given
to
make
of
it
a
square
You
must
set
one
Leg
of
the
compass
,
at
the
point
A
;
and
with
the
other
leg
take
the
length
A
B
,
and
holding
firm
at
the
point
A
,
with
the
other
leg
of
the
Compass
,
make
the
Arch
B
C
,
and
make
also
from
the
point
B
,
the
Arch
A
D
,
which
shall
divide
themselves
at
the
point
E
,
without
the
side
of
the
section
,
he
must
transport
the
half
of
the
Arch
A
E
,
or
B
E
,
which
shall
be
in
the
points
D
C
,
by
the
which
drawing
right
lines
one
shall
have
a
perfect
square
.
After
another
manner
.
Upon
the
line
A
B
,
draw
from
the
point
A
,
a
Perpendicular
C
A
,
equal
to
A
B
,
then
having
taken
with
a
Compass
the
length
A
B
or
A
C
,
you
must
set
the
leg
of
the
Compass
at
the
point
B
,
and
with
the
other
make
an
Arch
,
and
do
altogether
the
same
from
the
point
C
,
the
section
of
these
two
Arches
shall
be
the
point
D
,
for
to
frame
the
square
A
B
C
D.
2.
For
to
make
a
parallelogram
or
long
square
:
Draw
a
Perpendicular
greater
or
smaller
then
E
F
,
as
E
G
,
then
ha●ing
taken
the
height
E
G
,
set
a
leg
of
the
Compass
at
F
,
and
with
the
other
make
an
Arch
,
take
also
the
l
ngth
E
F
,
nd
set
a
leg
of
the
Compass
in
G
,
and
make
a
second
Arch
then
divide
the
first
at
H
,
and
you
shall
have
that
which
you
desire
,
you
must
always
observe
the
same
thing
,
for
all
the
four
right
Angles
.
Of
Polygones
Circular
,
which
are
Figures
with
divers
Angles
within
one
Circle
.
3.
For
the
Triangle
equilateral
You
must
set
the
half
Diameter
,
at
the
point
A
,
and
describe
the
Arch
D
E
,
and
draw
a
line
D
E
,
this
line
shall
be
the
side
of
the
Triangle
,
D
E
F.
4.
For
the
square
draw
2
Diameters
at
right
Angles
,
&
joyn
their
ends
,
this
shall
be
the
square
A
B
C
D.
5.
For
the
Pentagone
or
five
Angles
.
Make
2
Diameters
,
and
take
D
G
,
the
half
of
the
Demy-Diameter
D
I
,
and
from
the
point
G
,
of
the
Interval
G
A
,
make
the
Arch
A
H
,
the
subtendent
H
A
,
shall
be
the
side
of
the
Pentagone
.
6
For
the
Hexagone
,
or
six
Angles
.
The
half
Diameter
is
the
side
of
the
Hexagone
.
7.
For
the
Heptagone
or
seven
Angles
.
Take
the
half
of
the
side
of
the
Triangle
Equilateral
A.
8.
For
the
Octogone
or
eight
Angles
Take
the
half
of
the
quarter
of
the
Circle
9
For
the
Ennagone
or
9
Angles
.
Take
the
2
thirds
of
the
half
Diameter
,
as
E
B
,
for
its
side
.
10.
For
the
Decagone
or
ten
Angles
:
Take
an
half
Diameter
and
divide
it
in
two
at
the
point
G
,
then
from
the
point
G
,
and
the
interval
G
A
,
make
the
Arch
A
B
,
the
part
of
the
half
Diameter
B
C
,
shall
make
the
side
of
the
Decagone
.
11
For
the
Hend●cagone
or
eleven
Angles
.
Make
two
Diameters
at
right
Angles
,
and
from
the
point
A
,
make
the
Arch
B
C
,
of
the
interval
of
the
half
Diameter
,
then
from
the
intersection
C
,
unto
the
E
,
draw
a
line
C
D.
This
is
the
side
of
the
Hendecagone
.
12.
For
the
Dodecagone
,
or
twelve
Angles
,
divide
into
2
the
Arch
of
the
Hexagone
A
B
,
the
subtendent
shall
be
the
side
13.
The
Oval
is
made
of
many
fashions
and
all
composed
of
portions
of
the
Circle
,
or
of
one
only
line
by
two
Centers
,
the
most
commonly
used
are
these
.
Having
made
a
Circle
with
2
Diameters
,
as
A
B
C
D
,
from
the
points
A
B
,
we
must
make
more
two
circles
equal
to
the
first
,
then
from
the
point
D
they
draw
a
●ine
by
the
Center
of
the
l●st
Circle
A
,
unto
the
circumference
E
,
then
setting
a
leg
of
the
Compass
at
the
point
D
,
with
the
other
,
you
must
take
the
interval
E
,
and
make
the
Arch
E
F.
You
must
do
as
much
on
the
other
side
,
and
the
Wall
will
be
made
.
14
For
an
Oval
more
round
.
You
must
draw
one
only
line
,
and
make
a
Circle
,
of
the
Center
A
,
and
from
the
section
of
this
circle
upon
the
right
line
at
the
point
B
,
this
shall
be
the
Center
of
another
Circle
.
To
frame
the
Oval
,
you
must
take
with
a
Compass
all
the
Diameter
of
one
of
the
Circles
,
as
from
the
point
A
to
the
point
E
,
and
set
at
the
sections
of
the
two
Circles
D
E
,
a
leg
of
the
Compass
,
and
with
the
other
leg
make
the
Arch
D
G
H
,
and
to
do
the
same
from
the
point
E.
15.
There
is
another
manner
of
making
of
Ovals
very
easie
,
and
more
useful
then
the
former
,
seeing
that
by
one
and
the
same
Order
,
they
be
made
long
,
narrow
,
large
,
short
,
&c
See
here
how
they
are
made
.
You
must
upon
a
right
line
set
two
nails
,
or
two
pins
,
which
serve
for
the
Center
,
as
A
B
,
for
to
fasten
a
thread
or
small
cord
of
the
height
and
largeness
that
you
would
have
the
Oval
,
as
is
the
pack-thread
A
B
C
:
you
must
hold
this
thread
bended
with
a
feather
or
pencil
,
which
you
shall
turn
,
until
that
you
be
arrived
where
you
have
begun
.
If
you
would
make
it
longer
,
lengthen
out
the
Center
,
and
do
the
contrary
,
if
you
would
have
it
short
:
for
if
you
set
the
two
nails
close
one
to
the
other
,
you
shall
have
a
Round
.
16.
For
the
Volute
,
or
line
like
unto
the
Spiral
,
take
two
points
upon
one
line
,
as
A
B
,
let
these
two
points
serve
for
a
Center
,
the
one
after
the
other
:
for
example
,
having
made
the
half-round
A
B
,
set
again
the
leg
of
the
Compass
on
B
,
and
with
the
other
leg
take
the
length
A
,
and
make
an
half-Circle
A
C.
Then
holding
one
leg
of
the
Compass
at
A
,
you
must
take
the
distance
A
C
,
and
make
the
half-Round
C
D
,
and
s●
often
as
you
please
,
changing
only
the
Centers
.
Vignola
giveth
it
another
fashion
.
Of
the
Rayes
VISUAL
.
THe
Object
being
a
Point
,
then
there
is
but
one
Ray
Visual
made
from
the
Object
to
the
Center
of
the
Eye
;
And
this
Ray
is
called
Axe
or
Centrical
,
which
is
the
most
lively
,
and
the
strongest
of
all
the
other
Rayes
,
as
you
see
in
the
Figure
A
B.
It
is
this
which
divideth
always
the
Horizontal
line
,
and
which
giveth
the
Point
of
the
fight
.
If
the
Object
be
a
right
line
,
the
Rayes
Visual
make
a
Triangle
,
whereof
the
line
C
D
is
the
Base
,
and
the
two
sides
are
the
Rayes
on
the
outside
,
which
come
from
the
Eye
A
,
and
make
the
Triangle
C
A
D.
And
A
B
is
the
Centrical
Radius
.
If
this
line
were
viewed
by
one
end
,
it
would
seem
as
one
point
.
If
the
Object
be
a
Superficies
plane
or
spherical
,
the
Visual-Rayes
will
make
a
Pyramid
,
the
Base
of
which
is
the
Object
C
D
E
F
,
and
the
top
is
the
Eye
A
,
the
rest
of
this
Pyramide
are
the
Rayes
Visual
;
if
the
Superficies
were
view'd
by
the
side
,
it
would
make
but
a
line
.
Of
all
the
Rayes
Visuals
the
strongest
is
the
Centrical
A
B
:
and
so
much
as
the
others
are
further
off
,
by
so
much
they
are
the
weaker
,
and
keep
nevertheless
a
reasonable
strength
unto
the
opening
of
a
right
Triangle
,
at
G
A
P.
Those
which
pass
the
right
Angle
,
are
so
weak
,
that
they
are
not
seen
but
confusedly
,
and
therefore
there
is
need
that
the
out-side
Rayes
which
may
comprehend
the
Object
,
make
at
least
a
right
Angle
within
the
Eye
.
Wherefore
one
may
see
better
a
Perspective
with
one
Eye
only
,
then
with
two
.
According
as
some
say
,
the
whole
object
is
better
seen
with
one
eye
only
then
with
two
;
because
,
say
they
,
that
the
sight
is
then
more
piercing
,
in
respect
that
all
the
Visual
spirits
of
the
Eye
closed
are
directed
and
brought
to
the
other
,
and
this
union
of
Visual
spirits
giveth
a
great
force
,
and
maketh
the
sight
very
strong
:
for
every
Virtue
united
is
much
more
vigorous
,
then
when
it
is
dispersed
:
which
is
the
cause
,
as
they
say
,
that
by
closing
one
of
the
Eyes
all
the
Visual
Vertue
which
was
dispersed
in
the
two
,
cometh
to
joyn
it self
,
and
to
be
gathered
into
one
,
and
by
this
means
it
is
the
better
.
See
here
wherefore
they
hold
it
for
a
certain
thing
,
that
any
one
seeth
more
exactly
,
having
one
Eye
closed
,
then
being
both
open
.
Howsoever
it
be
,
it
is
certain
,
that
one
may
see
a
Perspective
better
with
one
Eye
alone
then
with
two
,
because
that
the
Centrical
Radius
seeketh
out
the
point
of
the
sight
,
where
all
the
radials
of
the
Picture
do
m●et
,
which
causeth
the
whole
to
be
seen
in
its
Perfection
:
which
is
the
reason
that
we
do
not
say
the
point
of
the
eyes
,
but
the
point
of
the
eye
:
for
to
give
to
understand
that
the
Perspective
is
more
pleasing
,
when
it
is
viewed
with
one
eye
only
.
1
fig
2
fig
The
First
Definition
.
PErspective
is
the
Art
which
representeth
every
Object
,
seen
by
some
Diaphane
or
transparent
Medium
,
through
which
the
Visual
Rayes
penetrating
,
are
terminated
or
bounded
at
the
Object
:
and
generally
all
that
is
seen
through
somthing
,
as
through
the
Air
,
through
the
Water
,
through
the
Clouds
,
through
Glass
,
and
the
like
,
things
may
be
said
to
be
seen
in
Perspective
.
And
because
we
can
see
nothing
,
but
through
these
things
,
we
must
say
,
that
all
that
we
see
is
seen
in
Perspective
.
The
end
of
Perspective
is
to
represent
upon
a
Plane
,
as
is
E
F
G
H
,
the
objects
which
are
beyond
such
as
you
see
here
A
B
C
D
,
represented
in
I
K
L
M
:
for
to
understand
this
better
,
let
us
suppose
that
there
is
upon
the
Ground
an
object
A
B
C
D
,
and
that
the
Eye
of
the
Beholder
is
in
O
,
if
one
put
between
the
one
and
the
other
a
transparent
Body
,
marked
with
E
F
G
H
,
the
Sections
which
the
Rayes
of
the
Eye
would
make
of
the
Perpendicular
Q
R
S
T
,
would
make
the
Figure
I
K
L
M
,
such
as
the
object
would
appear
in
the
transparent
Body
:
which
maketh
us
to
understand
,
that
all
Perspective
is
no
other
thing
,
then
sections
of
a
line
:
This
is
the
reason
that
Monsieur
Marolois
,
calleth
always
that
which
he
putteth
in
Perspective
;
The
Appearance
of
the
Section
,
because
that
the
Plane
E
F
G
H
,
divideth
the
visual
Pyramid
A
B
C
D
and
O
,
and
giveth
for
the
Section
I
K
L
M.
The
reason
of
these
Sections
is
,
that
one
only
line
can
determine
nothing
,
&
that
it
is
necessary
,
that
there
be
two
of
them
which
divide
themselvs
for
to
have
a
Point
:
seeing
that
it
is
certain
,
that
from
our
eye
to
the
object
there
is
always
made
a
Radius
or
right
line
,
this
cannot
fail
us
:
but
for
to
have
another
,
which
must
divide
it
,
we
must
imagine
,
that
from
our
foot
there
is
made
a
Center
,
from
whence
divers
Lines
or
Rayes
do
proceed
which
go
to
the
Angles
of
the
objects
,
which
we
behold
as
from
the
Center
P
to
the
Angles
A
B
C
D
,
the
which
Rayes
being
divided
by
some
transparent
Plane
,
as
is
E
F
G
H
,
all
these
Rays
P
B
,
P
A
,
P
C
,
P
D
,
which
were
Horizontal
,
raise
themselves
,
and
become
Perpendiculars
,
as
P
B
,
becometh
Q
M
,
P
D
,
becometh
R
L
,
&c.
For
if
they
remained
Horizontal
,
the
visual
Rayes
would
not
divide
them
,
but
at
the
object
it self
where
both
of
them
do
meet
.
This
is
the
Reason
that
we
always
suppose
a
Plane
,
the
which
making
the
Rayes
to
reflect
,
giveth
the
means
to
divide
them
,
and
so
to
finde
all
the
Points
,
to
frame
the
appearance
of
the
objects
whatsoever
they
be
.
The
Second
Definition
.
IChnography
,
is
the
Pourtraiture
of
the
Platform
or
the
Plane
,
upon
the
which
we
would
raise
any
thing
,
as
A
B
C
D
is
the
Ichnography
or
the
plane
of
a
square
body
.
The
Third
Definition
.
Orthography
is
the
Pourtraict
of
the
face
,
or
the
fore-part
of
the
object
,
as
of
a
Building
,
or
else
it
is
the
Representation
of
the
Body
,
or
of
the
Edifice
directly
opposite
to
our
eye
,
so
as
E
F
G
H
is
the
orthography
or
the
fore-part
of
a
Cube
,
or
of
a
Building
;
for
as
the
Ichnography
representeth
the
Plane
,
so
the
Orthography
giveth
the
representation
of
the
side
opposite
to
the
Eye
.
The
fourth
Definition
.
Scenography
,
is
that
which
representeth
the
Object
wholly
elevated
and
perfect
,
with
all
its
diminutions
and
umbrages
,
as
well
on
the
fore-part
as
on
the
sides
,
which
may
be
seen
,
and
are
above
,
as
I
K
L
M
N
O
P
,
is
a
perfect
Cube
;
in
brief
,
it
is
the
work
wholly
accomplished
,
which
conteineth
in
it self
the
other
Parts
.
That
we
may
make
these
words
more
Intelligible
,
we
shall
name
hereafter
the
Ichnography
,
the
Plane
;
the
Orthography
,
the
face
or
fore-part
;
and
the
Scenography
,
the
Elevation
.
1.
fig.
2.
fig
3.
fig
Wherefore
the
Objects
that
are
far
distant
seem
to
approach
and
joyn
themselves
together
,
although
they
be
in
equal
distance
.
THis
Figure
will
help
to
satisfie
this
question
,
which
is
difficult
enough
;
let
us
suppose
then
,
that
some
body
hath
his
eye
†
at
the
midst
of
a
line
:
it
is
evident
,
that
if
he
would
see
the
two
Ends
thereof
A
B
,
he
must
make
an
half-round
V
X
,
the
center
of
which
is
the
Eye
,
and
the
centrical
Ray
†
†
,
and
making
this
half-Circle
,
he
discovereth
the
objects
,
which
are
on
the
one
side
and
other
in
such
manner
,
that
it
seemeth
to
him
.
that
the
farthest
distant
of
the
side
A
,
seem
to
come
near
to
the
center
†
.
And
those
on
the
side
B
go
thither
also
,
and
seem
as
if
they
would
joyn
themselvs
,
as
much
as
the
one
and
the
other
side
can
.
If
one
ask
why
the
things
so
distant
,
approach
the
one
to
the
other
,
whether
they
be
of
the
side
either
above
or
below
us
:
for
it
seemeth
,
that
that
which
is
on
our
sides
would
joyn
themselves
,
and
that
the
planchers
both
above
and
below
,
do
raise
up
and
abase
themselves
the
farther
they
are
distant
from
us
.
Behold
the
Answer
and
the
Reason
in
two
words
:
It
is
that
all
the
objects
appear
,
under
the
visual
Angle
,
under
the
which
they
are
seen
:
now
it
is
that
the
columns
,
trees
,
or
whatsoever
objects
they
be
,
which
are
on
the
side
A
,
the
farthest
distant
will
appear
to
draw
towards
the
center
T
,
because
they
are
viewed
by
an
Angle
,
or
by
a
Radius
that
draweth
thitherward
;
and
as
for
example
,
the
Ray
†
K
,
is
much
nearer
the
centrical
T
,
then
is
†
C
,
and
†
E
,
and
by
consequent
it
ought
to
appear
so
:
and
if
the
the
objects
were
produced
infinitely
,
they
would
still
approach
nearer
to
the
centrical
T
,
until
that
they
would
seem
to
make
but
one
point
,
which
would
be
infinite
,
as
all
the
points
of
sight
ought
to
be
.
Now
in
Perspective
the
sides
A
K
,
B
S
,
remain
not
Parallels
,
but
are
changed
into
visual
Rayes
,
which
divide
themselves
at
the
point
of
sight
,
and
by
this
means
cause
the
Diminutions
of
the
body
and
sides
of
the
objects
.
For
example
in
the
second
Figure
,
the
eye
being
in
a
distance
capable
of
seeing
the
line
A
B
,
from
the
two
Angles
A
B
,
two
Rayes
begin
to
be
made
,
which
go
to
finde
out
the
point
of
sight
T.
And
these
Rayes
A
T
and
B
T
,
receive
the
sections
that
the
point
of
distance
giveth
to
objects
,
which
do
close
together
proportionally
,
as
we
shall
declare
in
its
place
,
so
that
the
whole
Parallellogramne
A
K
,
B
S
,
and
all
the
objects
that
are
on
the
one
part
and
the
other
,
come
to
be
reduced
to
the
little
space
A
V
,
B
X
:
and
if
the
eye
were
farther
distant
,
this
space
would
be
yet
lesser
,
by
reason
that
the
objects
,
view'd
afar
off
,
seem
very
small
,
as
I
shall
make
it
appear
in
the
next
leaf
.
1.
Fig.
2.
Fig
Wherefore
the
Objects
draw
near
to
each
other
,
being
view'd
afar
off
.
WE
have
already
said
,
that
things
do
appear
according
to
the
Angle
,
in
the
which
they
are
view'd
;
this
Angle
is
taken
at
the
Eye
,
where
the
lines
do
meet
that
do
compute
the
Object
:
for
example
,
the
first
Object
being
B
C
,
if
the
Eye
A
look
upon
it
,
it
will
cause
the
Rayes
A
B
and
A
C
,
which
give
the
Angle
B
A
C
:
so
that
an
Object
seen
in
a
great
Angle
will
appear
great
,
and
another
seen
in
a
little
Angle
will
appear
little
:
Now
it
is
,
that
the
Objects
being
equal
,
those
that
are
farthest
off
are
view'd
in
a
less
Angle
:
we
must
conclude
then
,
that
the
Objects
farthest
off
,
ought
to
be
the
least
in
Perspectives
:
for
example
,
if
the
Eye
be
in
A
the
Object
B
C
,
which
is
the
first
,
will
appear
to
it
the
greatest
,
because
that
it
is
viewed
by
a
greater
Angle
,
the
2
3
4
and
5
Objects
,
will
appear
to
it
always
the
less
,
although
that
they
be
equal
:
the
reason
is
,
because
that
the
Angles
diminish
;
according
as
the
Objects
are
farther
distant
if
the
Eye
were
remitted
into
N
L
K
L
,
it
would
appear
the
greatest
,
and
B
C
would
be
no
bigger
then
N
O.
This
second
figure
is
in
pursuit
of
that
which
we
are
speaking
of
:
for
supposing
,
that
the
Objects
appear
such
,
as
is
the
Angle
within
which
they
are
viewed
;
it
followeth
thence
,
that
if
one
draw
many
lines
under
one
and
the
same
Triangle
,
that
they
ought
to
appear
equal
amongst
themselves
:
so
we
say
,
that
all
the
lines
which
are
comprised
between
the
lines
of
the
Triangle
N
O
P
,
will
appear
equal
amongst
themselves
.
Now
seeing
that
all
the
Objects
comprised
by
the
same
Angle
seem
equal
,
those
which
shall
be
comprised
by
a
greater
Angle
will
seem
greater
,
and
those
that
shall
be
comprised
by
a
less
Angle
will
seem
less
.
Supposing
that
which
we
have
said
,
if
there
were
a
quantity
of
Columns
or
Pilasters
of
one
side
and
the
other
in
an
Hall
,
it
would
be
of
necessity
that
the
Objects
should
be
under
the
same
Angle
,
and
that
all
should
proceed
unto
one
point
,
which
is
within
the
Horizon
O.
For
example
,
the
Eye
being
in
A
,
discovering
the
first
Object
D
E
if
from
the
points
D
E
,
one
draw
the
visual
Rayes
,
D
O
,
E
O
,
they
will
make
the
Triangle
D
O
E
,
which
will
enclose
the
Pilasters
D
E
,
F
G
,
H
I
,
K
L
,
M
N
,
whence
they
ought
to
appear
all
equal
.
That
which
we
have
said
concerning
the
sides
,
ought
to
be
understood
likewise
of
the
pavements
and
planchers
:
for
the
diminutions
of
the
Angles
,
under
the
which
we
see
the
Objects
that
are
far
off
,
are
made
as
well
both
above
and
under
us
as
on
the
sides
.
Wherefore
we
shall
say
thereof
no
other
thing
,
but
only
that
we
must
observe
that
there
be
as
many
squares
between
the
Objects
farthest
off
,
as
between
those
that
are
nearer
:
for
although
that
the
Objects
which
are
remotest
do
close
themselves
,
the
more
far
they
are
off
:
yet
they
cease
not
to
keep
their
said
distance
,
as
we
may
see
between
B
C
D
E
,
which
is
the
Interval
of
the
Pilasters
,
there
are
sixteen
squares
.
There
are
also
sixteen
between
the
most
distant
K
L
M
N.
1.
Fig.
2.
Fig.
Fig
3
Fig
4
IT
followeth
on
that
which
we
were
speaking
of
,
that
if
one
joyn
together
two
Triangles
,
as
in
the
last
,
but
one
for
the
sides
;
and
two
of
the
last
for
the
top
and
the
bottom
,
that
all
four
together
will
bound
themselves
in
one
only
point
A
,
which
is
the
point
of
sight
where
all
the
visual
Rays
come
to
joyn
together
;
and
by
this
means
it
cometh
to
prove
that
which
we
are
speaking
of
,
That
according
to
the
measure
of
the
distance
of
the
Objects
,
they
come
to
close
together
;
those
which
are
below
raise
themselves
,
and
those
which
are
above
abase
themselves
,
and
those
of
the
sides
close
themselvs
,
as
we
may
see
in
the
first
Figure
,
the
which
maketh
us
see
by
the
Eye
the
hollowings
which
flie
from
,
and
seem
to
be
far
distant
from
us
,
although
we
have
them
all
near
to
our
Eye
.
The
Trees
being
produced
by
the
same
cause
,
bring
forth
the
same
effect
that
the
columns
do
:
for
being
all
comprised
under
the
same
Angle
,
and
the
two
ranks
having
each
a
Triangle
,
the
Triangles
joyn
themselves
in
one
point
A
,
and
frame
a
third
,
which
is
the
Earth
;
and
the
fourth
,
if
you
will
,
shall
be
the
Air
:
and
so
affordeth
us
a
delight
which
rejoyceth
us
,
and
recreateth
the
sight
.
We
will
now
begin
to
shew
,
how
it
must
be
proceeded
to
bring
into
Perspective
,
any
plane
,
body
and
figure
whatsoever
.
Of
the
Horizon
.
THE
Horizon
in
the
Art
of
Perspective
,
is
no
other
thing
then
a
line
which
giveth
us
the
height
of
our
Eye
,
in
such
manner
,
as
,
if
we
be
rais'd
as
the
first
man
,
our
Horizon
shall
be
high
:
if
we
be
but
of
our
own
height
,
as
the
second
man
:
it
will
be
but
of
our
height
:
and
if
we
be
lying
or
set
,
as
the
third
,
our
Horizon
will
be
low
:
so
that
the
Horizon
sheweth
how
much
the
Eye
is
elevated
from
the
Earth
.
This
is
the
principal
Piece
of
the
Picture
,
and
which
ought
to
give
the
Rule
to
all
the
rest
,
as
well
for
the
bending
of
the
Buildings
and
Architectures
,
as
for
the
Measures
and
heights
of
the
Figures
.
The
which
hath
caused
a
petty
dispute
between
the
best
Painters
;
for
the
one
say
,
that
it
must
needs
be
that
all
Pictures
have
their
Horizon
within
the
work
,
and
that
the
Perspective
suffereth
that
a
Picture
elevated
above
the
Eye
,
beareth
its
particular
Horizon
.
Others
will
not
have
this
second
Horizon
,
and
use
always
the
Natural
,
in
what
place
soever
the
Picture
be
placed
,
imagining
that
all
the
height
and
bredth
which
they
have
before
them
is
as
a
great
Piece
or
Picture
,
of
which
that
which
is
elevated
in
effect
ought
to
take
its
Measures
:
The
honour
that
I
bear
to
the
one
and
the
other
,
suffereth
me
not
to
determine
upon
it
,
seeing
that
many
good
Authors
have
suffered
them
both
.
But
if
any
one
should
press
me
to
speak
my
opinion
,
I
would
say
freely
that
I
am
of
the
opinion
of
the
latter
,
by
reason
that
all
that
is
in
the
Picture
would
appear
there
more
natural
.
This
line
beareth
always
the
Points
of
sight
,
of
distance
,
and
sometimes
the
Contingents
or
Accidental
:
in
brief
,
this
is
that
which
separateth
the
Heaven
from
the
Earth
,
and
which
limiteth
the
sight
:
it
is
always
Parallel
to
the
bottom
of
the
Picture
or
Plane
,
upon
the
which
the
Object
is
placed
:
whence
it
appeareth
,
that
one
cannot
set
any
thing
above
the
Horizon
,
which
surpasseth
not
the
height
of
the
Eye
.
But
if
the
Object
be
so
high
,
that
it
passeth
this
Horizon
,
it
must
be
then
,
that
the
Plane
of
the
same
Object
be
above
:
as
for
example
,
a
Tree
or
a
Mountain
may
well
have
its
Top
above
the
Horizon
;
but
nevertheless
the
foot
thereof
is
far
on
this
side
.
All
that
is
below
the
Horizon
,
maketh
its
upper
part
appear
,
and
as
soon
as
one
is
past
it
,
one
can
see
it
no
more
.
For
example
,
the
two
Pieces
placed
upon
the
foundation
of
the
first
figure
A
B
shew
their
Top
,
because
that
the
Horizon
is
above
that
of
the
second
figure
D
C
,
do
not
shew
it
:
and
if
they
be
as
it
were
in
the
same
line
,
by
greater
reason
,
those
of
the
third
E
F
ought
less
to
shew
it
,
seeing
that
they
exceed
it
very
much
:
they
are
nevertheless
as
high
the
one
as
the
other
,
it
is
then
the
Horizon
that
causeth
this
difference
.
1
fig.
2
fig.
3
fig.
Of
the
Base
.
THE
Base
of
the
Plane
.
This
is
the
line
upon
the
which
the
Object
ought
to
be
,
and
every
Object
hath
its
own
,
the
which
is
always
Parallel
to
the
Horizon
,
as
is
A
B
of
the
first
Figure
:
F
G
of
the
second
:
N
O
of
the
third
:
This
line
serveth
sometimes
to
give
the
lengths
and
the
bredths
,
as
we
shall
see
afterwards
.
It
is
always
the
bottom
of
the
Picture
which
must
give
all
the
Measures
.
Of
the
Point
of
sight
,
Point
of
Perspective
,
Point
Ocular
,
or
Point
Principal
.
THE
Point
of
Sight
,
of
Perspective
,
Principal
or
Ocular
.
This
is
a
Point
which
maketh
the
Axis
of
the
Eye
,
or
the
Centrical
Ray
above
the
Horizontal
line
,
as
E
of
the
first
Figure
is
the
point
Ocular
above
the
Horizon
C
D
,
at
which
all
the
lines
or
visual
Rayes
ought
to
joyn
themselves
:
It
is
called
also
the
point
of
the
Eye
,
by
reason
that
it
is
opposite
to
him
which
looketh
upon
it
.
Of
the
Points
of
Distance
.
THE
Point
of
distance
,
or
Points
of
distances
.
Is
a
point
or
points
(
for
they
make
two
,
although
it
be
not
necessary
)
which
are
to
be
set
equally
distant
from
the
point
of
sight
:
They
call
them
points
of
distance
:
because
that
the
Person
must
be
as
much
distant
from
the
Figure
,
or
Picture
,
and
from
the
base
,
as
these
points
are
distant
from
the
Point
Ocular
,
and
they
must
always
be
within
the
horizontal
line
,
as
H
I
is
the
Horizon
:
K
,
the
point
of
sight
:
L
and
M
are
the
points
of
distance
,
which
serve
to
afford
all
the
Abridgements
.
As
for
example
,
if
from
the
ends
of
the
line
E
G
,
one
draw
two
lines
to
the
point
K
,
and
from
the
same
points
F
G
,
one
draw
two
lines
to
the
points
of
distances
M
and
L
,
where
these
two
lines
G
L
and
F
K
shall
be
divided
at
the
point
X
,
and
G
K
,
and
F
M
,
at
the
point
Y
,
this
shall
be
the
line
of
sinking
or
hollowing
,
and
the
abridgment
of
the
square
,
whereof
F
G
is
a
side
and
the
base
:
the
lines
that
go
to
the
point
of
sight
are
all
visual
Rays
,
and
those
which
go
to
the
points
of
distance
are
Diagonals
.
Of
Points
Accidental
.
POints
Contingent
or
Accidental
.
Are
certain
Points
where
the
Objects
do
end
,
which
may
be
cast
negligently
,
and
without
order
,
under
the
Plane
:
it
is
because
they
are
not
drawn
to
the
Point
ocular
,
nor
to
the
points
of
Distances
:
but
by
chance
and
at
adventure
,
where
they
meet
each
other
in
the
Horizon
:
as
for
example
,
these
two
pieces
of
wood
X
and
Y
,
do
make
the
points
V
,
V
,
V
,
V
,
above
the
Horizon
P
and
Q
,
and
go
not
to
the
point
of
sight
which
is
R
,
nor
to
the
points
of
distance
S
and
T
:
And
sometimes
the
Bodies
or
Objects
are
so
ill
ordered
,
that
one
must
make
these
points
without
the
Horizon
,
as
we
shall
cause
to
be
seen
in
its
place
.
They
serve
also
for
the
Openings
of
doors
,
of
windows
,
of
stairs
,
and
such
like
things
.
The
which
shall
be
seen
hereafter
.
1.
Fig.
2.
Fig.
3.
Fig
Of
the
Point
of
the
Front
.
THE
point
of
sight
direct
,
or
of
the
front
:
it
is
when
we
have
the
Object
whole
before
us
,
without
being
more
on
the
one
side
then
the
other
,
and
then
one
hath
the
Object
wholly
right
;
that
is
to
say
,
that
it
sheweth
nothing
but
the
fore-part
,
when
it
is
elevated
,
and
a
little
above
,
if
it
be
under
the
Horizon
,
but
it
never
sheweth
its
sides
,
if
the
Objects
be
not
a
Polygone
.
For
example
,
the
Plane
A
B
C
D
is
wholly
the
front
,
so
that
one
can
see
nothing
of
the
sides
A
B
nor
C
D
if
it
were
elevated
,
but
only
the
fore-part
A
D.
The
reason
is
,
for
that
the
point
of
sight
E
,
being
directly
opposite
to
it
,
it
causeth
the
diminution
of
the
one
side
and
the
other
;
this
ought
to
be
understood
if
the
Object
were
an
Elevation
:
for
when
there
is
nothing
but
the
Plane
,
it
sheweth
all
,
as
A
B
C
D.
Of
the
Point
of
the
side
.
THE
oblique
point
of
sight
,
or
on
the
side
.
Is
when
we
see
the
Object
on
the
side
of
us
,
and
that
we
see
it
not
but
athwart
,
or
with
the
corner
of
the
Eye
,
our
Eye
being
nevertheless
always
over
against
the
point
of
sight
:
for
then
we
see
the
Object
on
the
side
,
and
it
sheweth
us
two
faces
:
for
example
,
if
the
Eye
be
in
F
,
the
point
of
sight
the
Object
G
H
I
K
,
will
appear
to
it
athwart
,
and
will
shew
to
it
two
faces
G
K
and
G
H
,
and
then
it
will
be
a
point
of
the
side
.
We
ought
to
do
altogether
the
same
in
the
points
of
the
sides
,
as
in
the
points
of
the
front
,
setting
a
point
of
sight
,
and
those
of
distances
,
&c.
briefly
,
the
same
is
to
be
done
,
as
at
the
view
of
the
front
.
1.
Fig
2.
Fig.
Of
the
visual
Rayes
.
THIS
is
a
general
Maxime
,
That
all
the
lines
which
are
Perpendicular
to
the
base
,
within
a
Geometral
Plane
,
ought
always
to
be
drawn
at
the
point
of
sight
,
when
one
would
set
the
same
Planes
in
Perspective
;
for
example
,
in
the
little
Plane
of
the
first
figure
the
base
is
A
B
,
upon
which
all
the
lines
Z
are
Perpendicular
to
it
.
This
being
supposed
,
that
if
one
give
a
less
or
a
greater
line
then
that
of
the
Plane
,
as
the
great
line
A
B
,
which
hath
the
same
number
of
divisions
with
the
little
one
,
and
from
all
these
divisions
Z
,
one
draw
to
the
point
of
sight
all
these
lines
of
Z
to
E
,
they
will
all
be
perpendicular
to
the
base
,
according
to
the
Reasons
of
Perspective
,
we
may
also
name
them
Radial
,
and
properly
visual
Rayes
:
the
last
of
which
are
called
Extremes
,
by
reason
that
they
are
at
the
end
of
the
base
,
as
are
these
A
B.
Of
the
Diagonals
or
Diametrals
,
and
of
their
sections
.
IT
is
also
a
Maxime
,
that
all
the
Diagonals
of
squares
in
Perspective
,
are
drawn
at
the
Point
of
distance
.
For
example
,
at
the
little
Plane
of
the
second
Figure
,
the
Diagonals
D
O
,
F
O
,
are
drawn
at
the
points
of
distances
in
the
Plane
in
Perspective
,
the
which
maketh
that
the
points
of
distances
do
give
us
the
Abridgements
of
the
Objects
,
that
the
point
of
sight
doth
remove
from
us
:
in
such
manner
(
as
we
have
already
said
)
that
if
one
draw
from
the
ends
of
the
line
of
the
base
F
G
to
the
points
of
distances
L
M
,
they
shall
be
Diagonals
;
and
where
the
lines
shall
divide
the
outmost
Rayes
F
K
and
G
K
,
at
the
points
O
;
this
shall
be
the
Abridgment
of
the
square
,
whereof
F
G
is
one
side
:
and
where
the
same
lines
shall
divide
the
lines
Z
at
the
point
Q
,
one
must
draw
Parallels
which
shall
give
the
Abridgement
of
all
the
squares
,
and
a
like
number
of
all
the
sides
,
as
in
the
little
Plane
.
And
the
more
these
points
of
distances
are
removed
from
the
point
of
sight
,
the
more
the
Objects
do
abridge
themselves
and
close
together
.
And
this
is
it
,
why
all
the
Beauty
of
the
Perspective
dependeth
on
the
points
of
distances
,
which
ought
neither
to
be
too
near
,
nor
too
far
off
from
the
point
of
sight
:
the
which
made
me
set
this
third
figure
,
with
diversity
of
removals
,
for
to
cause
a
belief
of
the
verity
of
that
which
I
am
speaking
.
Let
us
suppose
then
that
R
is
the
point
of
sight
,
and
S
S
the
outmost
Rays
;
if
one
sets
the
point
of
distance
at
T
,
he
shall
divide
the
Radius
S
R
,
at
the
point
V
,
which
shall
be
the
abridgement
of
the
square
,
whereof
S
S
is
one
side
,
the
which
is
ridiculous
to
see
a
square
which
should
appear
three
times
more
hollow
then
it
ought
to
be
,
by
reason
that
the
point
of
the
distance
T
is
too
near
to
the
point
of
the
sight
R
,
for
it
must
be
at
the
nearest
,
that
the
point
of
distance
be
as
far
removed
from
the
point
of
sight
,
as
the
half
of
the
Picture
,
or
of
the
Perspective
,
which
one
would
have
seen
,
as
is
X
,
removed
from
R
,
by
reason
that
these
Removals
do
always
give
a
right
Angle
to
the
Eye
of
the
Beholder
.
In
V
it
would
be
more
pleasing
,
dividing
the
square
at
2
,
and
at
3
,
it
would
be
better
,
dividing
it
at
4.
At
5
it
would
be
far
enough
removed
,
and
would
make
the
square
more
short
in
6
,
as
we
shall
give
the
reason
in
the
figure
following
.
Some
one
may
say
to
me
,
why
have
I
then
set
in
all
the
Figures
of
this
Book
,
the
points
of
distances
so
near
,
seeing
that
being
removed
farther
,
the
whole
would
have
been
more
pleasing
:
And
he
might
by
reason
,
if
I
had
made
the
book
only
to
have
bin
seen
for
curiosity
:
but
it
being
made
for
to
teach
,
there
was
need
that
all
should
be
seen
,
the
better
to
understand
our
Orders
:
this
is
the
cause
,
that
I
have
put
into
the
works
as
much
as
I
could
.
If
one
answer
me
,
that
it
were
better
to
make
the
book
longer
:
I
must
then
have
made
it
much
bigger
,
and
have
set
but
one
figure
in
every
page
:
the
which
I
would
avoid
and
make
a
book
,
convenient
for
carriage
and
it
will
suffice
to
advertise
that
amongst
the
works
that
one
shall
make
,
he
ought
to
enlarge
them
:
the
which
is
easie
,
keeping
the
Rules
which
we
have
given
.
1
Fig.
2
Fig
3
Fig
Of
the
Distance
,
or
Removal
and
Setting
.
WE
have
said
,
speakingf
of
far
off
visual
Rayes
,
that
the
Eye
could
not
conveniently
discover
more
,
then
that
which
may
be
comprised
within
one
right
visual
Angle
.
That
is
to
say
,
that
the
sight
receiveth
not
clearly
nor
entirely
the
Objects
,
when
the
Rayes
go
beyond
the
right
Angle
:
And
behold
the
reason
,
The
apple
of
the
eye
being
near
to
the
center
of
the
eye
,
cannot
receive
clearly
more
then
a
quarter
of
a
circle
,
so
that
the
Rayes
which
are
beyond
that
have
but
a
confused
and
troubled
sight
,
when
the
Angle
is
more
then
90
degrees
:
this
is
the
cause
that
it
is
better
to
make
it
rather
lesser
then
greater
,
as
it
may
be
of
two
thirds
,
which
are
60
degrees
,
but
not
less
:
because
that
the
Rayes
being
so
streightned
or
restrained
,
would
not
give
Contentment
to
the
Eye
,
because
that
the
Angles
being
so
little
,
make
as
it
were
but
one
point
between
the
Apple
of
the
Eye
:
let
us
see
this
difference
by
figures
.
Supposing
that
these
Planes
and
these
Squares
were
the
same
that
are
in
the
last
figure
.
The
distance
of
the
point
T
to
R
,
will
give
us
the
distance
of
T
to
the
Base
,
where
being
,
it
would
be
necessary
that
the
Angle
open
it self
much
more
;
for
to
see
the
Extremes
Y
,
Y
:
for
if
it
open
but
as
a
right
Angle
,
the
Eye
shall
not
be
able
to
see
all
,
as
T
the
right
Angle
,
cannot
see
but
the
points
V
,
V
,
the
which
would
make
the
Perspective
wholly
faulty
,
by
reason
that
that
which
should
give
us
a
square
,
would
frame
us
a
Parallelogramme
.
The
nearest
that
one
can
set
it
is
at
the
point
X
,
which
is
,
as
I
said
even
now
,
the
true
Measure
of
the
right
Angle
,
which
containeth
all
the
Piece
Y
,
Y
:
If
one
withdraw
it
yet
further
from
the
point
of
sight
,
it
will
be
yet
more
pleasing
,
as
in
I
,
which
hath
but
an
Angle
of
72
degrees
.
But
if
one
withdraw
it
unto
Z
it
will
be
the
perfection
,
because
that
the
Rayes
being
not
so
much
dilated
,
have
the
more
force
,
and
conteine
better
the
Objects
:
but
I
would
never
goe
any
farther
then
5.
for
the
reason
whereof
we
are
speaking
;
that
the
Angles
are
but
as
one
point
within
the
Eye
,
and
a
confusion
within
the
Object
.
The
which
ought
to
oblige
us
to
take
good
heed
,
where
we
set
the
Points
,
seeing
that
they
are
so
important
and
necessary
.
And
to
hold
for
a
general
Maxime
,
that
it
must
be
at
least
,
that
the
distance
be
equall
to
the
space
,
which
is
from
the
right
Radius
,
unto
the
Corner
of
Perspective
.
For
xample
✚
R
,
is
the
right
Radius
and
X
✚
,
the
lesser
distance
which
is
equall
to
✚
Y
,
whereof
having
taken
the
Measure
,
we
must
Carry
it
on
the
one
and
other
side
of
the
Point
sight
as
here
R
S
S.
Or
of
one
side
onely
,
as
shall
be
seen
in
the
Leaf
following
.
Behold
what
may
be
said
herein
,
by
the
reasons
of
the
Eye
,
but
the
Practice
giveth
this
Excellent
Rule
,
which
may
be
Generall
,
so
that
one
use
it
with
diseretion
.
That
having
chosen
the
place
,
where
you
would
make
the
Perspective
,
you
may
determine
on
what
side
it
will
be
the
better
in
sight
,
and
whence
it
ought
to
be
looked
on
:
and
then
you
must
take
the
measure
of
this
last
place
unto
the
former
,
and
set
this
Interval
by
a
little
scale
from
the
point
of
sight
unto
the
point
of
distance
:
provided
that
it
be
not
too
far
removed
:
and
it
is
in
this
,
that
the
discretion
is
requisite
,
that
one
do
not
set
it
too
near
,
and
to
avoid
that
which
we
are
speaking
of
,
nor
too
far
off
,
for
fear
that
we
finde
no
returns
where
one
would
have
it
set
:
for
Objects
so
far
removed
from
the
sight
do
yield
no
return
.
This
is
why
we
ought
to
give
but
the
draught
to
Buildings
far
distant
,
as
we
shall
say
hereafter
.
1
Fig
2
Fig.
3
Fig
The
first
Advice
about
the
Point
of
the
side
.
THey
never
change
the
Rules
of
the
Point
of
the
Front
for
the
points
of
the
sides
;
for
they
have
all
for
a
principle
one
&
the
same
cause
,
which
produceth
always
the
like
effects
;
Wherefore
I
shall
not
speak
thereof
in
particular
seeing
that
the
Order
of
the
point
of
the
side
,
is
the
same
with
the
Point
of
the
Front
as
one
may
see
in
the
first
figure
where
the
Base
A
B
,
hath
as
many
,
and
the
same
divisions
,
as
the
foregoing
.
Let
the
Point
of
sight
be
in
C
,
and
the
point
of
distance
in
D
,
from
which
if
you
draw
the
line
A
D
,
you
shall
have
the
sections
Q
,
which
give
the
abridgement
of
the
squares
in
the
same
Number
with
the
other
.
The
rest
shal
be
known
in
the
Orders
following
.
The
Second
Advice
of
the
Hollowing
or
deepe
sinkings
.
ONe
may
sink
or
hollow
the
Perspectives
,
asmuch
as
one
would
,
by
the
Means
of
the
Base
E
F
,
if
one
draw
lines
to
the
points
of
distances
H
I
;
for
which
they
shall
divide
the
Visuals
E
G
and
F
G
at
the
point
K
,
it
shall
be
the
Abridgement
of
the
first
square
,
as
we
have
already
said
twice
or
thrice
.
Now
if
we
take
his
line
K
K
for
the
base
,
and
from
the
ends
K
K
,
we
draw
lines
to
the
points
of
the
distances
,
where
they
shall
divide
the
same
line
E
G
and
F
G
at
the
point
L
L
,
that
shall
be
the
Abridgment
of
the
second
square
,
which
shall
have
as
many
divisions
and
squares
as
the
former
;
if
we
shall
take
further
this
line
L
L
,
and
shall
make
the
same
Operations
,
we
shall
have
the
Abridgment
of
the
third
square
at
the
point
M.
And
if
we
shall
begin
again
further
by
that
,
we
shall
have
a
fourth
,
and
so
we
shall
go
unto
a
Point
:
the
which
would
be
a
length
which
would
appear
infinite
;
And
by
this
means
it
is
easie
to
sink
and
to
abridge
the
Perspectives
:
for
if
you
would
have
the
double
of
its
bredth
,
do
as
we
tell
you
;
if
you
would
have
but
the
half
,
draw
a
line
where
the
lines
of
the
points
of
the
distances
cross
themselves
,
as
in
N
,
and
you
shall
have
that
which
you
desire
.
Seeing
that
this
is
so
infallible
,
that
as
many
visual
Rayes
as
divide
the
Diagonal
line
drawn
from
the
points
at
the
distances
to
the
base
,
so
many
squares
one
hath
of
sinkings
:
we
may
,
as
I
said
,
give
as
many
hollowings
as
we
would
to
the
Perspective
;
for
if
in
stead
of
taking
from
the
point
of
distance
O
,
at
the
Ray
F
,
you
draw
it
from
the
Ray
Q.
There
will
want
two
squares
,
but
that
you
have
abridged
the
whole
square
R
,
as
we
see
in
S
,
which
is
that
which
you
have
fail'd
to
take
of
the
whole
square
.
And
if
besides
the
square
,
you
would
have
yet
two
little
squares
,
make
a
line
from
the
same
point
O
,
which
divideth
two
Rays
as
V
,
you
shall
have
that
which
you
desire
.
If
you
would
have
four
,
take
X
:
if
six
N.
If
the
square
whole
Z
,
the
which
is
a
great
easiness
,
when
one
understands
it
well
.
The
third
Advice
of
the
Measures
upon
the
Ease
THE
Base
only
may
serve
for
to
give
such
a
sinking
as
one
would
have
and
in
what
place
they
would
,
without
using
any
little
squares
,
this
is
a
means
very
ready
,
but
it
is
somewhat
hard
to
understand
;
Nevertheless
I
will
endeavour
to
make
it
be
understood
,
the
best
that
I
shall
be
able
,
for
we
do
often
use
it
.
For
example
,
let
the
Base
be
B
S
,
the
point
of
sight
A
,
the
points
of
distances
D
E
:
If
you
would
make
the
Plane
of
a
Cube
B
C
,
you
must
draw
to
the
points
of
sight
two
Occult
lines
,
or
pointed
from
the
ends
B
C
,
then
for
to
give
it
its
bredth
take
the
same
measure
B
C
,
which
you
shall
transport
upon
the
Base
C
F
,
equal
to
B
C
,
from
which
point
you
shall
draw
a
line
to
the
point
of
distance
D
,
and
where
this
line
shall
divide
the
first
Ray
C
at
the
point
G
,
this
shall
be
the
Abridgement
of
the
plane
of
the
Cube
B
H
G
C.
If
you
would
have
an
Object
more
forward
towards
the
midst
,
you
must
take
the
bredth
of
it
and
the
distance
above
the
Base
,
as
I
K.
Now
for
to
have
the
sinking
,
set
such
as
you
would
have
upon
the
same
Base
,
as
it
might
be
L
M
,
because
that
it
is
broad
at
that
point
L
,
and
asmuch
for
the
largenes
at
the
point
M.
Then
from
these
Points
L
M
,
draw
an
occult
line
to
the
point
of
distance
D
,
and
where
these
lines
shall
divide
the
Raye
K
,
at
the
points
N
O
,
you
must
draw
Parallels
to
the
Base
and
you
shall
have
the
square
Q
P
O
N.
By
this
manner
,
you
may
transport
on
the
other
side
the
square
,
which
would
be
above
the
Base
,
as
B
H
G
C
,
is
transported
to
V
,
and
the
Points
M
and
T
,
which
are
removed
but
2
feet
from
the
point
S
,
do
give
a
figure
very
narrow
,
because
that
they
are
very
near
,
and
the
same
distance
,
which
they
are
removed
,
as
we
see
X.
The
fourth
Advice
of
the
Base
and
of
one
only
point
of
distance
.
SEeing
that
one
may
have
the
bredths
and
the
depths
,
by
the
means
of
this
Base
,
one
shall
neede
no
more
to
take
the
Paines
to
make
the
little
squares
,
the
which
I
would
make
appear
to
the
sight
in
this
example
.
Let
us
suppose
,
that
you
would
make
a
Ranke
of
Pillars
,
or
Trees
on
each
side
:
You
must
set
upon
the
Base
the
place
and
distance
that
you
would
have
,
with
their
bredth
or
Diameter
,
as
A
B
C
D
E
F
G.
Then
placing
the
Rule
upon
the
point
of
the
distance
O
,
unto
each
of
these
Points
A
B
C
D
E
F
G
,
where
it
shall
marke
the
sections
upon
the
visuall
Raye
A
H
,
it
shall
be
the
Termes
of
the
Objects
which
you
desire
.
For
to
transport
them
on
the
other
side
,
upon
the
Raye
G
H
,
Set
one
leg
of
the
Compass
at
the
Ocular
Point
H
,
and
with
the
other
take
the
same
without
stirring
the
leg
from
the
Point
H
,
make
an
Arch
with
the
other
,
where
it
shall
divide
the
Raye
G
H
,
this
shall
be
the
same
Terme
;
as
M
is
the
same
with
N.
And
so
of
others
,
by
the
which
you
shall
draw
Parallells
,
which
will
give
you
the
bredths
.
And
for
the
length
,
give
it
such
,
as
you
would
have
it
,
and
set
it
from
A
,
as
it
might
be
P
,
then
draw
from
the
point
P
,
to
the
point
H
,
and
where
it
shall
divide
the
other
Parallells
,
it
shall
be
the
Planes
that
you
desire
,
which
you
may
make
rounds
or
squares
.
The
fifth
Advice
,
not
to
deceive
ones
self
in
the
Measures
.
YOU
must
never
set
on
the
side
of
the
point
of
distance
where
one
would
draw
for
to
give
the
sinking
,
the
Objects
which
one
desireth
to
produce
within
the
Plane
.
Example
,
The
visuall
Ray
,
upon
the
which
one
must
mark
,
let
it
be
A
B
:
If
you
would
produce
there
the
point
C
,
and
D
,
it
cannot
be
drawn
from
the
point
of
distance
E
,
but
well
from
that
which
is
opposite
to
it
F.
If
C
and
D
,
were
within
,
as
G
H
,
it
ought
to
be
drawn
from
the
point
E
:
because
that
the
line
of
the
section
meeteth
between
both
,
and
not
from
the
point
E
:
and
so
both
the
one
,
and
the
other
shall
divide
themselves
in
the
same
point
I
K.
1.
A
Fig.
2.
H
Fig.
3.
A
Fig.
The
sixth
Advice
,
of
the
Point
of
distance
only
.
SOmetimes
one
is
at
such
a
streight
for
the
smalness
of
the
place
that
one
hath
,
be
it
against
a
wall
,
or
cloth
,
or
paper
;
that
it
is
impossible
to
make
more
then
one
point
of
distance
,
and
then
those
that
are
always
accustomed
to
have
two
of
them
are
much
troubled
:
We
must
draw
them
,
and
cause
them
to
understand
,
that
one
Point
only
sufficeth
for
this
Practice
.
Let
us
suppose
that
we
would
make
a
Pavement
of
small
squares
,
and
that
we
have
already
drawn
all
the
visual
Rays
ar
the
point
A
,
for
to
have
the
Abridgement
thereof
,
we
ought
to
draw
at
the
points
of
distances
,
and
the
sections
will
give
us
the
points
where
we
ought
to
draw
,
as
we
have
already
said
:
but
if
there
be
but
one
as
B
,
we
must
draw
this
one
draught
Diagonal
C
B
,
which
will
divide
all
the
visual
Rays
.
Now
for
to
mark
the
same
sections
upon
the
Rays
opposite
,
for
to
draw
Parallels
there
:
We
must
,
as
I
said
but
now
;
set
a
leg
of
the
Compass
at
the
point
A
,
and
with
the
other
to
run
through
all
the
sections
,
as
I
P
:
But
this
is
not
good
,
but
only
for
that
which
is
viewed
in
front
:
Whence
there
is
need
of
one
,
which
serveth
likewise
for
that
of
the
side
:
behold
it
here
,
Take
a
Compass
,
and
set
one
leg
upon
the
base
,
with
the
other
;
take
the
most
perpendicularly
that
you
shall
be
able
,
the
section
that
you
desire
to
transport
as
D
,
and
carry
it
upon
this
line
Perpendicular
,
as
E
O
,
and
mark
your
measure
F
,
then
draw
from
D
to
F
,
and
you
shall
have
the
same
as
if
there
were
two
points
of
distances
:
And
so
of
all
other
sections
.
The
seventh
Advice
,
that
we
should
not
use
the
Diagonal
.
WHEN
one
would
use
the
outmost
Ray
for
the
line
or
section
,
as
it
might
be
G
H
;
He
ought
to
set
the
Objects
upon
the
base
,
as
are
K
L
M
N
O
,
and
from
thence
to
draw
them
to
the
point
of
distance
L
,
which
ought
to
be
drawn
back
as
far
as
shall
be
possible
,
to
the
end
that
the
Abridgement
of
the
Perspective
,
may
be
the
more
pleasing
thereby
:
for
if
the
point
were
nearer
to
the
point
of
sight
G
,
the
Objects
would
have
too
much
hollowness
,
(
I
mean
,
for
example
,
that
a
square
would
appear
a
Parallelogram
)
And
from
this
point
I
,
to
run
through
all
the
Objects
K
L
M
N
O
,
and
to
mark
the
section
of
the
Ray
G
H
:
And
from
these
points
to
draw
Parallels
to
the
base
,
or
of
the
Horizon
,
as
is
here
P
Q.
This
Method
is
the
least
in
use
,
although
some
do
take
it
.
The
Eighth
Advice
,
for
to
abridge
in
divers
manners
.
IF
sometimes
one
be
taken
in
a
strait
,
and
that
one
cannot
remove
the
point
of
distance
,
we
must
elevate
from
the
foot
of
the
Ray
S
R
;
a
small
Perpendicular
,
as
T
S
,
which
shall
receive
the
sections
,
and
give
a
lesser
Abridgement
;
and
if
one
would
have
it
yet
more
little
,
he
shall
but
only
bend
a
line
,
as
is
X
,
the
which
by
reason
of
its
inclination
,
causeth
that
the
sections
are
closer
together
.
Then
for
to
draw
the
Parallels
,
he
hath
only
to
transport
this
line
X
or
T
,
upon
the
foot
of
the
other
Ray
as
is
V
,
and
from
all
these
points
to
draw
lines
Parallels
to
the
base
,
and
you
shall
have
that
which
you
desire
.
1
Fig
2
Fig
3.
Fig
THE
ORDERS
OF
THE
ELEVATIONS
.
Some
Necessary
Advice
,
for
the
Orders
following
.
IT
seemeth
to
me
that
I
have
given
sufficiently
to
understand
that
which
belongeth
to
the
Ichnography
,
and
Planigraphy
,
or
description
of
Planes
,
which
is
necessary
for
the
foundation
of
Orthography
and
Scenography
.
The
Orthography
is
the
face
,
or
fore-part
&c.
As
one
may
see
in
the
Definitions
.
Scenography
,
is
the
Elevation
of
all
that
which
any
one
hath
a
designe
to
make
&c.
See
the
Definitions
which
are
at
the
beginning
of
this
Book
.
For
to
make
this
more
clear
to
those
that
are
not
acquainted
with
these
words
;
we
shall
Name
hereafter
(
as
I
said
already
in
the
Definitions
)
the
Ichnography
,
the
Plane
,
and
the
Orthography
,
and
Scenography
,
by
a
Word
common
to
the
one
and
the
other
,
the
Elevation
:
So
that
,
instead
of
saying
the
Orthography
,
we
shall
say
the
Elevation
of
the
fore-part
;
And
for
Scenography
,
the
Elevation
of
the
whole
.
Before
we
pass
any
further
it
must
be
observed
,
that
the
Elevations
do
never
give
to
the
eye
all
the
Angles
of
the
Plane
,
and
the
Quantity
of
faces
depend
on
the
Aspect
,
which
causeth
the
object
to
be
seen
:
for
if
it
be
seen
on
the
front
as
the
figure
A
,
it
will
shew
but
one
face
,
although
that
the
Plane
have
four
;
If
it
be
view'd
from
the
Angle
,
although
on
the
front
it
will
shew
two
,
as
B
,
and
never
more
,
with
what
Aspect
soever
one
look
on
it
.
This
ought
to
be
understood
of
a
square
,
seeing
that
figures
with
divers
Panes
,
may
give
thereof
3
4
5
and
more
.
Now
it
is
,
that
if
the
objects
decline
a
little
from
the
point
of
sight
,
they
are
seen
from
the
Angle
,
whence
they
ought
to
shew
two
faces
;
And
the
further
they
are
removed
from
the
point
of
sight
,
the
more
they
are
discovered
.
As
K
E
are
more
discovered
then
C
L
,
although
their
thickness
be
equal
.
Another
thing
also
that
is
further
to
be
marked
is
,
That
which
is
Parallel
to
the
Horizon
,
when
the
object
is
view'd
in
front
,
although
in
Perspective
,
as
C
D
E
F
from
the
Gate
in
the
first
figure
,
becometh
a
visual
Ray
;
when
the
same
object
is
view'd
being
in
a
Return
,
or
obliquely
.
As
in
the
second
figure
,
that
C
D
E
F
,
which
is
in
the
front
above
,
is
made
a
visual
Ray
to
that
which
is
under
:
And
on
the
contrary
,
that
which
is
a
Ray
to
that
above
,
is
made
a
Parallel
to
the
base
to
that
below
,
as
D
G
F
H
L.
The
Perpendiculars
are
always
Perpendiculars
.
1.
fig.
2.
fig.
Of
the
Line
of
Elevation
for
to
give
the
Heights
to
all
kinde
of
Bodies
and
Figures
,
and
in
such
a
Place
as
one
would
within
a
Plane
.
WE
must
endeavor
to
understand
well
,
and
remember
this
Rule
:
which
is
of
such
importance
,
that
he
that
shall
know
it
perfectly
,
will
not
be
troubled
in
the
Elevations
,
whatsoever
they
be
of
.
As
for
to
make
the
Planes
,
we
have
used
the
base
for
the
Elevations
:
we
ought
also
to
use
a
line
which
shall
direct
us
,
and
shall
bring
the
Measures
of
the
Heights
that
are
needful
to
every
thing
which
one
would
elevate
.
This
line
of
Elevation
must
be
Perpendicular
upon
the
base
A
B
,
which
is
always
the
nearest
to
our
sight
,
and
the
first
of
the
Plane
:
By
consequence
,
capable
of
giving
and
bearing
the
Measures
of
all
that
one
would
make
in
the
Picture
,
and
therefore
the
line
of
Elevation
C
D
is
placed
upon
the
line
A
B
Perpendicularly
,
as
all
those
must
be
upon
the
Plane
which
we
shall
use
henceforward
.
We
must
then
remember
,
that
when
we
shall
speak
of
Perpendicules
,
or
Perpendicks
,
in
the
rest
of
our
Orders
,
we
must
always
understand
of
Plumb-lines
upon
the
Plane
or
base
.
Seeing
that
this
line
of
Elevation
must
receive
and
give
the
Heights
to
all
the
Objects
that
one
would
elevate
from
a
Plane
:
it
must
have
the
same
Horizon
with
the
Plane
.
Therefore
we
must
from
the
foot
of
this
line
,
which
one
may
set
on
the
left
or
right
side
,
draw
within
the
Horizon
,
as
one
would
have
it
,
that
is
to
say
,
that
it
is
no
great
matter
where
the
Point
be
set
within
the
Horizon
:
for
in
what
place
soever
it
be
,
it
will
always
give
the
same
effect
,
as
it
is
from
the
foot
of
the
line
C
to
the
point
E
,
one
may
set
it
at
the
point
of
sight
,
if
one
will
.
I
have
set
this
line
on
the
one
side
and
other
in
the
first
Figure
,
and
their
point
different
within
the
Horizon
,
for
to
give
to
understand
that
it
is
well
throughout
.
If
from
the
point
H
,
which
is
in
the
Plane
of
the
second
Figure
,
you
would
elevate
a
line
of
two
foot
high
;
you
must
set
upon
the
line
of
Elevation
two
equal
Parts
,
which
you
shall
make
to
serve
each
for
a
foot
,
beginning
at
the
point
C
,
as
are
C
F
,
which
is
two
foot
high
,
to
draw
to
the
point
E
,
and
you
shall
have
an
Elevation
of
two
feet
,
between
the
two
lines
C
and
F
,
drawn
to
the
point
E.
For
to
give
the
height
of
two
feet
to
a
line
elevated
from
the
point
H
:
you
must
from
the
point
H.
draw
a
Parallel
occult
to
the
base
,
until
that
it
divide
the
line
below
C
E
,
which
shall
be
the
point
I.
If
from
the
point
I
one
elevate
a
Perpendicule
I
K
,
between
C
F
,
it
shall
be
the
height
that
it
ought
for
the
line
of
the
point
H
,
which
you
must
take
with
a
Compass
and
carry
it
to
the
point
H
,
which
will
give
H
L
of
two
feet
high
.
If
from
the
point
M
,
you
would
have
one
of
the
same
height
of
two
feet
,
you
must
make
the
same
Operation
,
and
you
shall
have
between
C
F
the
Perpendicule
N
O
,
which
shall
be
the
height
that
it
ought
at
the
point
M.
And
making
the
same
Operation
from
the
point
P
,
you
shall
have
the
Perpendicule
Q
R
,
for
the
height
of
the
line
of
the
point
P.
For
to
give
them
the
height
of
3
,
4
,
5
,
10
,
20
and
30
feet
.
It
is
always
the
same
Order
;
there
is
nothing
but
to
set
these
distances
and
heights
abovesaid
upon
the
line
of
the
Elevation
.
And
from
the
point
of
the
height
,
that
you
would
give
to
draw
to
the
point
of
the
line
within
the
Horizon
,
which
is
here
the
point
E
,
and
to
make
all
the
same
Operations
,
which
we
are
about
making
:
and
you
shall
have
that
which
you
desire
.
The
Elevation
of
a
Cube
in
Perspective
.
HAving
made
the
Plane
by
the
Orders
foregoing
,
and
having
set
the
line
of
Elevation
upon
any
side
of
the
Plane
,
as
is
F
L
upon
the
base
;
We
must
set
upon
this
line
F
L
,
the
height
of
a
Cube
,
which
is
a
Figure
square
on
all
the
sides
,
as
a
Dy
,
which
shall
be
F
M
,
from
which
points
F
M
we
must
draw
to
the
point
of
the
line
of
Elevation
E.
Then
from
all
the
Angles
of
the
Plane
A
B
C
D
,
to
bring
Parallels
to
the
base
,
until
that
they
meet
with
the
line
F
E
,
which
is
the
bottom
of
the
line
of
Elevation
,
and
from
their
sections
F
and
H
,
to
raise
the
Perpendiculars
F
M
and
H
K
,
between
the
lines
M
F
,
which
are
drawn
at
the
point
E.
Then
to
take
its
Measures
with
a
Compass
,
and
to
bring
them
Perpendicularly
upon
the
Angles
;
for
example
,
to
take
with
a
Compass
the
height
F
M
,
and
to
bear
it
Perpendicularly
upon
the
lines
elevated
from
the
Angles
A
B
,
which
will
be
A
G
,
B
G.
Then
to
take
also
the
height
H
K
,
and
to
carry
it
upon
the
Angles
of
the
bottom
C
D
,
which
shall
give
C
O
D
O
;
then
to
joyn
the
right
lines
G
O
O
G.
This
shall
be
the
Cube
elevated
.
If
you
would
have
the
Elevation
of
any
Figure
whatsoever
,
draw
always
from
the
Angles
of
its
Plane
,
Parallels
to
the
base
,
unto
the
draught
of
the
foot
of
the
line
of
Elevation
,
and
keep
the
same
Method
that
we
spake
of
for
the
Cube
,
and
you
shall
see
,
that
there
is
not
any
thing
,
how
difficult
and
unequal
soever
it
be
,
but
that
you
may
put
into
Perspective
;
as
we
shall
make
to
be
seen
in
the
Poligones
following
.
The
second
Figure
is
another
Cube
elevated
,
after
a
manner
,
very
little
different
from
the
former
,
which
I
shall
speak
of
in
three
words
:
And
he
that
will
may
use
it
,
not
to
be
rejected
.
Having
made
the
Plane
by
the
ordinary
way
,
we
must
from
all
its
Angles
B
C
D
E
,
elevate
Perpendiculars
;
And
upon
the
first
,
set
the
height
which
one
would
give
to
it
,
as
B
A
C
A.
And
from
the
points
A
A
,
to
draw
to
the
points
of
sight
F
,
or
to
the
points
of
distances
G
H
,
and
where
the
Perpendiculars
of
the
Angles
D
E
shall
be
divided
at
the
point
I
L
,
this
shall
be
the
line
of
sinking
,
and
the
top
of
the
Cube
wholly
elevated
.
This
last
Order
is
not
so
universal
as
the
former
,
which
hath
always
been
in
use
,
and
practised
by
the
Ancient
Authors
:
It
hath
nevertheless
some
benefits
,
which
we
shall
know
in
some
of
the
Orders
following
.
The
Triangle
in
Perspective
.
IN
the
first
Order
I
have
promised
to
make
the
easiness
of
elevating
all
Figures
appear
,
whereof
the
most
difficult
are
the
Poligones
or
Figures
with
many
sides
:
and
to
keep
some
Order
,
we
will
begin
by
the
Triangle
.
Having
framed
a
Plane
by
the
Orders
foregoing
fol.
21
:
where
we
teach
to
make
it
with
a
List
or
Border
:
we
must
,
as
we
were
speaking
,
set
the
line
of
Elevation
on
the
side
of
such
an
height
as
we
would
have
,
as
is
A
B
of
three
feet
:
Then
from
all
the
Angles
of
the
Plane
,
to
draw
Parallels
to
the
base
,
unto
the
bottom
of
the
line
of
Elevation
B
E
;
And
from
their
sections
elevate
Perpendicules
between
the
lines
A
B
,
and
to
bring
all
these
heights
upon
the
Angles
from
whence
the
Parallels
proceed
;
for
example
,
the
height
A
B
must
be
carried
to
the
Angles
C
D
,
which
will
give
C
R
and
D
S.
The
other
height
F
I
,
at
the
Angles
G
O
,
which
will
give
G
T
and
O
V
;
That
of
H
L
to
the
Angle
K
,
which
will
give
K
X
;
and
the
last
height
N
P
to
the
Angle
Q
,
which
will
give
Q
Y.
Then
to
joyn
with
right
lines
all
these
Points
R
S
Y
,
then
T
V
X
,
for
the
thickness
of
the
stone
in
the
first
figure
.
The
Pentagone
,
or
five-Angles
in
Perspective
.
THE
Pentagone
is
a
figure
with
five
faces
or
sides
;
and
with
five
Angles
.
We
have
given
the
Method
of
framing
it
,
and
setting
its
Plane
in
Perspective
in
the
Treatise
of
the
Planes
fol.
22.
It
would
be
loss
of
time
to
give
the
manner
of
elevating
it
,
seeing
that
the
second
figure
causeth
it
to
be
known
,
that
it
is
the
same
Order
,
with
that
of
the
Cube
and
the
Triangle
.
The
Hexagone
or
six-Angles
in
Perspective
.
THE
Hexagone
is
a
figure
with
six
Angles
,
and
six
faces
or
sides
,
as
is
to
be
seen
in
two
Manners
in
the
Treatise
of
Planes
,
fol.
23.
and
27.
where
it
is
abbreviated
.
The
Order
for
to
elevate
them
is
to
be
seen
sufficiently
in
the
third
figure
.
1.
fig
2.
fig
3.
fig
Of
the
Heptagone
,
or
Seven-Angles
,
in
Perspective
.
THE
Heptagone
is
a
figure
with
seven
sides
or
faces
and
seven
Angles
.
Of
the
which
we
have
set
heretefore
,
fol.
24
,
how
it
ought
to
be
made
,
and
to
set
its
Plane
into
Perspective
.
It
s
elevation
is
the
same
Orders
,
with
that
of
the
Triangle
,
as
one
may
see
in
the
first
figure
.
Of
the
Octogone
,
or
Eight-Angles
,
in
Perspective
.
THE
Octogone
is
a
figure
with
eight
angles
,
and
eight
faces
,
as
the
second
figure
sheweth
it
,
in
the
Treaty
of
planes
,
fol.
25.
and
26
:
One
may
see
how
it
ought
to
be
set
in
Perspective
in
two
different
Manners
.
The
elevation
is
as
in
the
fore-going
.
A
double
Cross
in
Perspective
.
I
have
set
this
figure
,
and
that
below
it
,
which
the
Sieur
Marolois
hath
in
his
Works
,
according
to
the
first
Order
that
we
follow
.
The
which
would
be
more
difficult
to
set
into
Perspective
by
another
manner
of
the
diversity
of
the
Angles
.
And
by
this
Method
it
is
very
easy
,
Elevating
it
from
all
the
angles
of
the
Plane
&c.
as
we
have
said
of
the
Polygones
,
and
may
be
seen
cleerly
in
the
first
figure
.
A
Stone-fluted
,
or
straked
like
a
starr
,
in
Perspective
.
HAving
not
set
the
Plane
of
this
figure
with
the
other
figure
;
I
thought
it
fit
to
set
it
under
its
figure
,
for
to
abbreviate
it
in
the
Ordinary
way
,
as
we
have
set
the
others
.
The
Geometrical
Plane
is
easy
to
make
.
This
is
a
Circle
divided
into
six
,
whereof
the
divisions
ought
to
be
joyned
with
right
lines
,
leaving
a
Point
between
two
;
As
for
example
,
from
I
,
to
3.
leaving
2.
Then
to
take
2
and
4
,
leaving
3.
and
so
others
the
rest
is
seen
sufficiently
in
the
second
figure
.
1.
fig
2.
fig.
Of
Pilasters
in
Perspective
.
WHEN
one
would
make
some
Pieces
,
as
Columns
,
Pilasters
or
Walls
,
which
shall
have
the
same
height
.
There
is
no
need
of
the
line
of
Elevation
:
It
sufficeth
to
do
as
in
the
second
Order
,
which
is
,
that
having
elevated
Perpendiculars
from
the
Angles
of
the
Plane
,
as
is
A
B
C
D
,
of
the
first
figure
;
we
must
set
the
height
that
we
would
upon
the
first
or
second
Perpendicule
,
as
is
A
F
,
or
D
E.
Then
to
draw
the
Ray
E
to
the
point
of
sight
F
;
All
the
Perpendicules
that
one
shall
elevate
,
must
be
unto
this
line
E
F
,
and
then
that
the
Pilasters
G
H
,
shall
be
equal
to
the
first
.
If
one
would
not
use
little
squares
in
the
Plane
,
we
must
set
upon
the
base
the
Measures
,
and
draw
the
Rays
to
the
point
of
sight
F
,
and
that
which
ought
to
abbreviate
at
the
point
of
distance
K
;
for
example
,
L
M
is
one
side
of
the
Pilaster
:
We
must
draw
these
two
Points
L
M
,
to
the
points
of
sight
F
for
the
bredth
of
all
the
Pilasters
which
one
shall
set
there
;
for
the
depth
of
each
Pilaster
,
which
we
would
make
square
,
we
must
take
the
distance
L
M
,
and
set
it
before
L
,
as
is
N
;
then
to
draw
the
line
N
K
,
which
is
the
distance
,
and
it
shall
give
the
depth
of
the
Pilaster
at
the
point
O
,
from
which
points
L
M
O
,
we
must
elevate
Perpendicules
,
and
do
the
rest
as
we
have
said
.
If
one
would
have
the
bredth
of
two
Pilasters
,
between
the
one
and
the
other
;
he
must
set
them
upon
the
base
,
and
after
set
the
depth
of
the
second
Pilaster
equal
to
the
first
,
as
is
P
Q
;
and
from
these
two
points
P.
Q.
to
the
distance
K
,
which
shall
give
the
points
R
S
,
upon
the
Ray
L
from
S
;
we
must
draw
a
little
Parallel
,
which
shall
divide
the
Ray
M
F
,
as
is
S
T
;
then
from
these
points
R
S
T
,
to
elevate
Perpendicules
,
and
to
do
as
in
the
first
:
The
third
,
and
more
,
if
one
would
have
them
,
ought
to
do
the
same
,
keeping
always
the
Measures
upon
the
base
,
as
in
the
first
Figure
.
Of
Pilasters
viewed
by
the
Angle
.
WE
have
said
heretofore
,
that
the
Plane
of
squares
is
made
,
hy
drawing
Measures
from
the
base
to
the
Distances
.
As
concerning
the
Elevations
,
it
is
the
same
that
we
are
speaking
of
.
For
having
set
the
height
A
B
,
upon
the
first
Perpendicule
,
we
must
draw
from
the
point
B
to
the
distances
C
D
,
which
shall
divide
and
give
the
heights
to
the
two
other
Perpendicules
elevated
on
the
sides
:
Then
having
given
the
Distances
,
which
one
would
,
between
the
two
Pilasters
,
which
are
here
two
little
squares
,
you
must
elevate
the
second
;
and
by
the
same
Order
the
third
:
Their
height
shall
be
found
drawing
a
visual
Ray
from
the
point
B
to
the
point
of
fight
E
,
at
the
section
,
which
this
Ray
shall
make
of
the
first
Perpendicules
,
at
the
point
F
F
,
and
from
the
points
F
F
,
to
the
distances
,
as
in
the
first
Pilaster
.
Those
which
are
made
without
a
Plane
,
must
take
their
Measures
upon
the
base
;
as
if
one
would
give
them
the
like
bredth
to
those
above
viewed
on
the
front
:
It
must
be
set
as
G
H
,
and
to
draw
the
Ray
G
,
to
the
point
of
sight
E
,
for
to
have
all
the
Middles
or
the
Diameters
:
Then
to
set
also
the
same
bredth
of
G
at
the
point
I
;
and
from
these
three
points
G
H
I
,
to
bring
lines
to
the
distances
C
D
,
for
to
frame
the
first
Plane
:
from
this
Plane
he
must
elevate
Perpendicules
:
And
upon
the
first
to
set
the
height
as
is
G
K
;
and
from
the
point
K
to
draw
to
the
distances
,
for
to
have
the
Abridgement
of
the
Perpendicule
;
of
the
sides
,
for
the
second
Pilaster
.
The
same
shall
be
done
from
the
Points
L.
M
;
And
the
third
,
from
the
points
N
O.
The
rest
is
easy
enough
to
doe
,
viewing
the
second
figure
.
1
fig
2
fig
The
Effects
of
the
diversity
of
Horizons
.
THE
more
that
any
one
is
Elevated
above
any
Object
,
the
more
he
discovereth
that
which
is
above
.
By
consequent
,
if
one
be
lower
,
he
shall
discover
less
;
and
if
one
be
under
it
,
he
can
see
but
that
which
is
under
,
and
nothing
of
that
which
is
above
.
The
first
Proposition
is
verified
by
the
first
Figure
:
The
second
,
by
the
second
:
and
the
third
,
by
the
last
.
The
first
and
second
Cube
,
is
made
as
we
have
taught
;
the
third
is
made
also
by
the
same
Orders
,
although
they
seem
more
hard
,
by
reason
that
we
see
the
Objects
by
the
upper
part
.
But
if
you
turn
up
the
Paper
,
or
the
Picture
,
and
draw
at
the
point
of
sight
,
and
at
the
distances
B
C
,
as
in
other
Orders
you
shall
have
the
same
facility
.
I
set
nothing
of
the
Objects
viewed
on
the
side
:
seeing
that
I
have
said
so
many
times
that
it
is
the
same
with
those
on
the
front
:
And
for
to
give
further
knowledge
how
to
set
them
in
order
;
There
is
one
in
a
single
●●aught
,
and
the
other
shadowed
also
.
Before
we
leave
this
third
Figure
;
we
must
observe
,
that
the
lowness
of
the
Horizon
,
is
the
cause
that
we
see
the
bottom
of
the
Objects
,
which
are
elevated
above
,
as
D
E
F
;
and
of
the
two
others
,
which
are
G
H
,
placed
above
the
Horizon
,
one
cannot
see
neither
above
nor
below
.
Above
,
because
the
Horizon
is
lower
;
nor
below
,
it
being
placed
upon
the
Horizon
.
There
are
many
Painters
,
that
do
fail
in
this
,
making
the
upper
part
of
many
things
appear
,
although
that
the
Horizon
be
much
lower
.
1
fig
2
fig
3
fig
The
Elevation
of
Objects
viewed
by
the
Angle
.
WE
have
snewed
by
the
two
Figures
of
the
19
h.
and
20th
.
fol.
how
the
Planes
are
made
,
drawing
to
the
points
of
distances
,
and
never
to
the
point
of
sight
,
if
it
be
not
for
to
finde
the
Diameter
,
We
must
keep
the
same
rule
for
the
Elevations
,
as
it
is
easie
to
see
by
the
first
Figures
;
which
have
all
their
lines
abutting
at
the
points
of
distances
B
C
,
and
not
one
at
that
of
the
sight
A.
The
first
Figure
D
is
for
to
shew
,
that
whensoever
there
shall
be
an
infiniteness
of
Parts
,
in
one
and
the
same
Object
viewed
by
the
Angle
,
we
must
draw
them
all
to
the
points
of
distances
B
and
C.
If
you
would
make
one
of
the
same
,
see
here
the
Order
:
Having
made
a
Plane
,
and
elevated
occult
Perpendiculars
,
as
we
have
said
,
you
must
set
the
height
that
you
would
give
unto
it
,
at
the
first
Angle
E
F
,
and
draw
from
the
point
F
to
the
points
B
C
,
for
to
have
the
height
of
the
second
and
third
Angle
at
the
point
G
:
Then
from
this
point
G
,
to
draw
again
to
the
points
B
C
,
and
you
shall
have
the
fourth
Angle
of
the
Platform
.
The
other
little
Bodies
are
elevated
in
the
same
manner
,
by
setting
the
height
that
one
would
give
them
,
upon
the
first
Perpendicular
,
as
from
F
to
H
,
and
from
H
drawing
to
the
points
,
as
we
said
but
now
from
the
point
F
,
we
shall
have
the
heights
of
all
the
Angles
;
And
the
points
I
K
shall
give
the
thicknesses
of
all
the
little
Bodies
,
and
the
Platform
of
that
of
the
midst
:
by
drawing
always
to
the
Points
B
and
C
:
The
rest
is
seen
sufficiently
by
the
Figure
,
which
one
may
make
to
serve
for
a
Castle
,
defended
with
four
square
Towers
,
or
for
a
Palace
quartered
with
four
Pavilions
.
The
two
other
Bodies
which
are
on
either
side
of
the
great
one
,
are
seen
from
the
side
,
whereof
the
Order
is
alike
to
that
which
is
seen
from
the
front
:
for
example
,
if
you
elevate
Perpendiculars
from
all
the
Angles
of
the
Plane
L
,
and
that
you
give
your
height
to
the
first
,
as
M
N
,
by
drawing
from
the
point
N
,
to
the
points
of
Distances
B
C
,
they
will
give
the
Angles
2
and
3
at
the
point
O.
Then
from
the
point
O
,
drawing
still
to
the
points
B
C
,
you
shall
have
the
fourth
,
which
is
the
Elevation
of
the
whole
.
This
being
practised
by
the
first
,
and
by
the
second
Order
you
shall
have
the
same
.
The
second
Figure
below
is
of
the
same
Order
.
There
is
no
difference
,
but
of
the
Horizon
,
which
is
lower
.
The
third
sheweth
the
under-part
of
the
Objects
,
but
the
order
is
altogether
the
same
with
that
above
,
drawing
all
to
the
points
of
distances
Q
R
,
which
is
the
Horizontal
line
.
1.
fig
2.
fig
3.
fig.
For
to
raise
Bodies
,
and
remove
them
as
far
of
as
one
would
.
IF
you
would
have
the
first
Body
of
two
feet
high
,
and
one
foot
deep
,
and
one
broad
,
at
two
feet
distance
one
from
another
,
of
two
feet
deep
,
of
one
foot
broad
,
and
three
feet
of
height
,
and
three
feet
distance
.
Another
of
one
foot
broad
,
five
feet
deep
,
and
four
feet
high
.
Thus
you
must
proceed
.
Having
made
a
Plane
of
little
squares
,
which
we
shall
make
to
a
foot
square
(
one
may
make
them
of
what
size
he
will
)
by
the
points
of
sight
A
;
and
distances
B
C.
You
shall
raise
from
the
first
Angle
a
Perpendicular
,
according
to
the
second
Order
,
which
shall
bear
the
Measures
that
you
would
give
to
the
Objects
as
this
D
E
,
upon
the
which
you
shall
transport
four
times
the
Measure
D
F
,
seeing
that
the
highest
ought
to
have
but
four
feet
.
From
all
the
Angles
of
this
first
little
square
F
I
G
D
,
you
must
raise
occult
Perpendiculars
.
And
having
given
the
Measure
to
the
first
distance
D
and
2
,
because
you
would
have
it
two
feet
high
;
you
must
draw
from
the
point
2
to
the
point
of
sight
A
,
and
it
shall
divide
the
Perpendicule
of
the
Angle
G
at
the
point
H
,
you
must
draw
Parallels
to
the
base
,
which
shall
divide
the
Perpendicule
of
the
Angle
I
,
at
the
point
K
,
and
another
Parallel
from
the
point
2
,
which
shall
divide
the
Perpendicular
of
the
Angle
F
,
at
the
point
L
;
And
joyning
these
4
points
H
K
L
2
,
of
right
lines
,
you
shall
have
your
first
Body
.
Then
because
you
would
give
2
feet
of
space
,
between
the
first
and
the
second
Body
,
you
must
leave
two
little
squares
of
the
Pavement
between
the
one
and
the
other
body
,
and
upon
the
first
Angles
of
the
third
to
raise
Perpendicules
,
and
to
do
all
the
same
as
at
the
first
body
,
with
these
differences
;
that
the
height
of
this
second
,
ought
to
be
taken
at
the
third
point
of
the
line
D
E
,
seeing
that
it
must
have
three
feet
of
height
,
and
must
containe
two
little
squares
,
seeing
that
it
must
be
of
two
feet
deep
.
Be●ween
this
second
and
the
third
Body
,
you
must
leave
3
little
squares
,
seeing
that
you
require
it
at
three
feet
distance
the
one
from
the
other
,
and
from
the
first
Angles
of
the
fourth
,
to
raise
Perpendiculars
as
at
the
first
and
the
last
after
5
little
squares
,
which
is
the
depth
of
your
body
,
and
the
Term
of
5
feet
,
which
the
third
Body
ought
to
have
of
depth
.
The
fourth
point
of
the
line
D
E
,
shall
give
to
it
,
its
height
,
which
ought
to
be
of
4
feet
,
by
dividing
the
Perpendiculars
,
as
you
have
done
in
the
first
.
Those
which
are
shadowed
on
the
other
side
,
are
made
by
the
same
Order
,
and
of
the
same
Proportion
;
But
the
Wall
of
the
midst
is
of
Equall
height
four
feet
only
,
an
Opening
of
3
feet
in
the
midst
.
In
the
second
figure
is
a
Wall
of
equall
heights
.
There
being
distances
of
3
foot
,
left
for
doores
or
windows
:
The
first
part
of
the
Wall
is
but
2
foot
deep
.
The
other
two
3
,
foot
in
depth
a
peice
,
on
the
other
side
there
is
a
Continued
Wall
of
14
feet
of
depth
,
and
of
height
like
unto
the
others
.
The
Order
is
the
same
with
that
of
those
above
.
That
which
we
have
called
a
Wall
,
may
also
serve
for
an
Hedge
;
or
Rowes
for
Gardens
.
Of
Walls
viewed
directly
.
BY
that
which
we
have
said
,
one
may
make
all
sorts
of
walls
viewed
obliquely
.
And
although
this
very
Order
may
serve
for
the
same
walls
viewed
directly
,
it
hath
seemed
necessary
to
me
to
set
also
this
figure
,
for
two
Reasons
:
The
first
,
for
that
they
do
not
always
make
Planes
,
and
in
this
case
one
should
be
troubled
for
thicknesses
.
The
second
,
for
to
give
the
thicknesses
to
the
doors
and
windows
which
may
be
to
be
set
in
those
walls
.
For
to
make
walls
Parallel
to
the
base
,
or
to
the
Horizon
upon
the
Plane
,
you
shall
give
them
such
a
length
as
you
shall
please
,
upon
the
Parallels
to
the
Horizon
;
for
the
bredth
,
you
may
take
that
of
one
little
square
,
from
the
Angles
of
which
you
shall
raise
the
Perpendicules
A
B
,
which
you
shall
make
as
high
as
you
shall
please
,
as
C.
Then
from
the
point
C
draw
unto
the
point
of
sight
D
;
this
Ray
C
D
shall
give
the
diminution
and
the
perfection
to
the
wall
.
When
one
hath
not
a
Plane
,
we
must
set
at
the
first
corner
of
the
wall
,
upon
a
Parallel
to
the
base
,
or
to
the
Horizon
,
the
thickness
that
we
would
give
to
the
wall
,
as
E
F.
Then
from
the
point
F
to
draw
to
the
point
of
sight
D
,
and
from
the
point
E
to
the
point
of
distance
G
,
from
the
section
of
these
two
lines
at
the
point
H
,
you
must
raise
a
Perpendicular
;
and
from
the
point
F
,
another
upon
this
last
:
you
must
take
the
height
of
the
Wall
F
I.
Then
from
the
point
I
to
draw
to
the
point
of
sight
D
,
for
to
have
the
diminution
of
the
wall
at
the
section
of
the
Perpendicule
H
;
for
the
length
,
you
shall
give
it
such
as
you
please
,
upon
the
first
Parallel
E
F
;
for
the
doors
and
windows
in
the
same
walls
;
you
must
mark
the
bredth
and
height
,
as
here
K
L
M
N
;
and
to
set
the
thickness
that
you
would
give
them
upon
a
Parallel
,
above
or
below
the
doors
or
windows
,
at
the
nearest
corner
to
the
point
of
distance
,
as
here
N
O
,
or
L
O.
Then
draw
from
the
points
L
and
N
to
the
point
of
sight
D
;
and
from
the
points
O
to
the
point
of
distance
G.
And
from
the
section
of
the
lines
P
,
you
must
draw
the
thicknesses
.
Another
Wall
viewed
from
the
Angle
.
HAving
the
Plane
,
you
are
only
to
raise
Perpendicules
from
the
Angles
,
which
one
hath
resolved
upon
,
and
to
mark
the
height
,
which
one
would
give
them
upon
the
Perpendicule
of
the
Angle
that
is
nearest
to
you
,
as
is
Q
R.
And
from
the
point
R
to
draw
to
the
points
of
distances
S
T.
The
sections
which
these
lines
shall
make
of
the
Perpendicules
,
elevated
from
the
Angles
of
the
Plane
,
shall
give
the
length
and
the
thickness
of
the
wall
:
If
you
have
not
a
Plane
,
you
must
sett
the
Measures
which
one
would
give
,
aswell
to
the
bredth
,
depth
of
the
doors
and
of
the
windows
upon
the
base
,
as
here
V
X
is
the
bredth
,
X
Y
the
depth
,
Z
I
the
bredth
of
one
window
:
Then
to
draw
from
all
these
points
to
the
points
of
distances
S
T
:
First
X
T
,
which
is
the
Radius
of
the
base
:
Then
from
V
T
a
small
line
occult
,
which
shall
divide
the
Ray
X
S
at
the
point
5
,
which
is
the
thickness
of
the
wall
.
For
the
depth
,
the
Ray
Y
S
shall
give
it
at
the
section
that
it
shall
make
of
that
X
T
,
at
the
point
6.
and
Z
I
,
the
bredth
of
the
window
at
the
points
7
,
8.
from
which
points
X
5
,
6
,
7
,
8.
you
must
raise
Perpendicules
,
and
set
above
the
first
X
the
height
2.
And
drawing
from
the
point
2
to
the
points
S
T
,
you
shall
have
the
height
of
all
,
at
the
sections
of
the
Perpendicules
,
from
the
height
of
the
window
marked
by
3
,
4
,
draw
to
T
,
and
where
it
shall
divide
the
Perpendicules
7
,
8
,
you
must
draw
right
lines
:
And
from
the
Corners
9
to
S
,
for
the
depth
10
,
at
the
point
T
,
and
from
the
section
11.
to
draw
a
line
Perpendicular
.
All
this
may
serve
for
a
Pallisadoe
as
for
a
wall
.
For
to
place
a
doer
in
what
place
one
would
of
a
Wall
.
WE
must
raise
a
Wall
,
as
we
have
said
,
of
1
,
or
2
,
or
of
3
,
feet
thickness
,
upon
the
Points
H
I
,
and
to
bring
it
to
the
bottom
of
the
same
height
,
then
if
you
know
near
upon
the
measure
of
the
door
that
you
would
make
;
set
the
breadth
upon
the
base
,
as
here
A
,
and
B
,
of
the
Plane
below
,
which
containeth
3
feet
:
and
upon
the
side
of
A
,
and
B
,
the
breadth
of
a
Band
C
D.
And
draw
these
4
Letters
A
B
C
D
,
to
the
point
of
sight
K
,
and
where
they
shall
divide
this
Parallel
to
the
Horizon
M
N
,
at
the
point
O
,
you
must
raise
Perpendiculars
of
such
height
as
one
would
:
see
here
already
the
breadth
of
the
Door
:
for
the
height
,
you
must
transport
D
F
E
,
of
the
Plane
below
to
the
Corner
of
the
Wall
I
,
and
draw
these
Points
F
E
,
to
the
Point
K
,
and
where
they
shall
divide
the
Perpendicular
M
P
,
at
the
Point
Q
,
draw
Q
R
,
Parallel
to
M
N
,
which
shall
give
the
height
of
the
Door
,
and
the
Band
above
.
It
s
thickness
,
or
depth
shall
be
the
same
,
with
that
of
the
Wall
,
which
is
G
F
,
and
if
you
draw
from
the
point
G
,
to
the
point
of
sight
K
,
it
will
divide
the
Perpendicule
M
P
,
at
the
point
S
,
draw
S
T
,
parallel
to
Q
R
,
you
shall
have
the
bottom
of
the
Door
V
,
which
is
its
thickness
,
and
of
the
whole
circuit
of
the
Door
.
For
to
make
the
Door
to
the
Wall
on
the
side
;
you
must
remember
the
Order
of
fol.
17.
which
is
,
that
one
set
all
the
measures
upon
the
base
,
and
drawing
from
these
measures
to
the
point
of
distance
,
one
hath
all
the
abridgements
that
he
desireth
.
Example
,
you
would
have
a
Door
4
feet
within
the
Chamber
,
you
shall
set
4
equal
distances
I
C.
Then
draw
to
the
point
of
distance
L
,
the
measures
of
the
Door
C
A
,
and
B
D.
And
where
the
Ray
I
M
,
shall
be
divided
by
the
points
elevated
of
the
Perpendiculars
X
Y
,
which
shall
give
the
breadth
of
the
Door
.
For
its
height
,
you
must
draw
to
the
point
of
sight
K
,
the
points
E
F
,
and
the
sections
of
the
Perpendiculars
X
Y
,
shall
give
you
it
!
For
the
thickness
above
and
below
you
must
draw
the
thickness
the
Wall
G
H
,
and
F
I
to
the
point
of
sight
K
;
then
drawing
a
little
parallel
to
the
base
or
to
the
Horizon
,
from
the
corner
of
the
Door
X
,
and
as
much
from
the
corner
above
,
you
shall
have
X
Z
,
the
thickness
above
and
below
,
which
you
must
joyn
with
a
Perpendicular
,
as
you
see
in
the
figure
.
If
you
would
also
have
a
Door
on
the
other
side
,
you
have
only
to
draw
lines
parallels
to
the
base
from
the
point
X
,
to
the
Ray
I
N
,
and
then
to
elevate
them
as
we
have
said
,
the
rest
is
the
same
with
the
side
shadowed
.
The
Door
of
the
bottom
is
not
in
the
midst
,
that
is
to
say
,
a
foot
and
half
;
the
which
I
have
made
on
purpose
for
to
reprove
the
error
of
those
,
who
without
other
measures
,
draw
two
Diagonals
from
their
Picture
,
although
it
be
of
an
enormous
greatness
,
and
would
that
all
the
Objects
should
be
equally
distant
from
the
section
of
these
lines
:
that
is
to
say
,
from
the
midst
of
the
Picture
,
so
that
according
to
their
account
,
it
should
be
alwayes
mounted
for
to
see
their
work
in
its
perfection
,
in
which
they
deceive
themselves
;
for
when
a
Picture
shall
have
fourty
foot
of
height
,
and
that
it
should
be
for
to
be
seen
set
upon
the
Ground
,
we
should
not
set
the
Horizon
higher
then
five
feet
,
and
rather
less
then
more
.
And
according
to
their
Rule
this
Horizon
would
be
twenty
foot
high
.
For
to
frame
Windows
in
Perspective
.
THE
Order
for
to
make
a
window
,
is
altogether
the
same
with
that
of
a
door
,
for
if
you
make
an
Ascent
or
a
Cross-bar
within
a
door
,
it
will
be
a
window
and
no
more
a
door
,
so
that
there
is
no
more
then
to
learn
to
make
a
single
Cross
or
double
,
and
you
shall
know
to
make
windows
.
If
you
would
make
one
in
the
wall
A
B
of
such
largeness
as
you
shall
please
;
you
must
set
its
measure
upon
the
base
,
as
D
E
,
and
draw
from
these
points
D
E
,
to
the
point
of
distance
F
,
and
from
the
section
which
the
points
G
shall
make
at
the
Ray
A
C
,
you
must
raise
the
Perpendicules
G
H
,
which
shall
give
the
bredth
of
the
window
,
which
is
here
but
of
two
little
squares
:
for
the
height
,
they
make
them
ordinarily
the
nearest
that
they
can
to
the
Plancher
above
;
But
,
the
Rest
or
Stay
ought
not
to
be
higher
then
of
three
feet
,
or
three
feet
and
an
half
.
Having
then
taken
this
Measure
,
you
must
set
it
upon
the
Perpendicular
A
B
,
as
A
I
,
and
to
draw
I
K.
And
where
this
line
shall
divide
G
H
,
that
shall
be
the
rest
,
a
stay
:
And
likewise
drawing
L
,
which
is
above
to
the
point
of
sight
K
,
the
section
of
G
H
shall
be
the
upper
part
of
the
window
,
the
which
will
give
us
a
long
square
,
or
Parallelogramma
,
to
the
which
adding
a
Cross
,
it
will
be
a
window
;
for
to
make
this
Cross-bar
,
you
must
divide
the
space
D
E
into
two
equal
parts
.
And
at
this
division
to
give
such
a
bredth
as
you
shall
please
,
ordinarily
it
is
four
inches
,
or
at
the
most
halfe
a
foot
.
And
to
draw
this
bredth
M
,
to
the
point
of
distance
F
,
and
from
the
section
of
the
Ray
A
C
,
to
elevate
the
Perpendicules
N
O
,
which
shall
be
the
ascent
or
Rising
of
the
midst
of
the
window
for
the
Cross-bars
,
you
shall
set
therein
as
many
as
you
please
;
there
is
nothing
but
to
observe
this
,
that
they
ought
to
have
as
much
thickness
as
the
rising
pillar
;
wherefore
having
taken
this
Measure
M
,
you
must
transport
it
upon
the
Perpendicule
A
B
,
as
is
P
,
and
draw
this
Measure
to
the
point
K
,
and
the
section
that
these
Rays
shall
make
of
the
Perpendiculars
G
H
,
G
H
,
shall
be
the
Cross-bars
;
and
by
consequent
the
window
made
,
for
its
thickness
,
it
is
not
here
but
of
the
half
of
the
wall
;
for
to
give
it
to
this
window
,
you
must
draw
lines
occult
from
the
point
Q
to
the
point
K
,
and
drawing
little
Parallels
to
the
base
,
from
the
corners
of
the
window
S
,
they
shall
give
the
thickness
at
the
point
,
that
they
shall
divide
the
line
Q
X
,
as
we
have
said
of
the
door
.
This
window
is
equal
with
the
wall
within
side
which
is
not
ordinary
,
because
there
are
that
make
them
with
Chamfrettings
or
Scunches
,
that
is
to
say
,
that
they
enter
within
the
wall
,
sometimes
a
foot
more
or
less
.
The
Order
thereof
is
altogether
the
same
,
except
that
in
stead
of
taking
the
sections
upon
the
Ray
A
C
K
;
we
must
take
it
at
that
which
entreth
within
the
wall
;
as
far
as
one
would
cause
the
windows
to
enter
,
as
may
be
seen
in
the
figure
under
the
Ray
O
K
,
which
receiveth
the
Measures
which
one
hath
set
upon
the
base
;
and
that
he
must
draw
at
the
point
of
the
distance
F
all
the
rest
,
as
at
those
above
,
taking
the
thicknesses
of
the
window
,
between
the
Perpendicule
O
unto
that
F
,
which
is
the
last
.
Then
when
the
window
shall
be
all
finished
upon
the
Ray
O
K
,
and
of
the
bredth
of
the
wall
O
F
,
we
must
raise
the
Perpendicule
A
,
and
draw
it
to
the
point
K.
Then
from
the
corner
below
the
window
to
the
points
P
,
to
make
a
little
Parallel
,
which
divideth
the
Ray
A
K
at
the
point
Q
,
which
shall
be
the
thickness
of
the
wall
,
which
shall
cover
a
little
of
the
window
,
and
shall
make
the
thickness
R
P
to
be
seen
from
the
point
R
,
you
must
elevate
the
Perpendicule
R
V
,
which
shall
divide
the
Ray
T
K
at
the
point
V
,
which
shall
be
the
thickness
above
the
window
.
Of
the
Measures
of
that
,
one
shall
make
as
much
as
they
will
,
keeping
therein
always
the
same
Order
.
Of
the
Planchers
above
.
THE
Perspectiff
(
or
Practiser
of
this
Art
)
ought
,
as
it
were
,
to
follow
the
same
Order
which
the
Masons
keep
,
which
do
raise
and
cause
to
come
forth
from
the
Earth
,
by
little
and
little
,
very
fair
Houses
.
The
Pavement
or
Plancher
below
,
serve
him
for
a
Foundation
,
upon
the
which
he
raiseth
the
Walls
,
which
he
pierceth
in
so
many
places
as
he
will
(
yet
not
without
reason
)
for
to
have
doors
and
windows
,
as
we
have
said
.
Let
the
walls
raised
be
A
B
,
upon
the
which
we
must
first
set
Beams
or
Girders
,
and
upon
these
Girders
the
Quarters
or
Joysts
.
Having
taken
the
Measure
of
the
Square
of
its
Piece
(
as
it
might
be
here
on
foot
)
it
must
be
carried
to
the
height
of
the
wall
,
as
C
D
,
from
the
which
Points
C
D
,
we
must
draw
occult
lines
to
the
point
of
sight
E
,
which
shall
give
the
Rays
C
G
D
F.
You
must
also
carry
this
Measure
C
D
,
upon
the
Parallel
to
the
Horizon
D
H
,
which
ought
to
bear
the
Measures
and
Quantity
of
Beams
,
which
you
would
set
upon
the
wall
,
as
we
have
set
these
three
I
K
L
,
and
draw
all
those
Measures
to
the
point
of
distance
M
,
and
from
the
sections
of
the
Ray
,
D
F
,
at
the
point
O
,
to
cause
Perpendiculars
to
fall
,
which
shall
divide
the
Rayes
C
G
,
at
the
points
P.
Then
drawing
Parallels
to
the
Horizon
from
the
Points
O
and
P
,
unto
the
other
side
,
you
shall
have
the
Beams
laid
,
as
you
see
in
the
first
figure
.
Let
us
set
now
Joysts
upon
the
Beams
,
or
to
do
more
properly
,
let
us
mortaise
them
there
:
The
line
Q
R
shall
serve
for
the
base
,
upon
which
you
shall
set
your
Joysts
,
in
such
number
,
and
so
near
and
far
from
each
other
as
you
shall
please
:
these
are
distant
from
each
other
twice
their
thickness
.
Then
when
as
we
would
embox
them
,
we
must
take
their
thickness
within
●hat
of
the
Beam
Q
S
,
as
is
Q
T
,
and
draw
an
occult
line
T
V
;
then
between
Q
R
and
T
Y
,
to
set
your
Joysts
X
,
and
from
all
their
Angles
which
may
be
seen
,
to
draw
to
the
point
of
fight
Y
;
and
that
you
may
not
pass
the
half
of
the
other
beams
,
you
must
draw
from
the
midst
of
the
first
,
which
is
the
point
T
,
an
occult
Ray
to
the
point
of
sight
Y
,
which
shall
divide
all
the
other
beams
by
the
midst
at
the
point
Z.
Then
from
the
po●nt
Z
to
draw
Parallels
to
the
Horizon
,
that
one
may
not
pass
them
by
drawing
Joysts
to
the
point
Y.
If
you
would
not
take
so
much
pains
,
set
your
Joysts
Z
,
upon
the
line
Q
R
,
as
they
are
under
:
Then
draw
boldly
from
one
beam
to
another
,
from
all
the
Angles
X
to
the
point
Y
,
and
you
shall
have
that
you
demand
THIS
Figure
is
set
here
only
to
cause
one
to
see
the
effect
of
the
Order
that
we
are
about
to
teach
,
where
we
shall
observe
,
that
the
Quantity
of
stories
,
the
one
above
the
other
,
do
not
make
the
Order
more
difficult
.
The
Joysts
are
not
Tenanted
within
the
Beams
in
the
upper
story
,
as
in
the
under
story
.
Another
Ordering
of
Planchers
in
Perspective
.
THIS
fashion
ought
to
be
ordered
in
the
same
manner
with
that
which
we
are
now
leaving
:
We
ought
only
to
change
the
setting
of
the
Pieces
;
that
is
to
say
,
that
we
must
set
the
beams
at
length
,
for
to
draw
them
to
the
point
of
sight
.
and
the
Joyst
a
cross
,
which
is
contrary
to
the
other
.
The
Walls
shall
be
A
B
,
upon
the
which
,
or
upon
the
Cattozes
that
come
from
them
,
you
shall
place
the
thickness
of
the
beam
C
D
,
from
the
which
points
C
D
,
you
must
draw
Parallels
to
the
Horizon
C
E
D
F
,
between
the
which
one
shall
set
such
a
number
of
beams
as
he
will
,
as
here
three
G
H
I
,
which
he
ought
to
draw
to
the
point
of
sight
K
,
and
to
take
heed
where
the
Ray
D
P
shall
divide
the
Perpendicular
L
P
;
Then
from
the
point
P
,
to
draw
a
little
Parallel
to
the
Horizon
P
M
,
which
shall
be
the
term
of
bound
of
the
other
Rays
,
as
P
N.
And
from
the
point
N
to
raise
a
Perpendicule
N
O
,
and
so
to
all
the
Pieces
.
Here
is
that
which
is
for
the
beams
,
for
to
set
the
Joysts
across
upon
these
beams
,
you
must
set
their
thickness
upon
the
line
Q
R
,
and
draw
these
Measures
V
,
to
the
point
of
distance
S
,
and
from
the
section
which
the
Angles
V
,
shall
make
at
the
Ray
Q
T
;
you
must
draw
Parallels
to
the
Horizon
,
unto
above
the
beam
of
the
other
side
.
If
you
would
mortaise
them
within
the
beams
;
you
must
take
the
thickness
of
the
Rafters
within
the
beam
,
as
is
Q
X.
And
from
X
to
draw
a
Parallel
to
the
base
,
unto
the
other
side
X
X.
And
between
these
two
lines
Q
R
and
X
X
,
to
set
the
divisions
V
,
which
shall
be
Y.
And
from
all
the
points
,
to
draw
to
the
distance
S
,
for
to
have
the
thicknesses
of
the
side
,
and
of
below
,
which
shall
be
taken
in
the
section
of
the
Ray
X
T
,
at
the
point
Z
,
from
which
drawing
Parallels
to
the
Horizon
,
you
shall
make
the
Plancher
,
as
is
seen
in
the
second
figure
.
You
see
how
you
must
set
into
Perspective
single
Planchers
of
Carpenters
work
;
If
yet
after
,
or
in
the
stead
of
those
you
would
have
some
fair
Plat-found
of
Pictures
,
or
some
other
Compartment
;
follow
that
which
we
have
said
in
the
35
fol.
speaking
of
the
Compartments
of
the
Gardens
,
and
you
shall
use
the
line
Q
R
for
the
base
.
You
may
make
there
whatsoever
it
shall
please
you
.
For
the
Planchers
below
,
there
are
of
some
fashions
in
the
folio's
30
31
32
33
and
34
of
the
Planes
,
for
to
give
an
open
way
to
him
that
useth
this
Art
to
Invent
others
by
.
You
may
see
hitherto
,
how
to
make
any
Halls
or
Chambers
perfectly
.
We
will
teach
the
moveables
at
the
end
of
this
first
part
.
THIS
Figure
sheweth
clearly
the
Plancher
which
we
are
about
to
express
,
and
where
the
lines
do
make
the
Figure
a
little
confused
.
WE
will
teach
in
another
place
to
make
this
Gate
with
Panes
.
A
single
Draught
of
Doors
and
round
Arches
view'd
directly
.
HAving
spoken
that
which
is
necessary
for
Halls
,
Chambers
,
Windows
and
square
Gates
;
We
must
now
know
how
the
round
ones
are
made
;
for
to
set
such
where
one
would
have
them
.
Supposing
that
A
B
C
D
E
F
were
Pilasters
,
or
small
Pillars
elevated
upon
some
Plane
;
for
to
place
there
Arches
,
you
must
divide
the
bredth
above
G
H
,
into
two
equal
Parts
,
at
the
point
I
,
upon
the
which
having
set
one
leg
of
the
Compass
,
you
shall
make
with
the
other
a
demi-round
G
H
,
which
shall
give
the
first
Arch.
For
to
make
all
the
others
of
the
same
height
and
bredth
,
you
must
draw
lines
from
the
points
H
G
,
to
the
point
of
sight
K
,
and
these
two
Rays
shall
divide
the
Perpendicules
C
D
E
F
,
at
the
points
L
,
from
the
which
points
L
,
you
must
draw
Parallels
to
G
H
,
the
which
Parallels
L
L
,
you
must
divide
into
two
,
for
to
make
there
demi-rounds
,
as
in
the
first
.
For
to
finde
the
Center
of
these
Parallels
L
,
there
is
but
only
to
set
the
Rule
to
the
first
Center
I
,
and
to
draw
it
to
the
point
K
,
it
will
divide
them
all
just
at
the
midst
M
M
,
at
the
which
points
you
shall
set
one
leg
of
the
Compass
,
and
shall
make
the
half-Circle
as
in
the
first
.
Those
which
are
view'd
in
front
,
and
those
which
are
view'd
on
the
side
,
are
ordered
in
the
same
manner
,
as
may
be
seen
in
the
first
Figure
.
When
one
would
make
a
thickness
or
a
band
equal
throughout
all
,
there
is
need
but
of
one
Center
,
as
O
,
of
which
they
have
framed
the
thicknesses
N
P
,
of
the
figures
below
:
All
the
rest
is
made
,
as
we
have
said
,
drawing
to
the
point
of
sight
K
:
These
two
last
figures
shew
how
all
kind
of
single
Vaults
,
or
bending
Roofs
should
be
made
,
which
have
but
an
half-round
;
One
may
enrich
them
,
as
we
shall
shew
hereafter
.
1.
fig
2.
fig
Round
Arches
above
the
Pilasters
view'd
directly
.
THE
single
draught
that
we
are
about
to
pass
from
,
giveth
the
means
to
make
this
,
being
the
same
Order
,
there
are
a
few
more
draughts
,
and
not
more
difficulties
,
for
having
drawn
from
above
the
Pilasters
A
B
C
D
,
Parallels
to
the
base
.
We
must
divide
the
first
into
two
,
and
from
the
center
I
,
to
make
with
a
Compass
the
first
half-Round
A
B
,
and
without
stirring
it
from
the
same
center
,
to
make
the
band
A
G
F
C
:
Then
drawing
from
this
center
E
,
to
the
point
of
sight
H
,
the
Ray
E
H
,
will
give
all
the
Middles
of
the
Parallels
for
to
make
half-Rounds
above
all
,
beginning
at
B
D
until
the
last
I.
This
is
the
same
order
for
that
on
the
side
.
Of
the
third
Point
in
the
Arch.
THE
draught
is
as
easie
as
of
the
Round
:
When
one
hath
given
the
bredth
,
as
K
L
,
set
a
leg
of
the
Compass
in
K
,
and
turn
the
other
towards
O
,
which
will
frame
the
Arch
L
O
,
set
again
the
compass
in
L
,
and
make
the
Arch
K
O
,
you
shall
have
one
Arch
in
the
third
point
K
O
L
,
do
as
much
with
M
N
,
you
shall
have
the
second
Arch
of
the
bottom
M
P
N
:
The
second
figure
of
the
third
Point
is
with
a
Band
or
Border
about
it
,
which
is
made
from
the
same
Center
;
for
example
,
from
the
Center
R
,
they
make
the
Arch
S
X
and
T
V
:
And
from
the
point
S
,
the
Arch
Q
V
,
and
R
X.
All
the
rest
draweth
to
the
point
,
of
sight
Y.
The
true
third
Point
is
the
Figure
✚
,
they
divide
the
Diameter
a
b
into
three
equal
Parts
,
then
they
set
one
leg
of
the
Compass
in
one
division
as
c
,
and
with
the
other
leg
they
take
the
opening
c
b
,
for
to
make
the
Arch
b
e
:
then
setting
again
the
compass
in
d
,
they
make
the
Arch
d
a
e
,
which
is
an
Arch
in
the
third
point
as
well
as
the
other
,
you
may
use
which
you
will
.
The
Ancient
Churches
come
nearer
to
the
first
then
the
second
:
there
are
also
some
which
are
more
close
.
A
further
Pursuit
of
this
Figure
.
I
Have
set
an
Arbour
of
a
Garden
,
which
is
made
,
as
we
have
spoken
of
,
with
Arches
,
view'd
directly
.
For
to
frame
and
set
into
Perspective
Doors
and
round
Arches
.
THE
Round
being
hard
to
set
into
Perspective
,
hath
need
of
lines
and
of
points
which
go
before
it
,
ere
it
can
be
framed
:
And
for
to
finde
these
points
the
more
easily
,
we
must
understand
the
first
figure
,
by
the
which
we
see
,
that
he
which
would
have
a
demi-round
upon
the
Diameter
A
B
,
hath
only
to
set
a
leg
of
the
Compass
at
the
midst
of
A
B
,
at
the
point
C
,
and
with
the
other
leg
of
the
Compass
to
draw
a
crooked
line
from
A
to
B
,
and
so
to
carry
his
demi-round
upon
the
Elevation
D
E
,
for
to
have
a
Door
or
round
Arch
,
as
in
the
second
Figure
,
so
as
we
have
said
.
But
for
to
set
into
Perspective
,
we
are
to
divide
it
into
as
many
Parts
as
we
will
:
the
more
that
one
can
make
is
always
the
best
,
as
we
have
said
and
shewed
at
the
28th
.
fol.
and
as
we
shall
shew
,
speaking
of
cross
vaulted
Roofs
.
We
will
divide
this
into
eight
Parts
only
,
four
for
the
half
:
Having
made
the
half
Circle
,
as
we
have
said
,
we
must
upon
the
demi-round
draw
a
Parallel
to
A
B
,
which
toucheth
it
at
the
point
F
,
and
this
point
F
shall
be
the
midst
above
the
Circle
:
Then
to
elevate
from
A
B
two
Perpendiculars
,
which
divide
this
Parallel
F
,
at
the
points
G
H.
And
from
the
Corners
A
B
G
H
,
to
draw
two
Diagonals
A
H
G
B
,
which
shall
divide
themselves
in
I
,
and
from
this
point
I
,
to
elevate
a
Perpendicule
C
I
F
,
which
shall
divide
the
Circle
into
two
,
and
the
Diagonals
shall
divide
it
into
two
other
Parts
at
the
points
K
,
by
the
which
we
must
draw
a
Parallel
to
the
base
K
L.
Let
us
transport
all
these
divisions
and
measures
upon
the
third
Figure
,
for
to
set
them
into
Perspective
.
First
,
draw
the
Corner
E
to
&
point
of
sight
M
:
Then
from
the
point
N
equal
to
D
E
at
the
point
of
distance
P
,
which
shall
divide
the
Ray
E
M
,
at
the
point
Q.
Whereby
E
Q
will
be
the
bredth
of
the
first
Arch
D
E
,
in
Perspective
.
Draw
also
O
to
the
point
P
,
it
will
divide
the
second
Arch
at
the
Ray
E
M
,
or
point
R
,
not
having
more
space
upon
the
base
for
to
take
the
third
Arch
,
you
must
draw
from
the
point
N
to
the
point
of
sight
M
;
and
from
the
point
R
a
Parallel
to
the
base
R
S.
Seeing
that
R
S
is
under
the
same
Angle
with
E
N
,
it
is
then
of
the
same
bredth
as
we
have
proved
from
the
beginning
:
Drawing
then
from
S
to
P
,
it
will
divide
the
Ray
E
M
,
at
the
point
T
,
which
shall
be
the
third
Arch.
We
must
then
elevate
the
Perpendiculars
V
,
from
these
three
Points
Q
R
T
,
the
which
shall
be
divided
by
the
Ray
H
M
,
which
shall
be
the
highest
of
the
Arches
.
Then
from
the
Ray
B
M
,
which
shall
give
the
lower
part
of
the
demi-round
,
draw
Diagonals
from
the-points
B
V
H
X
,
which
crossing
themselves
,
shall
give
the
place
of
the
Perpendicular
Y
F
,
which
divideth
the
Arch
into
two
:
And
drawing
the
Ray
L
M
,
it
shall
divide
the
Diagonals
into
two
,
and
the
Arch
into
four
.
If
you
joyn
these
points
B
Z
F
Z
K
,
with
,
crooked
lines
,
you
shall
have
the
first
Arch
,
and
the
means
to
make
an
infinite
Company
of
the
same
fashion
.
This
Order
serveth
for
Vaults
,
Arches
,
Doors
,
B●idges
,
and
every
other
thing
that
requireth
the
demi-round
.
And
therefore
I
let
alone
making
the
two
others
,
speaking
no
more
.
This
Order
may
also
serve
for
the
Windows
of
a
Church
;
There
is
nothing
else
to
do
,
but
to
make
one
or
two
Ascents
,
to
fasten
the
Glass
.
1.
fig.
2.
fig.
3.
fig.
For
to
frame
and
put
into
Perspective
Doors
,
and
Arches
round
,
double
,
shewing
their
thicknesses
.
THAT
which
we
are
about
to
say
,
is
only
for
the
single
draught
,
the
which
being
doubled
,
giveth
the
bredths
and
thicknesses
of
the
Arches
,
and
of
that
which
beareth
them
,
joyning
thereto
right
lines
at
all
the
sections
of
the
one
to
the
other
;
as
for
example
.
Having
made
the
first
draught
D
E
,
as
we
newly
spoke
of
,
and
drawn
D
E
to
the
point
of
sight
A
,
we
must
set
the
thickness
upon
the
base
E
C
,
by
drawing
C
to
the
point
of
distance
B
,
it
will
divide
the
Ray
C
A
at
the
point
F
,
and
from
this
point
F
,
to
draw
the
Parallel
to
the
base
G
F
,
which
shall
divide
the
Ray
D
A
at
the
point
G.
And
from
F
and
G
which
shall
be
the
thicknesses
,
to
elevate
the
Perpendicules
I
F
G
:
If
from
the
point
H
,
you
shall
draw
to
the
point
A
,
this
Ray
shall
give
the
height
of
the
Perpendicular
H
I
,
upon
the
which
you
must
take
the
line
of
the
Center
of
the
demi-round
K
,
by
drawing
K
to
the
point
A
,
which
shall
give
the
point
L
,
from
which
draw
the
Parallel
L
M
,
and
this
Parallel
shall
be
the
line
which
must
bear
the
center
of
the
demi-round
behinde
:
As
N
,
is
the
line
of
the
center
of
the
demi-circle
before
:
you
must
divide
this
line
M
L
,
into
two
equal
parts
,
by
drawing
from
the
point
N
,
to
the
point
A
,
by
the
point
O
,
and
upon
this
point
O
you
must
set
a
leg
of
the
Compass
,
and
make
the
half-Circle
M
L
,
the
which
shall
be
divided
as
the
first
,
as
we
have
said
in
the
figure
foregoing
;
then
to
draw
right
lines
from
the
divisions
of
the
one
to
the
other
;
that
is
to
say
,
from
the
demi-round
before
to
that
behind
,
for
of
the
two
to
make
but
one
,
as
the
figure
sheweth
it
,
joyning
M
to
P
Q
to
R
S
F
to
T
V
,
to
X
L
,
to
K.
or
to
make
the
Arches
or
round
doors
seen
on
the
front
,
as
D
E
F
G
,
there
is
no
need
to
make
all
these
divisions
,
seeing
that
it
is
sufficient
to
have
found
the
line
M
L
,
for
to
make
the
demi-round
,
which
is
carried
again
to
the
first
N
P
K.
But
I
have
made
them
there
on
purpose
,
for
fear
of
confounding
the
letters
with
the
lines
in
this
Figure
below
,
where
the
Arches
are
view'd
obliquely
,
or
at
return
,
by
drawing
to
the
point
of
the
sight
Y
,
these
Arches
shall
give
their
thickness
,
by
doubling
the
order
,
which
we
have
spoken
of
in
the
figure
preceding
,
and
joyning
the
division
from
the
one
to
the
other
,
as
we
spake
but
now
,
and
the
which
is
seen
in
this
second
figure
:
to
the
which
having
given
the
thickness
E
Z
,
I
have
framed
the
draught
E
of
points
,
and
Z
of
full
lines
,
thereby
to
avoid
confusion
:
and
to
make
to
understand
,
that
all
that
which
is
made
of
Points
ought
not
to
be
seen
,
the
Picture
being
finished
.
Of
Figures
in
Arches
of
another
fashion
.
THE
Arches
view'd
in
front
,
that
we
have
set
heretofore
,
are
made
exactly
:
but
they
are
somewhat
long
in
the
Practice
.
Behold
another
fashion
as
right
,
and
more
short
then
the
other
.
Having
made
from
the
Center
A
the
demi-round
,
or
the
whole
Circle
B
H
I.
You
must
from
the
Center
A
,
and
from
the
end
of
the
Diameter
B
,
draw
Rays
to
the
point
of
sight
C
,
then
set
upon
B
I
the
bredth
or
thickness
that
you
would
give
,
as
is
D
A.
And
from
this
point
D
to
draw
to
the
distance
E
,
and
at
the
section
of
this
line
D
E
,
upon
the
Ray
A
C
to
the
point
F
,
you
must
draw
a
Parallel
to
the
base
,
until
that
it
divide
the
Ray
B
C
,
at
the
point
G
,
then
to
set
one
leg
of
the
Compass
at
the
point
F
,
and
with
the
other
leg
to
take
the
distance
G
,
for
to
make
the
demi-round
or
the
whole
round
,
which
shall
be
the
thickness
of
the
Arch
,
or
of
the
Round
,
as
may
be
seen
in
the
Figures
.
All
the
lines
K
,
ought
to
be
drawn
at
the
Center
A
,
and
the
other
L
,
at
the
point
of
sight
C.
This
may
serve
for
round
windows
made
of
stone
;
and
these
lines
shall
make
the
points
,
as
also
for
great
Vessels
,
Pipes
,
bathing
Tubs
,
&c.
Arches
view'd
obliquely
in
Perspective
.
THis
Order
may
serve
when
one
shall
be
in
haste
,
and
that
one
would
not
be
so
exact
,
and
also
to
avoid
a
multitude
of
lines
,
which
the
other
Order
doth
oblige
to
make
.
I
say
then
,
that
having
framed
the
first
Arch
N
O
,
as
we
have
said
heretofore
,
we
must
make
upon
the
first
draught
little
Parallels
to
the
base
,
in
such
number
as
you
shall
please
,
as
are
these
Q
;
then
to
take
with
a
Compass
the
bredth
,
where
the
Arch
beginneth
,
as
is
P
O
,
and
to
bring
it
upon
all
these
little
Parallels
Q
,
which
shall
give
the
points
R
,
by
the
which
we
shall
bring
a
crooked
line
,
which
shall
frame
the
thickness
of
the
Arch.
It
is
certain
,
that
according
to
Perspective
,
the
Objects
are
enlarged
,
when
they
come
near
to
us
,
and
that
the
line
O
P
ought
to
be
smaller
:
but
in
this
,
the
difference
of
these
bredths
is
so
small
,
that
it
signifies
nothing
.
And
yet
I
give
not
this
for
a
Rule
,
but
for
an
ease
to
those
that
are
in
haste
.
Of
Arches
flat
,
or
in
manner
of
an
Handle
of
a
Basket
,
or
demi-circles
.
THE
Order
to
set
them
into
Perspective
,
is
the
same
with
the
demi-Round
,
and
of
the
third
points
,
as
we
see
in
the
Figure
A
B.
All
the
difficulty
is
to
finde
the
draught
which
is
made
in
two
Manners
.
The
first
,
by
two
centers
,
and
a
line
or
thread
,
as
we
have
said
in
the
Orders
before
speaking
of
the
Oval
,
by
reason
that
the
Handle
of
a
basket
is
properly
an
half-oval
.
The
second
is
practised
thus
:
If
one
give
you
the
line
C
D
,
for
to
make
there
a
low
Arch
,
which
may
have
the
height
E
F
:
you
must
from
the
center
F
,
make
the
demi-round
C
G
D
,
and
to
divide
it
into
as
many
equal
Parts
as
one
would
,
as
this
here
into
twelve
;
and
from
all
those
divisions
to
draw
to
the
Center
F
:
then
again
from
all
these
divisions
to
draw
Perpendiculars
upon
the
line
,
or
Diameter
C
D
,
as
are
the
lines
L.
After
these
works
,
we
must
of
the
height
,
which
one
would
have
the
Arch
of
,
make
also
a
circle
,
as
from
E
F
,
the
demi-round
H
E
K
;
and
from
the
sections
which
this
little
circle
shall
make
upon
the
divisions
of
the
great
,
we
must
draw
little
Parallels
,
until
that
they
touch
the
Plumb
lines
,
or
Perpendiculars
,
which
fall
from
the
same
divisions
:
as
for
example
L
O
,
and
from
all
these
points
O
,
frame
the
Arch
,
as
we
see
it
here
made
of
Points
.
The
other
Figure
maketh
yet
the
Arch
lower
,
and
one
might
make
it
yet
more
couching
,
keeping
the
same
Rules
and
Orders
.
The
Figure
below
maketh
one
of
these
Arches
to
be
in
Perspective
,
view'd
in
front
,
as
it
ought
to
appear
,
being
finished
.
I
will
set
nothing
of
the
Practice
,
having
already
said
,
that
it
is
the
same
with
that
of
the
demi-Rounds
.
ONE
may
see
in
this
Figure
the
good
effect
of
the
Arches
,
when
one
giveth
them
well
the
Center
,
or
the
draught
of
the
Roundness
that
they
ought
to
have
,
For
the
Degrees
and
the
Figures
we
shall
have
here
after
the
manner
of
giving
them
their
just
Measures
.
For
to
set
Arches
or
half-Circles
upon
Pilasters
or
Columns
.
ONE
might
say
that
in
the
Figure
,
which
we
are
about
to
behold
,
there
are
Pilasters
,
which
are
not
in
the
draught
which
goeth
before
,
the
which
hath
made
me
resolve
to
set
this
here
,
which
shall
serve
to
make
it
known
that
it
is
the
same
Order
,
and
that
we
have
only
to
leave
the
place
and
bredth
of
the
Pilaster
,
which
we
would
give
them
between
two
Arches
,
the
which
is
done
by
the
means
of
the
Plane
or
of
the
Base
,
even
as
we
have
seen
the
demi-rounds
,
which
are
between
each
Pilaster
,
the
which
are
made
as
we
have
said
in
the
last
Order
.
Arches
in
the
third
Point
.
THE
Arches
,
and
the
Vaults
or
bending
Roofs
in
the
third
point
,
are
ordered
in
the
same
manner
with
the
demi-round
;
wherefore
,
having
made
one
of
them
,
we
may
very
well
make
the
other
:
it
sufficeth
only
to
know
the
draught
,
seeing
that
the
Figure
sheweth
sufficiently
the
rest
;
for
the
draught
,
we
have
already
said
that
there
is
nothing
so
easie
.
The
bredth
A
B
being
given
for
to
make
there
an
Arch
in
the
third
point
;
we
must
open
the
Compass
for
all
this
bredth
;
and
holding
firm
one
leg
at
the
point
A
,
with
the
other
to
make
the
Arch
B
C
,
then
to
bring
back
the
leg
to
B
,
and
with
the
other
to
make
the
Arch
A
C
,
where
they
shall
divide
themselves
,
it
shall
be
the
point
of
the
Arch
C
:
The
other
sort
of
the
third
point
is
the
true
,
which
we
have
set
heretofore
marked
✚
Seeing
that
all
the
rest
is
ordered
,
as
in
the
demi-round
,
we
will
not
make
any
repetitions
thereof
:
there
are
only
here
Pilasters
between
two
,
which
are
not
in
the
others
,
that
we
may
cause
the
better
to
understand
that
which
I
have
said
here
above
,
that
we
have
only
to
draw
these
Measures
from
the
base
to
the
point
of
distance
O
,
which
shall
divide
the
Ray
D
E
at
the
point
F
,
for
to
elevate
the
Perpendicules
before
:
then
having
set
the
thickness
G
,
to
draw
the
Ray
G
E
,
for
the
bredth
of
the
Pilasters
H
,
from
this
point
H
they
elevate
Perpendicules
,
which
bear
the
same
divisions
with
those
on
the
fore-part
,
the
which
are
joyn'd
,
with
right
lines
,
and
as
in
the
demi-tound
.
For
to
set
into
Perspective
Vaults
or
Cross
Arches
.
WE
must
remember
,
or
see
it
anew
,
that
which
we
have
said
at
the
28.
fol.
speaking
of
setting
the
great
Round
into
Perspective
,
by
reason
that
we
have
divided
the
Circle
into
many
Parts
,
for
to
make
it
the
most
exactly
that
may
be
,
and
by
consequence
the
Vaults
or
Arches
more
round
and
more
just
.
But
as
there
are
a
great
Company
of
lines
in
this
division
of
16
parts
;
I
thought
that
it
would
be
better
to
begin
by
a
division
of
8
,
although
it
be
not
so
exact
,
so
will
it
also
be
less
confused
.
We
will
take
again
the
other
in
the
following
leaf
.
Having
then
made
the
Plane
of
a
Round
divided
into
eight
parts
,
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8.
We
must
draw
from
all
its
divisions
,
Parallels
to
the
base
,
unto
the
Ray
B
A
,
which
shall
give
the
points
C
,
upon
the
which
we
must
elevate
the
Perpendiculars
C
D
;
We
must
transport
upon
the
first
Perpendicular
B
and
D
,
which
is
the
line
of
elevation
,
the
Measures
of
the
half-Circle
B
E
F
,
which
shall
give
the
points
D
H
G
;
from
the
which
we
must
draw
Rays
to
the
point
A
,
and
at
the
sections
of
the
Perpendiculars
C
D
,
we
shall
have
the
same
divisions
as
in
the
Plane
,
1
,
2
,
3
,
4
,
5.
for
an
half-Circle
we
must
draw
crooked
lines
,
as
may
be
seen
in
the
Arch
of
the
first
side
,
the
measures
of
which
we
must
transport
to
the
other
for
to
have
the
two
Arches
collateral
,
from
the
risings
of
which
we
shall
make
two
Circles
with
the
Compass
,
the
one
before
G
K
from
the
Center
M
;
the
other
at
the
bottom
5
L
,
from
the
Center
N
,
and
so
we
shall
have
the
four
Arches
,
which
do
meet
ordinarily
in
the
cross
Vaults
,
at
the
outmost
Mouldings
,
Ogees
or
Circlets
;
There
remaineth
nothing
but
to
make
the
Cross
,
or
the
crooked
Diagonals
,
which
ought
to
rest
and
bear
upon
the
corners
G
,
5
K
L
,
passing
by
the
knot
or
fcutcheon
O.
Seeing
that
the
Circle
is
divided
into
eight
Parts
,
the
Arches
which
are
but
the
half
of
the
Circle
,
ought
to
have
but
four
,
as
have
those
of
the
sides
:
whence
we
ought
also
to
divide
into
four
the
half-Circle
before
G
K
,
at
the
points
G
P
Q
R
K
,
the
which
ought
to
be
drawn
to
the
point
of
sight
A
,
unto
the
Circle
of
the
bottom
5
,
L
;
Now
that
which
followeth
,
is
the
secret
of
the
Cross
;
it
is
that
we
must
draw
Parallels
to
the
Horizon
,
or
to
the
base
,
from
all
the
sections
of
the
Circle
on
the
side
1
,
2
,
3
,
4
;
5.
at
the
divisions
of
the
Circle
before
,
in
such
manner
as
G
,
which
is
the
first
division
of
the
Circle
,
touch
in
a
point
the
first
section
1.
from
2
to
draw
a
Parallel
to
the
second
division
P
,
and
to
make
a
point
S
,
from
3
to
the
third
division
Q
,
which
shall
give
O
,
the
place
of
the
Knot
;
from
4
to
the
fourth
division
R
at
the
point
T
,
then
to
joyn
the
crooked
lines
G
S
O
T
L
,
and
you
shall
have
already
a
Diagonal
;
a
d
do
as
much
on
the
other
side
,
and
you
shall
have
the
Cross
entire
,
and
your
Vault
compleat
.
For
to
make
the
same
Vault
more
exactly
.
HE
that
shall
understand
well
the
foregoing
Order
,
will
not
be
much
troubled
to
do
this
,
seeing
there
is
nothing
but
to
double
the
lines
,
and
to
take
heed
to
the
sections
which
are
in
a
greater
Number
,
by
reason
the
Circle
is
divided
into
more
Parts
.
One
may
learn
to
make
the
plane
at
the
28.
fol.
you
must
draw
parallels
from
all
the
divisions
of
this
plane
,
from
i
unto
16.
or
the
half
only
to
the
Ray
B
A
,
which
will
give
the
points
O
,
upon
which
you
must
elevate
perpendiculars
,
&c.
All
the
rest
is
done
,
as
we
have
said
in
the
foregoing
Order
.
But
this
is
the
more
exact
,
and
doth
make
the
Vault
more
easily
,
because
the
divisions
are
more
near
the
one
to
the
other
.
For
to
make
the
Vaults
more
streight
then
large
.
THere
are
two
Orders
in
this
Figure
;
the
one
for
to
streighten
the
Vaults
on
the
sides
,
the
other
for
to
give
a
Thickness
to
the
Cross
.
We
will
begin
with
the
former
.
The
two
Orders
of
Vaults
,
which
we
are
about
leaving
,
supposing
that
they
are
all
square
;
that
is
to
say
,
that
the
distance
and
bredth
of
the
Arches
is
equal
,
as
well
on
the
sides
as
those
on
the
front
;
and
he
that
cannot
make
but
of
this
fashion
,
shall
finde
some
trouble
,
if
he
were
to
set
up
a
Church
,
where
ordinarily
the
Arches
of
the
sides
are
much
closer
then
those
of
the
front
.
See
here
a
fair
Invention
,
by
the
which
you
shall
give
such
Measure
as
you
please
,
to
those
of
the
sides
,
by
the
means
of
the
base
A
Q.
Suppose
then
that
the
Arch
before
it
Q
,
is
40
feet
broad
,
and
that
in
that
of
the
sides
,
you
would
allow
but
15
,
20
,
or
so
much
or
little
as
you
please
:
you
must
(
according
to
the
fourth
advice
in
fol.
17.
)
set
this
Measure
upon
the
base
,
and
draw
to
the
point
of
distance
,
which
will
give
the
sinking
of
the
same
Measure
in
A
E
;
as
by
example
,
we
have
set
here
A
C
of
20
feet
,
drawing
from
the
point
C
;
to
the
point
of
distance
,
which
is
a
little
farther
off
here
where
our
Paper
is
too
narrow
for
to
cause
it
to
be
seen
;
it
will
divide
the
sinking
of
20
feet
,
upon
the
Ray
A
D
,
at
the
point
E
;
then
coming
back
to
the
Base
,
you
must
make
an
half-Circle
of
this
distance
A
C
,
and
divide
it
into
as
many
parts
as
the
greater
Arcade
F
G
shall
have
of
division
,
as
here
8
;
and
from
all
these
divisions
I
,
to
elevate
Perpendiculars
I
H
,
and
from
the
points
I
H
,
being
drawn
to
the
point
of
distance
they
will
divide
the
Ray
A
E
,
at
the
point
O
,
which
you
must
also
elevate
into
the
Perpendicular
O
P
,
you
must
make
in
some
place
separate
the
Plane
of
this
demi-round
F
G.
Supposing
that
it
hath
not
been
made
,
for
to
take
the
divisions
thereof
,
and
to
carry
them
from
E
unto
B
:
And
seeing
that
the
Plane
of
the
Figure
foregoing
is
equal
to
F
G
,
take
the
Measures
of
the
half
B
C
D
E
F
,
and
carry
them
upon
the
Perpendiculcs
A
F
,
and
from
these
points
E
F
D
C
B
,
draw
to
the
point
of
sight
D
,
and
from
the
sections
which
these
Rays
B
C
D
E
F
,
shall
make
at
the
Perpendic●les
O
P
;
you
must
draw
crooked
lines
,
which
shall
frame
the
Arch
of
the
side
,
and
drawing
Parallels
from
the
sections
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
to
the
divisions
of
the
Arch
F
G
,
you
shall
have
the
points
F
R
S
T
V
X
Y
Z
,
for
to
frame
the
Cross
,
even
as
we
have
already
said
heretofore
.
For
the
Thicknesses
of
the
Joynts
of
the
Cross
,
you
are
only
to
make
a
little
line
of
Elevation
a
b
,
which
I
have
set
at
the
top
of
the
Perpendicule
elevated
from
the
point
O
:
and
this
line
a
b
being
drawn
to
the
point
of
sight
D
,
divideth
all
the
other
Perpendicules
at
the
points
c
d
,
for
to
give
the
heights
Proportionate
to
every
Perpendicule
elevated
from
the
sections
of
the
Cross
;
that
is
to
say
,
from
the
sections
which
must
be
made
for
to
finde
the
draught
of
the
Cross
,
following
their
Order
:
for
example
,
the
first
Elevation
a
b
shall
be
given
at
the
first
Perpendicule
G
:
The
second
Elevation
c
d
,
at
the
second
Perpendicule
F
,
c
;
and
so
following
for
all
the
others
,
which
shall
give
the
points
C
;
by
the
which
making
a
crooked
line
for
to
joyn
them
together
,
we
shall
have
the
thickness
of
the
Joynts
of
the
Cross
of
the
Vault
,
as
one
may
see
at
half
of
the
left
side
of
the
Figure
aforegoing
.
A
Vault
made
by
the
Orders
aforegoing
.
ALL
the
Orders
aforegoing
;
do
shew
sufficient
easiness
for
to
make
a
perfect
Vault
,
as
this
here
:
except
what
concerneth
the
Pillars
or
Columns
,
which
we
will
shew
hereafter
.
Of
Arches
and
Doors
with
three
squares
.
THere
is
another
kind
of
fretted
cieling
,
which
holdeth
the
place
of
a
Roof
for
Gates
and
Galleries
,
and
also
in
Churches
,
which
maketh
well
also
in
Perspective
;
and
is
very
easie
to
practise
:
I
have
set
it
after
the
Round
,
because
that
it
is
framed
of
a
demi-Circle
,
as
a
round
door
,
which
after
is
to
be
divided
.
Having
elevated
the
walls
A
B
,
we
must
make
a
demi-Circle
,
which
containeth
all
the
bredth
C
D
,
then
holding
the
Compass
open
of
the
bredth
of
the
half
Diameter
E
C
,
you
must
hold
one
leg
firm
at
the
point
C
,
and
with
the
other
E
to
draw
an
Arch
on
high
,
which
divideth
the
demi-round
at
the
point
G
,
and
to
make
likewise
from
the
point
D
the
Arch
E
H.
Then
to
joyn
these
four
Letters
C
D
G
H
,
with
right
lines
,
which
will
give
you
the
Arch
half-Hexagone
,
or
with
three
squares
.
You
must
also
make
a
demi-round
,
upon
the
bredth
I
K:
for
the
bottom
,
and
for
to
divide
it
,
you
have
only
to
draw
from
the
Angles
of
the
first
C
D
G
H
,
to
the
point
of
sight
F
,
at
the
sections
that
it
shall
make
of
the
demi-round
at
the
point
L
M
:
you
must
draw
right
lines
,
which
will
frame
the
Arch
of
the
hollow
.
Of
another
Arch
Half-Decagone
,
or
of
five
squares
.
THIS
Arch
is
ordered
altogether
as
the
former
,
and
there
is
no
difference
,
but
in
the
division
of
the
Circle
:
The
first
is
divided
into
three
,
and
this
into
five
;
so
if
you
divide
the
demi-Circle
L
M
,
into
five
Parts
N
O
P
Q
,
and
that
you
draw
from
all
these
points
to
the
point
R
,
you
shall
divide
the
demi-Circle
of
the
hollow
:
so
as
we
have
said
,
in
that
above
of
three
squares
.
The
Elevation
of
round
Figures
in
Perspective
.
THE
desire
that
I
have
to
shew
the
easiness
of
setting
all
things
into
Perspective
,
hath
made
me
set
here
also
,
how
one
ought
to
elevate
from
a
Round
or
Circle
,
such
an
height
as
one
would
have
;
and
this
Order
shall
serve
for
all
round
Figures
,
as
Tops
of
a
Church
,
Amphitheaters
,
Towers
,
&c
,
Having
made
the
Plane
of
the
Round
in
Perspective
,
as
it
is
ordered
heretofore
,
and
set
on
the
side
of
the
Plane
,
the
line
of
Elevation
A
B
,
according
to
the
height
that
one
would
give
it
:
We
must
from
the
Angles
of
the
Plane
which
are
here
,
the
Points
of
which
they
have
framed
the
Round
,
as
are
1
,
2.
3
,
4
,
5
,
6
,
7
,
8
,
9
,
to
draw
Parallels
to
the
bottom
of
the
line
of
Elevation
A
B
,
and
to
elevate
them
as
we
have
said
,
and
with
a
Compass
to
transport
them
upon
the
Perpendiculars
elevated
from
the
points
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9.
&c.
as
in
the
former
Orders
.
The
demi-round
before
,
hath
but
half
of
the
Elevation
of
that
behinde
;
and
the
one
and
the
other
,
but
the
single
draught
without
thickness
.
By
this
Order
there
is
no
round
thing
,
which
one
may
not
set
into
Perpective
;
I
mean
Rounds
,
Parallels
to
the
Horizon
;
The
other
Rounds
which
are
Perpendiculars
to
the
Horizon
,
are
taught
in
the
Orders
of
Vaults
.
The
Elevation
of
Pilasters
set
into
a
Round
.
WE
must
double
the
Round
,
as
is
taught
in
the
Plane
,
fol.
29.
and
between
the
two
Circular
lines
set
the
Plane
of
the
Pieces
,
which
one
would
elevate
,
as
we
see
the
Places
before
A
B
C
D
,
the
which
do
draw
to
the
Center
E
;
Then
from
all
the
Angles
of
these
Planes
to
raise
Perpendiculars
,
and
to
give
them
their
height
,
according
to
the
line
of
Elevation
F
G
,
by
the
ordinary
Rule
,
as
is
sufficiently
seen
by
the
second
figure
.
1
figure
2
figure
A
Vault
like
a
Scallop-shell
set
into
Perspective
.
THIS
Figure
may
serve
for
the
hollow
of
a
Church
,
for
a
Grotte
or
Cave
,
for
an
hollow
Nest
in
a
Wall
,
and
the
like
Pieces
;
the
Elevation
is
made
in
the
same
manner
,
and
by
the
Orders
that
we
have
spoken
of
.
For
this
flat
Band
A
B
which
may
serve
for
a
Cornish
,
its
diminution
must
be
taken
upon
the
line
of
Elevation
in
C
D
,
and
to
carry
it
upon
the
Pilasters
,
For
the
Vault
,
we
must
make
the
first
Arch
E
F
,
in
the
manner
that
we
have
said
,
and
in
the
midst
within
to
make
a
demi-Circle
O
,
to
the
which
we
shall
draw
crooked
lines
,
which
shall
rise
above
the
Pilasters
,
and
shall
make
the
sides
or
Nerves
of
the
Vault
,
as
we
see
G
H
I
K
,
the
heights
of
the
Windows
shall
be
taken
upon
the
line
of
elevation
,
between
L
and
M.
The
figure
will
help
for
the
rest
.
Of
open
Rounds
in
Steeples
,
or
Vaults
pierced
in
Perspective
.
HAving
made
the
Plane
of
the
double
Round
,
fol.
24.
and
marked
between
the
two
Circles
,
the
places
and
the
numbers
of
the
Pilasters
which
one
would
have
there
,
the
which
ought
to
draw
towards
the
Center
A
:
we
must
mark
the
height
,
which
we
would
give
from
the
ground
unto
the
hollow
of
the
Lovure
,
as
here
the
line
D
and
E
on
high
:
the
which
must
serve
for
the
base
,
where
we
shall
transport
the
same
Measures
,
which
are
upon
the
line
B
G.
And
from
the
same
point
of
sight
G
,
to
make
a
Plane
on
high
as
that
below
,
whence
all
the
places
of
the
Pilasters
shall
draw
towards
the
Center
H
,
for
to
frame
the
Pilasters
,
we
are
only
to
draw
lines
from
the
places
,
which
are
opposite
the
one
to
the
other
,
and
which
shall
give
their
bredth
and
their
thickness
.
I
have
not
drawn
lines
to
the
three
Pilasters
before
;
as
well
to
cause
these
of
the
bottom
to
be
seen
,
as
also
to
make
it
known
,
that
there
needs
on
high
,
as
below
.
For
to
give
the
thickness
of
the
Round
from
I
unto
H
,
and
from
K
unto
L
,
we
must
set
the
height
,
which
we
would
have
upon
the
line
of
the
Elevation
D
M
,
drawing
to
the
Horizon
at
the
point
F
;
And
from
all
the
points
whence
we
have
framed
the
Round
,
to
draw
to
this
line
D
,
upon
the
which
we
shall
elevate
Plumb-lines
,
as
D
M
,
which
we
take
with
a
Compass
,
for
to
transport
all
these
heights
upon
the
Perpendicules
,
which
shall
be
raised
from
the
points
,
as
K
L
N
O
P
Q
;
and
so
of
the
others
.
He
that
in
the
place
of
the
Round
,
would
have
a
square
or
a
Polygone
,
hath
need
only
to
keep
the
same
Method
;
and
he
shall
do
all
that
he
would
,
with
the
same
facility
,
seeing
that
this
,
which
is
the
hard
,
is
not
difficult
.
That
the
multitude
of
Objects
and
the
Plurality
of
stories
,
ought
to
have
but
one
point
of
sight
.
I
Have
already
said
elsewhere
,
that
one
never
ought
to
set
more
then
one
point
of
sight
in
one
Picture
;
and
that
hence
we
may
know
the
great
ignorance
of
Painters
,
which
do
give
as
it
were
as
many
points
of
sight
,
and
of
Horizons
,
as
they
make
lines
.
I
remember
I
have
seen
a
Picture
,
where
there
were
many
Chambers
,
the
one
above
the
others
,
and
each
had
two
or
three
points
of
sight
:
and
after
that
the
Master
thought
he
had
done
a
Miracle
.
The
present
Figure
is
to
correct
this
Errour
,
and
cause
us
to
know
,
that
there
ought
to
be
but
one
point
of
sight
only
,
as
is
A
,
to
the
which
all
the
Objects
ought
to
draw
,
and
all
the
Chambers
,
if
there
should
be
fifty
,
one
above
the
other
,
or
on
the
one
side
and
the
other
;
as
we
see
these
three
here
,
which
draw
all
to
the
point
of
sight
A.
All
the
rest
is
made
,
as
we
have
said
heretofore
.
For
to
set
Chimneys
into
Perspective
.
WE
must
take
the
Measures
upon
the
base
A
B
,
which
must
be
divided
into
equal
Parts
.
You
may
make
the
divisions
of
what
quantity
you
will
.
This
A
B
is
into
eighteen
,
of
each
one
foot
;
for
to
make
a
Chimney
at
the
Wall
A
,
three
feet
within
the
Chamber
,
we
must
take
three
Parts
,
as
A
C
,
and
draw
from
the
point
C
to
the
point
of
distance
D
,
which
will
give
the
sinking
of
three
feet
,
dividing
the
Ray
A
E
at
the
point
F
,
you
must
set
the
thickness
of
the
Jaumbs
of
the
Chimney
beyond
the
point
C
,
as
is
G
,
then
drawing
from
G
to
D
,
it
will
give
this
thickness
at
the
point
H.
You
must
also
set
the
bredth
of
the
Chimney
from
G
unto
I
,
which
is
of
four
feet
and
an
half
:
and
for
the
thickness
of
the
second
Jaumbs
an
half
foot
,
as
at
the
other
:
Beginning
at
the
point
I
unto
K
,
then
to
draw
from
I
K
to
the
point
of
distance
D
,
which
will
give
their
Measure
upon
the
Ray
A
E
,
at
the
points
L
M
,
from
which
four
points
F
H
L
M
,
you
must
draw
little
Parallels
to
the
base
,
as
F
N
H
O
L
P
M
Q
;
for
to
give
the
bredth
to
the
Jaumbs
,
you
must
take
a
foot
and
half
A
R
,
and
the
Ray
A
E
shall
divide
the
little
Parallels
at
the
points
N
O
P
Q
,
from
which
,
and
from
F
L
,
you
must
raise
Perpendicules
;
for
the
height
of
the
Mantle-tree
of
the
Chimney
,
you
must
take
five
feet
upon
the
base
,
and
carry
them
to
the
corner
of
the
wall
A
unto
S
,
and
from
S
to
T
for
Cornish
,
all
the
rest
is
seen
clearly
in
the
first
figure
.
The
other
Chimney
which
is
opposite
to
it
,
is
made
of
the
same
manner
,
for
we
ought
always
to
make
the
Jaumbs
as
in
the
first
;
and
of
these
Jaumbs
,
to
make
Columns
,
Termes
,
and
all
that
one
would
.
I
have
made
Brackets
to
this
.
The
Chimney
of
the
bottom
must
also
take
its
Measures
upon
the
base
1
,
2
,
3
,
4
,
drawn
to
the
point
of
sight
E
,
for
to
finde
the
hollow
of
the
Chimney
,
or
the
bredths
of
the
Jaumbs
,
you
must
draw
from
7
to
E
,
and
divide
the
lines
of
sinking
at
the
point
5
,
which
shall
be
a
foot
and
half
:
then
from
the
point
of
distance
V
,
to
draw
the
Diagonal
passing
by
5
,
which
shall
divide
the
Ray
2.
E.
at
the
point
6
,
and
from
this
point
to
draw
a
Parallel
which
shall
divide
the
four
Rays
1
,
2
,
3
,
4.
at
the
points
9
,
6
,
9
,
9
,
from
which
you
must
raise
Perpendiculars
,
and
make
all
the
rest
as
in
the
others
.
The
second
figure
sheweth
plainly
,
and
without
lines
,
that
which
we
are
speaking
of
.
Of
Stairs
in
Perspective
.
THere
is
nothing
that
giveth
so
great
a
grace
to
a
Perspective
,
nor
which
more
easily
deceiveth
the
eye
,
there
is
a
muititude
of
Returns
,
by
reason
that
there
is
need
of
many
lights
and
divers
shadows
,
which
give
such
force
to
the
Objects
;
that
they
seem
to
cast
them
out
of
the
work
.
Now
stairs
have
this
advantage
,
that
in
what
fashion
soever
one
set
them
,
they
have
always
lights
and
shadows
,
and
by
consequence
they
are
pleasing
to
the
sight
.
I
will
set
down
some
here
.
If
one
shall
use
little
squares
,
they
will
have
the
more
easiness
,
having
only
to
raise
Perpendicules
,
from
so
many
squares
,
as
he
would
have
steps
:
then
to
set
at
the
first
square
the
line
of
Elevation
,
divided
into
as
many
Parts
as
one
would
,
and
from
these
divisions
to
draw
to
the
point
of
sight
,
and
they
shall
divide
the
Perpendicules
where
the
steps
ought
to
be
.
For
example
,
you
would
have
a
stair-case
of
eight
steps
,
and
that
the
last
may
have
the
bredth
of
3
,
you
must
take
upon
the
Plane
the
number
of
little
squares
,
beginning
at
B
,
as
are
1
,
2
,
3
,
4
,
5
,
6
,
7.8
.
And
3
for
the
last
marked
11
,
from
all
these
Angles
we
must
raise
Perpendicules
,
which
we
shall
divide
,
according
to
the
divisions
of
the
line
of
Elevation
B
D
in
this
manner
.
The
first
division
(
four
inches
high
,
supposing
the
square
of
one
foot
)
shall
divide
the
first
Perpendicule
,
and
it
must
be
continued
unto
the
second
,
for
that
maketh
also
the
upper
part
of
the
step
,
as
is
E
F
,
and
so
of
the
others
.
You
shall
make
these
steps
as
long
as
you
would
as
these
are
of
three
feet
taking
,
as
I
have
said
,
the
square
for
one
foot
,
so
as
is
B
G
at
this
distance
.
You
must
also
raise
Perpendicules
,
as
we
have
done
on
the
side
B
;
but
for
to
save
this
pains
,
it
were
better
to
take
the
height
of
the
last
step
H
,
and
that
of
the
first
I.
Then
to
draw
the
line
H
I
,
which
must
grate
upon
the
Angles
,
or
the
outward
edge
of
the
Steps
,
as
E
K
,
grateth
upon
them
on
the
side
B
:
for
this
being
,
there
is
but
onely
to
draw
parallells
to
the
Base
from
all
the
Steps
on
the
side
B
,
untill
that
they
divide
the
line
H
I
,
as
we
see
L
M
N
O
P
Q
,
&c.
without
making
squares
;
we
need
only
to
set
the
Measures
upon
the
Base
,
and
to
draw
them
to
the
point
of
distance
.
We
may
have
the
same
Measures
upon
the
line
A
B.
I
set
no
other
figures
,
seeing
that
this
sufficeth
for
to
Understand
them
all
,
and
for
to
make
them
.
Other
steps
hollowed
underneath
in
Perspective
.
THIS
manner
of
steps
is
made
as
those
which
we
are
now
leaveing
.
As
for
the
hollowness
,
there
is
need
only
to
see
the
Figure
,
for
to
know
the
manner
of
setting
them
into
Perspective
:
These
two
that
I
present
shall
give
an
open
way
to
the
Practiser
of
this
Art
,
to
invent
others
by
.
Steps
in
front
in
Perspective
.
THIS
manner
of
steps
is
according
to
the
Order
of
the
line
of
Elevation
;
you
must
raise
as
many
Perpendicules
from
the
Angles
of
the
squares
of
the
Plane
,
as
you
would
have
of
steps
,
as
are
C
D
E
F
,
and
from
the
same
Angles
to
draw
little
Parallels
unto
the
bottom
of
the
line
of
elevation
A
,
which
shall
be
the
points
O
O
O
O
,
which
you
must
raise
until
that
they
divide
the
occult
Rays
of
the
divisions
of
the
line
of
Elevation
A
:
Then
to
take
these
Measures
with
a
Compass
,
and
carry
them
upon
the
Perpendicules
elevated
from
the
Angles
of
the
Plane
,
each
according
to
their
Order
.
The
first
,
for
the
first
step
;
the
second
,
for
the
second
,
&c.
For
to
finde
these
Returns
P
;
you
must
from
the
same
Corners
P
draw
to
the
distance
Q
,
and
to
take
heed
,
where
that
divideth
the
line
of
the
Plane
,
or
the
under-part
of
the
step
;
for
example
,
above
the
fourth
step
I
have
made
the
Plane
of
the
fifth
step
;
Now
to
have
its
Return
P
,
we
must
from
the
same
points
P
,
draw
to
the
distance
Q
,
and
take
notice
where
it
shall
divide
the
Ray
R
,
which
shall
be
at
the
point
S
,
and
this
point
S
shall
be
the
point
for
to
draw
the
line
of
Return
S
T.
And
so
of
others
.
For
to
make
stairs
,
which
one
may
shew
from
four
sides
.
THere
are
many
wayes
to
make
these
Stairs
,
see
here
are
two
,
which
seem
the
most
easi●
.
The
first
;
Being
about
to
make
one
of
these
Stairs
,
we
must
take
the
leng●h
of
the
first
Step
,
and
set
thereon
the
quantity
of
Steps
,
that
you
would
have
,
as
upon
the
line
A
B
,
I
have
set
the
points
C
C
C
,
for
four
steps
:
From
these
points
we
must
make
Rays
to
the
point
of
sight
D
,
the
Rayes
shall
be
divided
by
the
Diagonals
A
F
,
and
B
E
,
at
the
points
I
,
from
the
which
we
must
raise
Perpendicules
,
and
draw
little
parallels
unto
the
bottom
of
the
line
of
Elevation
G
,
which
shall
give
the
points
H
,
which
they
shall
raise
as
H
K.
We
must
upon
this
line
of
Elevation
G
,
set
as
many
equal
parts
,
as
we
would
have
Steps
,
as
here
4
,
from
these
four
points
1.
2.
3.
4.
We
must
draw
to
the
point
D
,
for
to
divide
the
Perpendiculars
H
K
,
and
to
give
to
each
the
height
that
it
ought
to
have
,
as
that
which
is
made
of
points
sheweth
it
.
We
must
take
these
measures
with
a
Compass
,
and
transport
them
the
one
after
the
other
,
beginning
at
the
first
G
,
1.
and
carry
it
upon
the
first
Perpendicular
,
to
the
corner
A
,
as
A
L
,
then
to
draw
a
parallel
unto
the
other
side
B.
(
but
here
I
have
not
set
it
but
at
the
half
,
for
to
make
the
plane
to
be
seen
in
the
other
)
for
the
second
Step
,
you
must
take
the
second
measure
H.
2.
and
carry
it
upon
the
second
Perpendicular
I
,
then
to
draw
Parallels
,
as
at
the
first
:
And
so
of
all
the
others
.
Another
manner
.
The
side
M
N
,
being
given
;
we
must
make
a
parallel
above
,
for
the
thickness
of
the
first
Step
,
as
O
P
,
from
which
points
O
P
,
we
draw
2
Rayes
to
the
point
of
sight
Q
,
and
also
to
the
distances
R
S
,
And
these
Diagonalls
shall
frame
the
square
in
the
ordinary
manner
and
this
shall
be
the
first
step
.
For
the
second
,
we
must
set
the
measure
of
the
breadth
,
which
we
would
give
it
upon
the
line
O
P
,
as
is
O
T
,
and
from
the
point
T
,
to
draw
to
the
point
of
sight
Q.
and
this
line
or
Ray
T
Q.
shall
divide
the
Diagonals
O
,
where
we
must
raise
the
second
Step
at
the
point
V.
The
height
of
this
Step
shall
be
taken
from
the
half
of
V
X
,
as
M
O
,
is
the
half
of
O
T.
This
measure
being
given
at
the
point
Y
,
we
must
draw
parallels
unto
the
Diagonal
of
the
other
side
,
which
is
drawn
from
the
corner
P
,
then
from
the
points
Y
Z
,
to
draw
to
the
points
of
sight
,
and
of
distance
;
for
to
frame
the
square
as
at
the
first
Step.
For
the
third
Step
,
we
are
only
to
carry
upon
the
line
Y
Z
,
the
measure
V
X
,
which
shall
be
Y
A
,
and
from
the
point
A
,
to
draw
to
the
point
of
sight
Q
,
for
to
divide
the
Diagonal
of
the
point
Y
,
which
shall
be
the
point
B
,
and
the
place
of
the
third
Step.
Its
height
shall
be
the
half
of
B
C
,
which
is
alwayes
that
of
O
T
in
Perspective
.
All
the
rest
is
the
same
,
as
in
the
first
and
second
,
if
there
should
be
an
hundred
,
you
must
work
always
in
the
same
manner
.
The
third
figure
causeth
these
Steps
to
be
seen
clearly
without
the
confusion
of
Draughts
,
which
we
should
make
for
to
find
their
places
:
these
Draughts
should
be
made
in
white
;
or
in
such
manner
,
that
nothing
may
be
seen
of
them
,
when
the
figure
is
finished
.
Stairs
viewed
on
the
side
in
Perspective
.
YOu
must
set
upon
the
base
,
the
number
of
steps
that
you
would
have
;
that
is
to
say
,
as
many
points
at
an
equal
distance
,
as
here
the
three
A
B
C
,
from
these
points
,
you
must
draw
to
the
points
of
sight
D.
Then
from
the
point
A
,
to
the
point
of
distance
E
;
And
this
Diagonal
A
E
,
shall
give
the
plane
,
and
the
place
of
the
steps
at
the
section
of
the
Rays
B
C
,
at
the
points
I
,
and
upon
the
Ray
F
,
which
is
the
foot
of
the
Wall
,
the
point
G
,
which
is
the
midst
of
the
plane
of
the
steps
,
from
this
point
G
,
you
must
draw
to
the
other
distance
H
,
for
to
find
the
corner
of
the
last
step
at
the
point
K
,
and
the
place
of
others
at
the
points
I.
Then
from
all
these
points
I
,
to
raise
Perpendiculars
.
For
to
give
them
their
height
,
you
must
from
the
points
A
B
C
,
which
are
upon
the
base
,
raise
little
lines
,
for
to
serve
for
the
line
of
elevation
,
upon
the
which
shall
be
set
the
heights
according
to
their
number
.
For
example
,
A
,
which
is
first
,
shall
have
but
one
,
B
,
which
is
the
second
,
shall
have
two
.
and
C
,
which
is
the
third
shall
have
three
.
Draw
from
all
these
points
1
,
2
,
and
3
,
to
the
points
of
sight
D
,
and
you
shall
divide
the
Perpendiculars
elevated
from
the
plane
,
to
the
points
O
,
which
shall
be
the
height
of
each
step
.
That
of
the
other
side
is
for
to
make
it
seem
without
points
,
and
without
lines
.
This
manner
of
steps
may
serve
for
many
things
,
as
for
an
Altar
,
for
a
Throne
,
for
the
forepart
of
a
Church
,
for
a
Gate
,
&c.
Stairs
within
a
Wall
in
Perspective
.
SEt
as
many
divisions
at
the
end
of
the
Wall
,
as
you
would
have
steps
,
as
here
,
for
three
,
between
A
and
B
,
and
draw
A
B
,
to
the
point
of
sight
C.
Then
having
determined
the
space
,
that
you
would
give
to
the
steps
,
as
D
E
,
you
shall
draw
the
parallel
to
the
base
E
F
,
which
shall
receive
at
the
points
I
I
,
the
sections
of
the
lines
drawn
from
the
points
G
H
,
to
the
point
of
sight
C
,
and
from
these
points
I
I
,
you
shall
raise
Perpendiculars
I
K
,
I
K
,
which
shall
receive
the
heights
of
the
steps
,
drawing
from
the
points
1.
2.
3
,
to
the
point
of
sight
C
,
as
is
to
be
seen
in
the
second
figure
.
2
Figure
For
winding
Stairs
with
Rests
in
Perspective
.
WE
must
remember
the
fore-going
orders
about
Steps
,
and
it
will
be
easie
to
frame
these
winding
Stairs
,
but
to
avoid
the
pains
of
searching
,
we
will
unfold
the
whole
matter
here
.
By
reason
that
the
winding
Stairs
of
this
figure
,
have
ordinarily
twice
as
much
at
the
bottom
,
as
they
are
broad
:
When
one
would
raise
then
into
Perspective
,
he
shall
first
set
the
Horizon
,
where
he
would
.
Then
he
must
make
a
square
,
according
to
the
ordinary
rules
,
and
double
it
according
to
the
second
advice
of
Fol.
16.
and
to
divide
this
square
by
an
unequal
number
of
little
squares
,
that
the
Walls
which
should
be
in
the
midst
,
may
be
of
the
measure
of
one
little
square
.
In
this
figure
each
square
hath
9
sides
,
or
little
squares
of
each
side
,
the
which
being
doubled
maketh
18.
for
all
the
hollow
:
Of
these
18.
you
must
leave
4
at
each
end
for
the
Rests
;
there
remains
10
little
squares
,
which
we
will
make
to
contain
1
foot
eevry
way
,
of
which
we
shall
make
ten
Steps
,
or
degrees
,
as
followeth
.
Having
left
4
squares
A
B
,
beginning
at
the
point
A
,
which
holdeth
the
place
of
the
Wall
,
we
will
raise
a
good
height
the
Perpendicule
B
,
then
the
second
C
,
and
the
third
D
,
and
so
from
the
other
Angles
of
the
squares
,
until
that
one
have
made
the
10.
which
we
have
here
:
This
being
done
on
the
one
side
;
you
shall
do
as
much
on
the
other
,
and
all
these
Perpendicules
shall
give
the
depths
of
the
steps
.
For
the
height
,
if
they
have
one
foot
of
depth
,
or
breadth
,
we
shall
give
them
one
half
foot
of
height
,
which
is
the
half
of
the
little
square
A
O
:
this
height
being
taken
with
a
compass
,
we
must
set
it
upon
the
first
corner
,
which
shall
serve
as
for
the
line
of
elevation
,
beginning
all
below
at
the
point
A
,
and
to
mark
it
as
many
times
,
as
we
would
make
Steps
,
as
here
10
unto
the
first
Rest
,
from
which
we
begin
to
ascend
again
on
the
other
side
opposite
,
where
which
we
shall
take
again
the
Rest
of
the
numbers
following
are
marked
there
on
the
one
side
,
and
other
unto
the
23.
From
all
these
23
points
,
we
must
draw
to
the
point
of
sight
E
,
and
to
take
heed
to
divide
the
Perpendicules
,
according
to
their
order
,
that
is
to
say
,
that
having
placed
the
rule
upon
the
first
point
,
and
at
the
point
of
sight
E
;
we
must
divide
the
first
Perpendicular
B
,
unto
C
,
with
a
small
draught
for
the
first
Step
:
For
the
second
Step
,
we
must
from
the
second
point
divide
the
second
Perpendicular
C
;
unto
D
And
so
of
all
as
well
of
one
side
,
as
the
other
From
all
the
Angles
of
these
small
draughts
between
the
Perpendiculars
,
we
must
draw
parallels
to
the
Horizon
,
unto
the
Wall
F
,
which
is
raised
in
the
midst
,
as
are
the
small
draughts
I
I
I
I
,
which
I
have
made
only
on
one
side
,
for
to
avoid
confusion
.
It
is
only
these
parallels
,
which
must
frame
the
Steps
:
All
that
is
,
made
unto
that
,
ought
to
be
of
occult
lines
,
which
ought
not
to
be
seen
,
when
the
figure
is
finished
.
The
Rests
ought
to
be
taken
from
the
defect
of
the
last
Perpendiculars
unto
the
Wall
,
as
from
G
,
unto
H
,
their
thickness
H
K
,
is
of
one
half
foot
,
as
of
one
Step.
The
figure
below
,
is
the
same
wi●h
that
above
;
but
this
is
made
,
and
the
other
sheweth
how
it
ought
to
be
made
.
Stairs
winding
upright
,
in
Perspective
.
YOU
must
set
upon
the
base
one
side
of
the
Ascent
,
and
divide
it
into
so
many
Parts
,
as
you
would
set
steps
there
:
for
example
,
the
side
of
the
stairs
let
be
the
distance
A
B
,
if
you
would
have
16
steps
for
the
whole
Circuit
of
the
square
,
each
side
shall
have
four
:
This
is
,
why
this
Measure
A
B
being
divided
into
four
,
you
must
make
thereof
a
square
divided
into
sixteen
,
according
to
the
Orders
afore-going
.
From
all
the
outward
divisions
which
divide
into
four
the
lines
of
each
side
,
you
must
raise
Perpendicules
which
will
give
the
bounds
of
the
steps
.
Let
then
the
Perpendicules
be
A
A
,
B
B
,
C
C
,
D
D
,
E
E.
This
E
E
made
for
three
,
by
reason
that
the
point
is
in
the
midst
;
for
that
it
serveth
for
the
Nuell
or
Spindle
,
which
is
the
Center
of
all
,
and
the
half
of
the
line
before
,
and
of
that
of
the
bottom
,
there
follow
F
F
,
G
G
,
H
H
,
I
I
,
K
K
,
L
L
,
M
M
,
N
N
,
O
O
,
P
P.
You
must
set
upon
the
first
Perpendicule
A.
which
we
will
make
to
serve
for
lines
of
elevation
,
the
height
of
one
step
or
degree
Q
A
:
And
from
the
point
Q
,
you
must
draw
to
the
point
of
sight
X
,
for
to
have
the
Measures
of
all
the
steps
at
the
sections
of
the
Perpendiculars
Q
R
S
T
V
:
A
Q
is
the
height
of
the
first
,
F
R
of
the
second
,
G
S
of
the
third
,
H
T
of
the
fourth
,
and
I
V
of
the
fifth
;
this
of
all
those
of
the
bottom
,
as
A
Q
,
is
of
all
those
before
.
Seeing
that
G
S
is
the
measure
of
the
third
,
which
is
the
midst
of
the
side
;
it
must
also
be
the
measure
of
the
Center
,
and
of
the
Nuell
of
the
stairs
;
therefore
having
taken
this
Measure
G
S
,
with
the
Compasses
,
we
must
carry
it
to
the
Center
of
the
square
;
and
mark
it
in
going
upwards
,
as
many
times
as
we
would
set
steps
in
the
whole
Ascent
,
as
I
have
set
it
here
eighteen
times
for
eighteen
steps
or
degrees
.
All
being
ordered
in
this
manner
,
the
rest
is
easie
enough
,
seeing
that
for
to
make
the
first
step
,
we
must
take
the
measure
A
Q
,
and
carry
it
upon
the
Perpendicular
D
,
to
the
point
I
;
and
from
this
point
I
to
make
a
Parallel
unto
the
other
Perpendicule
B
;
then
from
these
two
points
I
I
,
upon
the
Perpendiculars
to
draw
to
the
other
I
,
which
is
at
the
Center
of
the
square
;
these
three
III
will
frame
the
first
step
.
For
the
second
,
seeing
that
its
Corner
cometh
to
the
Perpendicule
B
,
which
is
on
the
side
before
,
you
must
give
it
the
same
measure
A
Q
,
which
shall
be
1
,
2.
And
from
the
point
2
,
to
draw
to
the
point
of
fight
X
,
for
to
divide
the
Perpendicule
P
,
or
the
point
2
,
from
the
which
points
2
,
2
,
Perpendiculars
,
you
must
draw
to
2
of
the
Center
,
which
will
frame
the
second
step
.
For
the
third
,
seeing
that
it
meeteth
upon
the
Perpendicular
P
,
you
must
take
the
measure
F
R
for
its
height
,
and
do
as
at
the
second
;
and
so
of
all
the
others
.
He
that
would
make
them
round
,
needeth
but
only
to
reduce
the
square
into
Round
,
according
to
the
Orders
aforegoing
,
and
he
shall
have
the
same
facility
wholly
as
in
the
square
,
in
whatsoever
remaineth
.
Squares
set
into
Round
,
in
Perspective
.
THIS
Order
is
the
same
that
we
have
given
in
the
Planes
,
for
to
set
into
Perspective
;
the
Round
divided
into
8
,
as
one
may
see
in
the
figure
A
,
where
the
perfect
Round
of
the
forepart
of
the
Cube
,
giveth
the
draught
how
to
abridge
that
above
;
And
that
above
with
that
before
,
for
to
abridge
all
the
other
sides
;
as
we
see
the
Figure
B
,
where
the
Round
is
abridged
on
three
sides
,
and
at
the
other
C
,
where
it
is
of
all
the
faces
of
the
Cube
.
The
third
Figures
D
E
F
,
are
pierced
or
hollowed
,
each
on
two
sides
,
according
to
the
Plane
of
the
Figure
,
where
the
Round
A
,
as
we
see
the
Cube
D
,
pierced
by
the
face
before
,
and
through
that
we
see
the
bottom
pierced
;
likewise
E
is
pierced
by
the
sides
,
and
F
by
the
upper
part
and
the
face
,
which
lieth
upon
the
Ground
,
which
cannot
be
seen
,
supposing
that
the
Cube
be
of
matter
,
which
is
not
transparent
.
These
three
Figures
which
are
under
,
are
as
the
Pieces
which
one
hath
drawn
from
each
Cube
;
this
G
should
be
drawn
from
the
Cube
D
,
H
is
drawn
from
the
cube
E
,
and
I
is
drawn
from
the
cube
F.
That
which
causeth
to
understand
the
easiness
of
setting
all
square
Figures
into
Round
,
and
that
one
shall
not
be
troubled
to
set
Columns
in
what
place
soever
he
would
.
The
reason
why
I
have
set
none
of
them
heretofore
,
hath
been
for
to
render
the
Elevations
more
easie
to
conceive
,
and
to
facilitate
the
Orders
;
the
which
being
well
understood
and
remembred
,
one
shall
be
able
to
make
a
round
figure
of
whatsoever
he
will
;
This
is
the
beginning
of
Columns
.
We
shall
further
speak
,
how
one
ought
to
proceed
for
to
make
them
perfect
.
Round
Stairs
,
in
Perspective
.
FOR
to
elevate
these
three
Stairs
,
or
round
Steps
view'd
by
the
front
,
which
are
in
the
first
figure
,
we
must
make
a
Plane
of
three
Rounds
the
one
within
the
other
,
as
it
hath
bin
said
in
the
Planes
,
fol.
28.
And
from
all
the
points
that
frame
the
round
to
draw
Parallels
to
the
Base
,
unto
the
Ray
A
,
which
is
the
foot
of
the
line
of
Elevation
A
B
,
which
shall
give
the
elevations
by
the
Ordinary
Rule
,
which
must
be
taken
with
the
Compasses
,
and
to
carry
them
upon
the
perpendicules
elevated
from
the
Points
of
the
Plane
,
as
we
have
done
at
the
Pilasters
,
set
into
Round
.
Round
stairs
viewed
from
the
side
in
Perspective
.
THE
Order
of
Figures
or
Objects
viewed
from
the
side
,
is
altogether
the
same
with
that
of
those
of
the
front
;
But
that
it
may
be
known
that
we
are
not
always
bound
to
follow
the
division
of
the
Circle
into
16.
I
have
made
those
of
the
side
into
8
,
as
may
be
seen
in
the
Circle
made
of
Points
in
the
Figure
,
which
is
not
shadowed
;
for
all
the
Rest
,
it
is
as
in
other
Orders
;
the
line
of
elevation
C
D
,
which
is
drawn
to
the
point
of
sight
E.
1.
Fig.
2.
fig.
For
the
winding
stairs
,
or
turning
Ascent
.
THIS
Figure
is
the
same
with
that
before-going
,
which
I
have
not
shadowed
,
on
purpose
to
make
the
Order
to
be
the
better
understood
.
And
for
this
reason
I
have
reserved
for
this
,
the
Tree
,
or
the
Nuell
of
the
Ascent
,
which
one
may
finde
by
making
at
the
center
A
,
a
Round
in
Perspective
,
or
rather
a
demi-round
,
seeing
that
we
can
see
but
the
half
as
is
B
C
,
at
which
demi-circle
we
must
draw
lines
to
the
Center
A
,
from
all
the
divisions
of
the
square
of
the
first
Plane
,
which
will
give
G
E
F
G
H
I
K
,
which
will
divide
this
Arch
B
C
into
eight
parts
.
And
from
the
section
O
we
must
raise
Perpendicules
,
and
observe
that
they
shall
divide
justly
at
the
point
,
where
we
must
place
the
steps
or
degrees
,
which
we
shall
have
made
:
as
for
example
,
the
step
I
,
shall
be
divided
by
the
Perpendicule
elevated
from
its
point
upon
the
demi-round
,
as
we
see
in
A
:
the
other
step
after
which
is
the
second
,
shall
be
divided
by
the
Perpendicular
of
the
point
,
which
K
shall
have
made
at
the
demi-round
;
and
so
of
all
the
others
.
The
rest
which
is
in
the
figure
,
as
the
doors
and
the
windows
,
shall
be
made
according
to
the
foregoing
Orders
.
Of
Columns
or
Pillars
in
Perspective
.
THat
which
we
are
speaking
of
,
is
not
only
for
the
Cube
,
but
it
ought
also
to
serve
for
all
that
we
would
make
round
.
For
example
,
if
from
the
square
A
you
would
elevate
a
round
peice
,
you
must
make
a
round
within
this
square
,
according
to
the
ordinary
Orders
;
and
at
the
height
,
which
one
would
give
to
this
piece
,
to
make
also
another
square
,
and
a
round
within
,
as
is
B.
For
to
know
to
give
the
2
lines
D
E
,
which
make
the
thickness
,
or
the
Diameter
of
the
round
:
We
must
take
notice
where
the
round
divideth
the
Diagonal
of
the
square
,
and
to
hold
for
a
general
maxime
,
that
it
ought
always
to
be
taken
at
the
round
pieces
seen
from
the
side
,
as
it
is
in
the
figure
C
,
that
the
Perpendicules
are
elevated
from
the
section
of
the
round
,
upon
the
Diagonal
of
the
square
,
at
the
points
D
E
For
the
pieces
viewed
by
the
Front
,
as
the
figure
F
,
they
ought
always
to
possess
the
Demy-round
G
H
I
,
and
to
elevate
the
Perpendicules
of
the
Diameter
right
G
H
,
and
from
the
one
and
the
other
,
as
well
on
Front
,
as
on
Side
,
we
must
elevate
a
line
from
the
Center
,
which
shall
serve
to
give
the
Diminutions
to
the
Columns
.
For
these
three
pieces
below
besides
that
they
serve
to
make
the
others
seen
clearly
,
and
with
their
shadows
,
they
serve
also
for
to
shew
how
we
must
proceed
for
the
Columns
.
This
piece
of
the
midst
K
,
is
exactly
round
,
without
ornament
,
nor
intent
to
make
any
there
:
The
second
marked
L
,
causeth
to
be
seen
,
that
when
we
desire
to
make
a
base
there
,
we
ought
upon
the
square
,
which
must
serve
for
a
Plinthe
,
whereof
M
N
is
the
upper
part
to
make
a
double
round
whereof
the
distance
from
one
to
the
other
,
may
be
the
Projector
of
the
base
,
and
the
round
from
within
the
plane
of
the
shaft
of
the
Column
,
from
which
they
shall
raise
the
Perpendicules
.
The
third
marked
O
,
is
a
Column
with
its
Ornaments
which
every
one
may
make
at
his
pleasure
,
and
we
must
take
notice
that
the
uppermost
square
of
the
Capital
answer
to
the
Plinthe
or
top
of
the
basie
,
Of
Cornishes
and
Mouldings
in
Perspective
.
IN
pursuit
of
Columns
,
which
are
the
principal
Ornament
of
Architecture
,
we
will
set
the
Cornishes
or
Mouldings
,
with
their
Projectors
,
which
we
have
not
set
hitherto
,
for
fear
of
giving
confusion
to
the
Elevations
,
which
it
behoveth
to
be
understood
with
clearness
and
easiness
.
It
is
true
that
there
are
not
many
Buildings
made
,
which
have
not
some
few
Mouldings
and
Projector
for
their
Ornament
,
for
to
make
them
more
pleasing
to
the
eye
:
where-I
thought
fit
to
set
here
the
manner
,
not
of
framing
them
,
seeing
that
dependeth
on
the
pleasure
of
every
one
,
nor
to
give
them
their
Measures
and
Projectors
,
for
that
were
to
oblige
my self
to
sit
down
here
,
the
Orders
of
Architecture
,
and
a
thousand
other
Inventions
of
Ornaments
,
which
one
may
finde
elsewhere
,
and
which
I
suppose
are
known
.
But
only
to
set
them
into
Perspective
,
according
to
the
Orders
following
,
when
any
shall
have
occasion
for
such
an
Order
.
For
to
set
then
the
Ornaments
for
a
Pilaster
in
Perspective
,
we
must
take
the
Measures
upon
the
middle
line
of
some
other
with
its
Ornaments
,
as
is
A
B
,
of
which
having
taken
the
bredth
,
and
made
a
square
Plane
in
the
ordinary
way
;
and
from
this
square
to
elevate
from
all
the
Angles
Perpendiculars
,
we
shall
frame
the
body
or
solid
part
of
the
Pilaster
.
Then
we
must
only
take
that
which
projects
it self
from
the
body
;
for
example
,
the
base
of
the
Pilaster
C
,
and
transport
its
measures
as
in
D
E.
for
to
set
it
in
Perspective
round
about
the
Pilaster
:
we
must
from
the
point
of
distance
F
draw
a
line
Diagonal
,
which
passeth
forth
of
the
square
to
the
point
E
unto
G
,
it
is
no
matter
for
the
length
:
Then
from
the
point
A
to
make
a
Ray
passing
to
the
lower
part
of
the
Projector
H
;
and
at
the
point
where
this
Ray
shall
divide
the
Diagonal
at
I
,
it
shall
be
the
advancement
of
the
whole
base
:
the
same
Ray
A
H
shall
give
the
Projector
of
the
bottom
,
by
dividing
the
other
Diagonal
at
the
point
K
:
Then
for
the
Projector
before
,
we
must
from
the
point
I
draw
a
Parallel
to
the
base
,
until
that
it
divide
the
Diagonal
,
which
shall
give
the
other
Corner
of
the
Projector
before
at
the
point
L
;
then
drawing
lines
of
the
height
of
the
Base
unto
these
points
,
as
are
M
to
L
,
from
D
to
I
,
from
N
to
K
,
you
shall
have
the
bredth
and
the
hight
of
all
the
Base
;
The
Capitall
is
made
of
the
same
fashion
.
Here
is
for
the
first
figures
above
.
Those
below
shall
Cause
the
rest
to
be
known
,
and
shall
avoid
Confusion
.
For
the
Pilasters
O
,
we
must
observe
that
above
P
,
where
the
line
D
H
,
bereth
all
the
sections
of
the
base
;
Wherefore
from
the
point
of
sight
A
,
we
must
draw
Rays
,
the
which
passing
by
the
divisions
of
D
H
,
must
marke
them
upon
the
lines
D
I
,
and
N
K
;
And
drawing
Parallels
from
the
points
of
D
I
,
to
M
L
,
there
will
be
no
more
then
to
give
the
Turnings
about
,
or
wheelings
as
the
shape
of
the
Colum.
When
you
shall
meet
with
squares
,
or
Flat-bands
,
either
above
or
below
they
are
made
by
Perpendicular
.
As
for
to
make
the
Plinth
,
you
must
raise
Perpendiculars
from
the
Points
L
I
K
;
the
from
the
point
of
sight
A
,
to
pass
by
the
Corner
of
the
Plinth
Q
,
it
will
give
the
height
upon
the
Perpendicules
I
,
and
K.
Then
L
must
be
equall
to
L.
I
beleeve
that
this
Instruction
for
the
Base
,
will
suffice
for
to
make
the
Capitall
being
the
same
Order
.
This
last
Pilaster
R
,
is
only
for
to
cause
one
to
be
seen
without
being
mingled
with
lines
.
We
have
broken
them
,
for
to
make
the
Bases
and
Capitall
to
be
seen
,
not
having
had
space
Enough
for
to
make
them
appeare
whole
,
A
great
Cornish
above
the
Horizon
in
Perspective
.
IT
is
the
same
Order
with
that
which
we
have
explained
,
but
as
it
is
somewhat
difficult
by
the
multitude
of
lines
,
I
thought
it
convenient
to
set
it
down
again
here
,
for
to
avoid
confusion
.
I
say
then
,
that
having
taken
the
pourfill
of
the
Projector
and
the
Cornish
,
that
one
would
make
,
we
must
set
it
at
the
place
,
where
one
would
make
it
,
as
C
which
is
the
pourfill
is
at
the
corner
of
the
Wall
A
B
,
for
to
find
the
height
which
it
ought
to
have
,
and
to
make
those
below
seen
,
we
must
from
the
point
of
sight
D
,
draw
a
Ray
passing
by
the
end
of
the
pourfill
E
,
as
is
D
F
;
then
to
make
a
line
Diagonal
from
the
point
of
distance
H
,
passing
by
the
corner
of
the
Wall
B
,
and
to
continue
it
until
that
it
divide
the
Ray
D
E
at
the
point
F
,
from
which
you
shall
draw
the
line
F
G
,
which
must
be
the
Angle
in
Perspective
,
for
to
receive
all
the
measures
F
G
,
the
corner
of
the
other
end
of
the
Wall
K
L
,
is
drawn
from
the
other
distance
I
,
as
being
the
other
Diagonal
.
In
the
figure
marked
2.
we
shall
see
,
that
all
the
figures
which
are
upon
the
line
M
N
,
must
be
transported
by
visual
Rays
from
the
point
of
sight
D
,
upon
the
line
N
O
,
for
to
draw
Parallels
to
the
Horizon
from
all
these
points
,
which
shall
give
the
whole
Cornish
perfect
.
But
before
we
pass
any
further
,
we
must
mark
,
as
I
have
already
said
,
that
all
the
flat-bands
and
squares
are
made
by
Perpendiculars
.
For
example
,
for
to
make
this
great
square
of
the
Cornish
,
having
made
the
Wave
or
Ogee
,
and
the
filet
under
the
filet
,
which
must
be
the
height
of
the
square
,
we
must
abase
the
Perpendicule
,
P
Q.
Then
for
to
know
where
it
must
be
divided
for
to
make
the
under
part
be
seen
,
we
must
draw
from
the
point
of
distance
I
,
by
the
point
above
the
quarter
of
the
round
R
,
unto
the
Perpendicule
P
Q.
and
you
shall
have
that
which
you
seek
.
That
which
I
have
said
of
the
great
square
,
must
be
understood
of
little
ones
,
as
are
small
mouldings
,
the
filets
,
&c
because
that
they
must
all
make
that
below
to
be
seen
.
The
third
figure
sheweth
,
that
having
found
all
the
points
,
and
drawn
Rays
upon
this
line
,
from
the
Angle
S
T
,
we
must
there
trace
out
or
shape
the
mouldings
out
proportionally
:
I
mean
,
that
when
these
shall
project
themselves
,
as
this
here
doth
,
because
that
its
point
of
distance
is
near
,
we
must
help
the
mouldings
,
that
is
to
say
,
a
little
bend
down
the
quarter
of
the
Round
,
set
up
the
Ogee
,
enlarge
the
filets
,
and
mark
at
one
end
the
same
that
at
the
other
;
as
at
V
X
,
the
same
that
at
S
T
after
that
,
there
is
no
more
but
to
draw
parallels
to
the
base
,
and
all
shall
be
done
The
fourth
figure
sheweth
the
Cornish
wholly
made
:
I
have
drawn
parallels
from
all
the
points
of
the
line
of
the
Angle
Y
Z
;
I
have
made
an
end
of
the
Wall
to
pass
upon
the
Cornish
,
for
to
give
to
understand
,
that
one
hath
liberty
for
to
make
it
throughout
,
and
that
our
rule
is
general
for
to
make
it
where
they
would
.
For
to
find
the
under
parts
of
the
Great
Projectors
.
FOR
to
find
the
Projector
of
the
Crown
of
the
Body
,
or
of
the
Wall
A
;
We
must
from
the
Corner
of
the
quarter
of
the
round
B
,
make
as
small
line
of
the
length
that
one
would
have
that
it
come
forth
,
as
is
B
C
,
then
from
the
point
of
sight
D
,
to
draw
a
Ray
,
E
,
passing
by
the
end
of
the
Measure
C.
After
that
you
make
a
Diagonall
from
the
distance
F
,
and
make
it
to
pass
by
the
quarter
of
the
Round
B
,
and
the
section
that
it
shall
make
at
the
Ray
D
E
,
at
the
point
G
,
that
shall
be
the
under
part
,
aswell
of
the
bottome
as
of
the
side
,
as
is
B
H
,
the
which
one
may
see
more
cleerly
in
the
opposit
,
in
the
body
marked
K
The
Projector
of
the
Body
,
or
Wall
marked
L
,
is
made
as
the
first
marked
A
:
There
is
only
this
difference
,
that
the
Body
L
,
hath
the
Projector
M
N
,
greater
by
one
half
,
then
that
above
B
C
,
for
to
Shew
that
by
the
same
Order
,
one
may
make
as
great
,
and
as
short
,
as
one
will
.
One
may
observe
further
in
this
same
Body
L
,
how
we
must
find
the
Return
of
the
Project
,
and
of
the
Hollow
;
we
must
from
a
quarter
of
the
Round
of
the
bottom
of
the
wall
at
the
point
O
,
draw
a
Diagonal
to
the
distance
opposite
P
;
and
the
section
of
this
line
upon
the
Ray
E
D
,
shall
be
the
point
for
to
make
a
little
Parallels
to
the
Horizon
R
Q
,
which
shall
be
that
which
was
demanded
.
This
may
serve
for
all
the
squares
,
which
are
met
with
in
Cornishes
and
Mouldings
as
well
great
,
as
little
.
The
Body
,
or
Wall
,
marked
S
,
maketh
the
Mouldings
of
the
Body
I
,
to
be
seen
cleerly
.
Of
the
Cornishes
and
Mouldings
under
the
Horizon
.
THE
Orders
are
the
same
with
the
foregoing
:
But
because
of
an
Accident
which
hapneth
sometimes
by
the
diversity
of
Horizons
one
might
be
in
some
trouble
,
not
knowing
the
reason
wherefore
that
cometh
to
pass
,
I
say
then
,
that
when
we
see
Cornishes
,
which
are
below
our
eyes
,
and
by
consequence
below
the
Horizon
;
the
Advancings
which
the
Projectors
cause
,
do
hide
from
us
,
sometimes
the
half
,
and
sometimes
less
or
more
,
according
as
one
is
raised
above
them
.
For
to
finde
justly
that
which
should
be
covered
,
and
that
which
should
not
be
,
we
must
set
,
as
we
have
said
,
the
Pourfil
or
Mid-line
of
the
Moulding
at
the
Corner
of
the
Body
which
we
would
adorn
,
and
having
found
the
line
of
the
Angle
,
as
we
have
said
in
the
Orders
aforegoing
,
there
we
must
draw
the
divisions
of
the
Pourfil
;
and
we
shall
finde
that
the
square
or
the
flat-band
,
will
wholly
cover
the
Astragal
or
small
Boultel
below
,
or
the
demi-round
,
and
will
suffer
but
the
half
of
the
Filet
to
be
seen
;
As
is
to
be
seen
,
that
having
drawn
a
line
from
the
point
of
sight
A
,
by
the
Pourfil
B
C
,
it
divideth
the
Perpendicular
of
the
line
of
the
Angle
at
the
point
D
;
which
maketh
known
that
which
ought
to
be
covered
;
for
the
moulding
below
,
it
is
the
same
thing
with
the
Orders
foregoing
.
1.
fig.
2.
fig.
For
Cornishes
with
many
Returns
.
WHEN
there
are
many
Returns
in
the
Cornishes
or
Mouldings
,
they
must
always
take
their
under-parts
from
the
points
of
the
distances
,
as
may
be
seen
,
that
having
drawn
the
Rays
A
and
B
,
at
the
point
of
sight
E
:
We
must
from
the
point
of
distance
C
or
D
,
make
a
Diagonal
passing
by
the
corner
of
a
quarter
of
the
Round
O
,
until
that
it
divide
the
Ray
A
or
B
at
the
point
I
,
from
the
which
point
I
we
must
make
a
Parallel
to
the
base
,
for
to
have
the
under-part
,
or
the
Projector
of
the
square
,
even
as
I
have
said
at
fol.
98.
I
would
willingly
have
made
a
greater
Cornish
,
seeing
that
it
would
not
have
bin
more
difficult
,
but
the
paper
hath
obliged
me
to
content
my self
with
this
.
If
one
would
make
Returns
by
the
Ground
,
as
these
are
upon
the
Horizon
,
he
must
observe
the
same
Order
;
And
for
proof
of
that
which
I
say
,
turn
this
Paper
upside
down
,
and
you
shall
see
the
same
effects
.
For
the
Openings
of
Doors
in
Perspective
.
SEeing
that
hitherto
we
have
followed
very
near
the
Order
which
they
keep
in
raising
of
Buildings
;
whatsoever
they
be
,
we
ought
to
follow
in
teaching
the
manner
of
Garnishing
them
,
and
making
them
fitting
for
to
lodge
in
:
I
will
begin
by
the
doors
of
wood
;
afterwards
we
will
speak
of
other
Openings
,
as
of
Windows
,
Cupboards
,
Chests
,
&c.
Then
of
Moveables
,
Tables
,
Beds
,
Chairs
,
Coffers
,
Settles
,
Benches
,
&c
,
All
the
doors
,
which
are
made
for
to
open
and
shut
,
depend
of
the
Will
of
every
one
,
who
may
open
them
more
or
less
,
as
he
pleaseth
;
wherefore
I
will
teaeh
to
set
them
into
Perspective
,
at
such
opening
as
one
would
have
.
We
must
observe
that
the
Doors
,
Windows
,
Cupboards
,
Chests
,
and
in
short
all
things
that
may
open
and
shut
,
do
make
always
a
demi-round
in
their
whole
opening
.
The
reason
is
,
that
the
side
which
is
fastned
by
the
hinges
or
hooks
,
doth
not
stir
from
its
place
;
and
the
other
side
moveth
and
maketh
a
demi-Circle
,
as
a
pair
of
Compasses
would
do
.
For
example
,
in
the
Plane
under
the
Figure
,
if
the
side
fastned
be
at
the
point
A
,
and
the
other
side
at
B
,
if
you
would
open
the
door
fully
,
the
side
B
shall
make
the
demi-round
B
C
D
,
whereof
the
center
shall
be
A
,
as
one
may
see
:
from
whence
one
may
know
,
that
if
the
door
hath
theee
feet
of
bredth
,
as
these
have
;
it
shall
have
also
three
feet
for
its
Diameter
A
C
;
And
6
feet
for
the
Diameter
entire
B
A
D
,
of
which
six
feet
in
length
,
and
3
of
bredth
,
we
must
make
a
Plane
of
18
little
squares
,
for
which
we
shall
make
the
demi-round
A
B
C
D
,
for
to
give
a
facility
to
make
the
same
demi-rounds
in
the
Perspective
.
by
observing
where
the
demi-round
of
the
Plane
divideth
the
little
squares
,
for
to
divide
in
the
same
proportion
those
of
the
Perspective
,
and
there
to
make
a
demi-round
,
which
shall
take
up
as
many
of
the
little
squares
,
and
shall
divide
them
in
the
same
place
,
as
we
see
at
the
door
E
,
where
the
sections
are
marked
,
as
in
the
plane
below
1
,
2
,
3
;
4
,
5
,
6
,
7.
When
one
would
make
an
open
door
in
Perspective
,
he
must
upon
its
Plane
make
a
demi-round
;
then
to
set
the
point
of
the
opening
in
what
place
he
will
,
upon
this
demi-round
;
as
for
the
door
E
,
the
point
of
the
opening
is
at
the
point
2.
from
this
point
2
,
he
must
elevate
a
Perpendicular
2.
H.
And
again
from
the
same
point
2
,
draw
a
line
passing
by
the
corner
of
the
door
F
,
and
continue
it
until
that
it
divide
the
Horizon
which
is
at
the
point
G
,
from
which
he
must
draw
another
line
,
making
it
to
pass
by
the
other
corner
of
the
door
I
,
and
to
continue
it
till
it
divide
the
Perpendicule
raised
from
the
point
2
,
which
shall
be
at
the
point
H
,
and
you
shall
have
the
door
open
,
as
is
F
I
H
,
2.
All
the
Openings
are
made
by
the
same
Rules
,
as
are
seen
by
the
doors
K
and
L
;
the
door
K
sheweth
its
out-side
,
and
the
door
L
sheweth
its
inside
;
nevertheless
,
the
one
and
the
other
are
ordered
in
the
manner
as
the
first
;
the
point
accidental
of
K
is
the
point
M
,
within
the
Horizon
.
And
that
of
the
door
L
is
O.
If
one
make
to
these
doors
,
barrs
,
locks
,
and
such
like
things
,
they
must
be
drawn
from
the
same
accidental
point
,
as
the
barr
and
the
lock
of
the
door
L
,
draw
to
the
point
O.
These
are
the
points
which
they
call
Accidental
,
as
I
have
expressed
in
the
beginning
of
our
Orders
,
and
all
the
Openings
make
but
one
within
the
Horizon
,
except
two
sorts
of
Openings
.
The
one
when
the
door
is
wholly
opened
,
for
then
it
hath
its
point
at
the
point
of
sight
,
because
it
is
at
the
wall
.
The
other
,
when
it
is
Parallels
to
the
Horizon
,
because
the
Parallels
never
divide
themselves
but
are
drawn
right
,
as
is
the
door
N.
For
the
Openings
of
Windows
in
Perspective
.
ALL
the
difference
that
there
is
in
the
openings
of
windows
,
from
those
of
the
doors
,
is
,
that
the
doors
have
the
demi-round
of
their
opening
upon
the
Plane
,
and
the
windows
have
it
in
the
Air
:
by
reason
that
the
windows
make
their
Openings
being
elevated
from
the
Ground
,
and
the
doors
do
grate
upon
it
:
wherefore
we
must
make
this
demi-round
above
or
below
the
windows
;
and
within
this
demi-round
to
take
the
point
for
to
open
them
.
For
example
,
if
the
side
of
the
window
hath
2
small
squares
of
bredth
,
as
A
B
,
and
that
one
give
it
its
whole
opening
,
it
will
take
up
two
more
squares
C
A
,
whereof
A
is
the
middle
,
and
the
center
of
the
demi-circle
A
B
C.
But
by
reason
that
the
windows
are
elevated
from
the
Ground
,
the
demi-round
also
must
be
elevated
,
as
they
are
here
above
the
windows
from
the
corners
D
and
E
,
which
are
the
centers
of
these
demi-rounds
,
which
shall
be
easily
framed
,
raising
Perpendiculars
from
the
squares
,
which
are
between
C
and
B
,
until
that
they
divide
the
Rays
,
which
pass
by
the
corners
of
the
windows
D
E.
And
from
these
sections
you
must
draw
to
the
base
,
and
give
them
the
measures
of
the
little
squares
of
the
plane
1
,
2
,
3.
from
which
points
1
,
2
,
3.
on
high
,
you
must
draw
lines
to
the
point
of
sight
F
,
which
shall
divide
the
Parallels
of
points
,
and
frame
the
little
squares
,
for
to
make
the
rounds
of
the
openings
,
which
shall
be
taken
in
the
same
manner
as
at
the
doors
;
as
if
one
give
within
the
highest
demi-round
the
point
G
,
for
the
point
of
the
opening
from
this
point
G
,
you
must
draw
2
lines
,
the
one
which
falleth
plumbe
G
H
,
the
other
which
passeth
by
the
corner
of
the
window
E
,
for
to
divide
the
Horizon
where
it
can
,
which
is
here
the
point
I
;
from
this
point
I
you
must
also
a
line
by
the
corner
of
the
window
K
,
until
that
it
divide
the
line
plumb
at
the
point
H
,
which
shall
give
the
window
open
K
E
G
H
;
we
must
do
the
same
of
all
the
others
,
and
take
the
point
within
the
Horizon
;
as
L
is
the
point
for
the
window
M
;
and
N
is
that
of
the
window
O.
The
window
P
hath
none
,
being
Parallel
to
the
Horizon
.
The
windows
which
are
opposite
are
made
by
the
same
method
,
without
the
confusion
of
lines
,
the
one
and
the
other
are
equal
with
the
wall
,
for
to
facilitate
the
ordering
thereof
.
The
door
at
the
bottom
is
made
as
we
have
said
,
and
the
window
followeth
the
Method
of
these
.
For
the
Opening
of
the
windows
with
Chamfrettings
.
THE
Order
of
this
is
as
the
others
upon
the
side
of
the
wall
,
except
that
these
cannot
be
opened
wholly
,
by
reason
of
the
thickness
of
the
Chamfring
;
which
causeth
,
that
the
whole
demi-circle
is
not
allowed
,
but
as
much
as
the
opening
can
have
of
it
.
They
ought
always
to
take
their
point
within
the
Horizon
,
as
we
see
Q
and
R
,
for
the
opening
of
the
windows
on
high
;
that
below
is
Parallel
to
the
Horizon
.
Of
divers
other
Openings
.
THE
Openings
of
Cupboards
and
of
Chests
,
are
at
least
as
Necessary
,
as
those
of
Doores
,
and
Windows
;
and
the
fault
would
not
be
less
to
forget
these
,
then
not
to
set
down
those
.
Let
us
see
the
Order
in
these
two
Figures
.
The
Cup-boards
A
,
are
opened
according
to
the
Orders
of
the
Windows
,
and
it
would
be
loss
of
time
to
busie
Ones-self
in
repeating
them
here
,
we
are
to
observe
only
,
that
one
height
is
Parallel
to
the
Horizon
,
and
the
other
below
draweth
to
the
point
of
distance
B.
This
Manner
of
Shop
,
which
is
on
the
other
side
,
hath
its
Opening
with
two
Shuts
,
whereof
one
is
lifted
on
high
,
and
the
other
cometh
down
below
,
and
each
maketh
its
demi-round
from
the
Center
C
and
D
which
one
maketh
with
the
Compasses
then
we
may
take
the
Openings
where
we
will
,
as
here
at
the
point
E
,
from
which
we
draw
a
Ray
to
the
point
of
sight
F
,
untill
we
divide
the
demi-rounds
of
the
other
end
,
at
the
point
G
,
from
which
points
E
G
,
we
must
draw
to
the
Centers
C
D
,
for
to
have
the
Shuts
,
which
close
up
the
Shop
as
we
see
.
In
the
figure
below
,
there
are
3
Chests
opened
several
ways
for
to
open
the
first
H
,
I
have
made
the
quarter
of
a
round
M
,
in
Perspective
,
following
the
Measure
of
the
little
squares
of
the
Plane
,
keeping
the
bredth
of
the
Chest
,
as
this
is
of
2
little
squares
,
from
which
we
must
raise
Perpendiculars
,
and
thereof
frame
the
half
or
quarter
of
a
Round
,
for
the
opening
which
we
may
take
at
pleasure
,
as
here
the
point
N
,
from
which
we
must
draw
a
Parallel
unto
the
other
quarter
of
the
round
O
,
and
from
these
2
points
N
O
,
to
draw
to
the
Center
P
,
If
we
would
open
it
wider
,
we
must
make
a
demi-round
instead
of
a
quarter
.
The
Chest
I
,
is
the
most
easie
of
all
the
Openings
;
for
having
taken
the
bredth
of
the
Chest
Q
R
,
we
must
from
the
center
R
,
make
with
the
Compasses
the
demi-round
Q
S.
Then
to
take
what
opening
you
will
,
as
T
,
and
to
draw
a
Ray
to
the
point
of
sight
V
,
which
shall
divide
the
other
demi-round
at
the
point
X
,
and
from
these
2
points
T
X
,
to
the
corners
R.
He
that
would
open
them
further
,
hath
but
to
set
the
point
of
the
opening
higher
,
within
the
demi-rounds
as
Y
,
is
to
the
Coffer
K
;
All
the
rest
is
ordered
like
as
in
the
Coffer
I
,
as
one
may
see
.
Of
planes
,
and
the
first
elevations
of
moveables
.
I
Had
set
these
planes
in
their
order
,
among
the
others
,
had
there
not
been
one
consideration
,
which
made
me
defer
them
until
now
,
which
is
,
that
if
I
had
handled
them
in
the
beginning
,
without
making
known
the
necessity
thereof
,
they
would
have
been
also
too
soon
forgot
and
held
as
unuseful
:
they
are
now
more
seasonable
,
and
without
doubt
they
will
be
well
received
,
pleasing
,
and
learned
with
pleasure
,
seeing
there
are
not
only
moveables
,
nor
peices
of
houshold-stuff
,
which
depend
not
thereon
.
The
first
plane
A
,
serveth
for
Beds
,
Tables
,
Chairs
,
Stools
,
low
Stools
,
&c.
The
other
B
,
which
beareth
in
length
,
two
times
its
breadth
,
serveth
for
long
Tables
,
Cabinet
,
Court
Cup-boards
,
Coffers
,
Trunks
.
The
third
C
,
which
is
long
and
narrow
,
serveth
for
Benches
or
Forms
,
and
other
things
which
have
need
of
six
Feet
,
or
Pillars
,
as
great
Tables
,
and
Cup-boards
.
The
knowledge
that
one
hath
of
other
planes
,
will
give
the
facility
of
making
these
,
seeing
there
is
nothing
but
to
set
their
measures
upon
the
base
,
to
draw
them
to
the
point
of
sight
,
and
to
abridge
them
by
the
points
of
distances
.
For
example
,
for
the
plane
A
,
you
must
set
upon
the
base
these
two
measures
D
E
,
and
draw
them
to
the
point
of
sight
F
,
then
from
one
of
the
distances
,
you
must
draw
to
one
of
these
measures
,
as
here
E
,
to
the
distance
G
,
and
where
that
shall
divide
the
Rayes
at
the
points
H
I
,
you
must
draw
parallels
,
for
to
frame
the
4
little
squares
,
which
one
may
make
to
be
for
as
much
,
or
as
little
as
he
will
.
Because
for
a
Table
,
they
must
be
of
more
bigness
then
for
a
settle
or
stool
,
that
is
to
say
,
that
they
must
have
more
breadth
,
for
if
for
this
we
allow
2
inches
,
for
that
there
must
be
four
.
The
plane
B
,
is
made
of
the
same
manner
,
except
that
by
reason
of
its
length
,
which
is
the
double
of
the
breadth
,
we
must
draw
from
the
point
B
,
to
one
of
the
distances
,
for
to
find
the
half
K
,
for
if
one
should
draw
from
the
point
L
,
he
would
divide
at
the
point
M
,
which
would
be
the
whole
square
;
and
we
would
have
but
the
half
:
Wherefore
from
the
point
K
,
we
must
draw
parallels
to
the
sections
of
the
Ray
;
and
from
the
corner
L
,
we
shall
divide
also
the
Ray
for
the
first
squares
at
the
point
N.
The
other
plane
C
,
hath
no
need
of
explication
;
for
we
see
well
,
that
it
is
made
as
that
A
,
and
that
you
must
double
the
square
for
to
have
6
little
squares
.
We
see
at
the
figure
below
,
that
from
all
the
Angles
of
these
squares
,
you
must
raise
Perpendiculars
for
to
begin
to
give
the
frame
to
the
pieces
that
we
shall
make
hereafter
.
Of
the
Elevation
of
Moveables
.
HAving
raised
the
Perpendiculars
of
the
Plane
,
as
aforesaid
,
we
must
in
some
Place
of
the
Picture
make
the
line
of
Elevation
,
upon
the
which
we
shall
set
the
cross-lines
or
Travers
,
and
the
height
that
one
would
give
them
.
For
example
,
the
line
C
D
shall
be
the
line
of
Elevation
,
and
C
E
and
D
F
shall
be
the
bredths
for
the
Travers
;
from
all
these
four
points
,
we
must
draw
in
some
place
within
the
Horizon
,
as
here
at
the
point
G.
Then
having
from
the
Planes
A
B
,
raised
the
Perpendiculars
from
all
the
Angles
,
we
must
from
the
same
Angles
draw
Parallels
to
the
base
unto
the
Ray
C
G
,
which
is
the
bottom
of
the
line
of
Elevation
,
which
will
give
the
points
1
,
2
,
3
,
4.
which
we
must
raise
into
Perpendiculars
;
and
the
sections
which
these
Perpendiculars
shall
make
,
at
the
Ray
C
E
,
D
F
,
shall
be
the
points
to
divide
the
Perpendiculars
of
the
Planes
,
whither
we
carry
them
with
the
Compasses
,
or
that
we
divide
them
with
Parallels
,
as
we
see
in
the
Figure
.
That
drawing
a
Parallel
from
the
point
E
,
we
shall
divide
the
first
Perpendicules
of
the
Planes
A
B
,
at
the
points
O
,
from
which
drawing
to
the
point
of
sight
H
,
we
shall
divide
the
other
Perpendiculars
of
the
Planes
at
the
points
P
;
and
doing
the
same
from
the
point
F
,
we
shall
frame
a
Cube
pierced
round
on
all
sides
,
or
composed
of
square
pieces
;
the
which
being
well
understood
,
we
shall
easily
make
all
the
Pieces
following
,
and
whatsoever
other
may
be
.
It
is
easie
to
see
that
the
two
frames
or
feet
of
the
Tables
I
and
K
,
are
made
by
the
same
Order
that
those
above
A
B
,
they
having
no
difference
but
in
the
Barre
below
,
which
is
more
elevated
in
the
line
of
Elevation
at
the
point
L
,
which
giveth
the
Barre
M
,
and
that
which
is
under
may
be
made
into
Bowles
,
or
to
leave
the
feet
square
as
they
are
.
For
the
latter
frame
N
and
Q
,
there
is
no
more
then
in
I
and
K
,
except
that
they
are
seen
by
the
Angle
,
and
the
others
are
seen
in
front
:
the
Planes
of
these
I
and
K
draw
to
the
point
of
sight
R
,
and
these
draw
to
the
distances
S
T.
These
Figures
shews
the
ordering
of
all
Pieces
of
Houshold-stuffe
;
for
example
,
if
of
the
Figures
I
or
K
,
we
would
make
a
bed
,
there
is
nothing
but
to
give
to
it
its
bredth
and
height
:
for
it
is
the
same
Order
in
all
the
rest
;
and
if
one
would
make
a
low
stool
or
flat
base
for
a
Table
;
there
is
nothing
but
to
make
that
above
for
a
stool
;
besides
that
above
,
we
must
give
it
more
height
then
bredth
,
but
all
the
rest
is
ordered
in
the
same
manner
.
For
to
make
the
upper
part
of
Tables
,
Stools
,
&c.
HAving
raised
the
Perpendicules
from
the
plane
,
as
we
have
spoken
,
and
given
the
height
,
that
we
would
they
should
have
,
we
shall
have
the
frame
,
for
to
make
there
an
upper
part
wholly
by
the
line
,
and
which
passeth
not
the
frame
;
we
have
only
to
leave
the
upper
part
of
the
cube
,
without
marking
any
thing
there
,
and
this
shall
be
the
uppermost
,
be
it
of
a
Table
,
Stools
,
low-stools
,
&c.
But
if
one
would
that
the
upper
part
should
have
any
Projector
or
Border
,
we
must
from
one
of
the
corners
of
the
Frame
,
or
foot
of
the
Table
,
draw
a
little
parallel
as
A
B
,
and
upon
this
parallel
set
th'
measure
of
the
Projector
one
would
give
it
,
as
we
have
set
here
A
B.
Then
from
the
distances
C
and
D
,
we
must
from
the
corners
of
the
square
made
of
points
,
which
is
the
breadth
of
the
Frame
,
or
feet
of
the
Table
,
draw
small
occult
lines
,
as
are
A
E.
Now
for
to
know
how
this
measure
A
B
,
shall
give
in
Perspective
the
breadth
equal
to
all
the
sides
,
and
corners
of
the
Table
;
We
must
from
the
point
of
sight
F
,
draw
a
Ray
,
passing
by
the
point
B
,
and
continue
it
until
that
it
divide
the
line
C
A
E
,
which
shall
be
at
the
point
G
:
from
this
point
G
we
must
make
a
parallel
which
shall
divide
the
other
occult
line
at
the
point
H.
Then
drawing
from
the
points
G
H
,
to
the
point
of
sight
F
,
we
shall
divide
the
other
lines
Diagonal
of
the
corners
at
the
points
L
and
K
,
and
then
we
shall
have
the
upper
part
of
the
Table
,
with
the
Projector
which
we
have
given
to
the
line
A
B.
For
the
thickness
of
this
upper
part
,
we
may
give
it
at
pleasure
.
This
order
may
serve
for
to
make
the
upper
parts
in
all
whatsoever
we
would
,
whether
they
be
above
or
below
the
Horizon
,
whether
they
be
on
the
front
,
or
sides
;
In
short
,
they
make
them
all
after
the
same
manner
.
For
to
Elevate
a
Court-Cupboard
and
Cabinet
.
HAving
made
the
Plane
,
and
Elevated
Perpendiculars
from
all
the
Angles
,
as
we
have
said
,
we
shall
set
upon
the
line
A
B
,
which
shall
serve
here
for
the
line
of
Elevation
,
the
Measures
that
we
will
give
,
as
well
to
the
distance
of
the
boards
,
as
in
their
thickness
,
as
are
C
D
E
,
from
the
which
points
C
D
E
,
we
must
draw
Parallels
to
the
Base
,
unto
the
other
Ascent
or
Column
F
G.
Then
from
the
points
which
shall
be
marked
upon
this
Ascent
G
F
,
we
must
draw
Rays
to
the
point
of
sight
H
,
unto
the
other
Ascent
of
the
Hollow
I
K.
This
Hollow
is
given
at
pleasure
,
setting
upon
the
base
,
that
which
we
will
give
it
;
for
example
,
for
to
have
the
hollow
or
bredth
of
this
Cupboard
,
I
have
set
the
Measure
F
L
,
from
this
point
L
,
we
must
draw
to
the
distance
M
,
and
where
the
Ray
F
H
shall
be
divided
at
the
point
L
,
that
shall
be
the
place
of
the
last
Ascent
.
The
Cup-board
which
is
over
against
on
the
other
side
,
is
ordered
in
the
same
manner
,
and
for
to
finde
the
Measure
of
this
little
Cabinet
which
is
in
the
midst
,
bore
up
by
two
little
Columns
,
we
must
take
the
points
L
P
,
which
are
in
the
midst
of
Q
N
,
and
the
bredth
of
the
little
Cabinet
,
and
draw
them
to
the
distance
O
;
and
where
the
Ray
N
H
shall
be
divided
,
we
must
draw
Parallels
to
the
base
,
which
shall
divide
the
Ray
T
H
at
the
point
V
,
from
which
raising
Perpendiculars
,
we
shall
have
for
the
little
Cabinet
of
the
middle
.
The
great
Cabinet
of
the
second
figure
,
are
of
the
same
Order
with
the
Court
Cup-boards
above
.
There
is
none
but
that
of
the
midst
,
which
is
at
the
bottom
,
which
we
must
a
little
explain
,
by
reason
that
it
is
of
the
front
,
and
that
one
might
be
in
some
trouble
for
to
determine
its
hollow
,
I
say
then
,
we
must
frame
its
Plane
,
as
we
have
said
heretofore
,
and
as
we
see
it
finished
in
the
half
;
for
to
give
it
the
Traverses
equal
to
the
first
in
the
fore-part
;
we
must
from
the
first
Ascent
R
,
draw
occult
Rays
to
the
first
Perpendicular
of
the
hollow
S
,
and
there
to
make
little
sections
,
from
which
we
must
draw
little
Paralels
to
the
base
;
and
we
shall
have
that
we
desire
.
For
the
Elevations
of
Chairs
.
FOR
to
elevate
a
Chair
,
you
must
of
the
Measures
A
B
C
,
make
a
Plane
by
the
ordinary
Rules
,
and
from
the
Angles
of
this
Plane
,
elevate
Perpendicules
,
and
follow
the
same
Method
that
we
have
given
,
speaking
of
the
feet
of
the
Table
,
or
of
the
frames
for
windows
,
without
the
upper
part
:
there
is
nothing
more
in
this
then
the
Back
of
the
Chair
,
which
one
may
make
of
such
an
height
as
they
will
:
here
it
is
the
height
of
A
,
unto
the
seat
K
,
and
this
height
is
as
well
for
the
single
Chairs
,
as
for
those
with
Rests
to
lean
on
.
We
see
sufficiently
by
the
Figure
,
that
for
to
make
them
with
backs
,
we
must
only
prolong
the
Perpendicules
of
the
Ascents
on
the
side
,
that
we
would
make
it
,
as
is
here
the
first
A
E
;
and
from
the
point
E
drawing
to
the
point
of
sight
G.
We
shall
divide
where
it
ought
the
Ascent
elevated
from
the
Plane
,
or
from
the
foot
H
,
which
shall
be
the
point
F.
The
rest
is
clear
enough
by
the
Figure
.
When
we
would
have
Rests
there
,
we
need
only
to
prolong
the
Ascents
before
,
as
they
have
made
these
behind
for
the
back
.
Then
to
make
there
a
Barr
which
serveth
for
a
Rest
,
as
is
L
M.
In
the
second
Figure
below
you
see
a
Form
or
a
Bench
garnished
with
carving
,
and
two
little
Couches
to
rest
in
,
whereof
one
hath
the
back
turned
on
this
side
,
and
the
other
view'd
obliquely
:
It
would
be
to
lose
the
time
to
instruct
how
to
make
them
,
seeing
that
the
Order
to
elevate
them
,
is
the
fame
with
the
foregoing
,
which
we
have
given
for
the
Moveables
,
which
is
,
that
having
made
the
Plane
,
we
must
elevate
Perpendiculars
,
&c.
One
other
fashions
of
Moveables
in
Perspective
.
CErtain
moveables
,
which
close
themselves
.
Those
which
they
make
to
serve
for
Seats
,
Tables
,
and
Beds
,
&c.
are
very
easie
to
set
into
Perspective
.
We
must
only
make
the
elevation
,
as
if
for
a
Cube
;
as
is
A
B
,
C
D
,
or
E
F
G
H.
Then
to
make
there
two
Diagonals
A
C
,
and
B
D
,
for
that
of
the
midst
of
the
Front
,
or
E
H
,
and
F
G
,
for
that
of
the
side
,
which
shall
serve
to
bring
in
the
2
crosses
,
to
take
notice
,
that
there
be
an
half
which
entreth
within
the
other
,
as
G
K
,
do
pass
within
H
I
;
and
the
one
and
the
other
are
fastned
by
the
midst
for
to
make
them
bend
.
In
this
piece
which
is
below
,
I
have
made
a
Table
upon
Tressels
,
that
we
may
have
the
smallest
moveables
for
to
set
them
into
Perspective
.
We
must
from
the
measures
A
B
,
which
is
the
interval
for
the
Feet
of
the
Tressels
,
draw
to
the
point
of
sight
C
:
Then
having
set
upon
the
base
the
thickness
of
the
same
Feet
,
as
are
D
and
E
,
we
must
draw
them
to
the
point
of
distance
F
,
and
observe
where
we
shall
divide
the
Ray
B
C
for
to
draw
little
parallels
to
the
base
,
which
shall
give
the
little
squares
,
or
the
planes
of
the
Feet
,
as
we
see
in
A
B
,
between
this
distance
D
and
E
,
we
must
set
the
breadth
,
which
we
will
give
to
the
top
of
the
Tressel
,
and
draw
it
to
the
distance
F
,
which
shall
divide
the
Ray
B
C
,
at
the
points
G
H
,
from
the
which
points
G
H
,
we
must
elevate
2
Perpendiculars
,
to
such
an
height
as
we
would
have
,
as
here
at
the
point
I.
Then
from
the
Angles
of
the
small
squares
of
the
plane
,
to
draw
lines
bending
unto
the
piece
I.
The
second
Tressel
is
ordered
all
alike
with
the
first
The
form
K
,
nor
the
Table
,
or
high
Stool
L
,
have
no
need
of
Explication
,
nor
Instruction
for
to
set
them
into
order
,
seeing
that
they
have
nothing
,
which
is
not
common
to
them
,
with
the
fore-said
pieces
.
Of
Moveables
set
without
Order
.
WHen
the
moveables
are
set
in
order
along
by
the
Wall
,
or
according
to
the
Rays
and
the
base
,
it
is
easie
to
set
them
into
Perspective
,
by
the
Rules
that
we
have
given
;
but
supposing
that
one
set
them
by
chance
,
and
without
order
,
as
these
are
,
we
must
do
as
I
shall
say
.
You
must
make
the
Geometrical
plane
R
S
T
,
for
the
plane
of
three
Chairs
,
which
you
must
abridge
by
the
Order
that
we
have
set
at
the
irregular
figure
,
Fol
40.
and
the
planes
shall
remain
turned
,
as
are
the
Chairs
,
or
rather
the
Chairs
turned
,
as
are
the
planes
.
I
say
then
,
that
having
set
these
planes
into
Perspective
,
as
it
is
taught
,
you
must
set
the
Rule
along
by
one
of
the
sides
,
for
to
see
what
accidental
point
,
you
shall
have
within
the
Horizon
:
For
example
,
having
set
the
Rule
along
by
the
side
A
B
,
I
shall
have
within
the
Horizon
the
point
C
,
for
the
accidental
point
,
at
which
we
ought
to
draw
all
the
lines
of
this
side
,
and
of
that
which
is
opposite
to
it
,
as
we
see
that
A
and
D
,
draw
to
the
same
point
C
:
It
is
true
that
every
plane
set
irregularly
must
have
2
;
But
they
meet
sometime
so
far
within
the
Horizon
that
it
is
a
hazard
when
one
can
find
them
both
together
These
have
each
one
within
the
Horizon
,
as
A
B
,
giveth
C.
A
D
,
which
is
the
other
side
,
should
give
another
point
,
but
our
paper
is
not
long
enough
.
E
F
,
giveth
G
And
H
I
,
giveth
K
,
for
these
small
squares
1.2.3.4
.
they
are
the
plains
of
the
Feet
of
these
Chairs
,
which
one
may
make
more
large
,
or
more
streight
,
at
the
pleasure
of
the
Artist
.
Now
from
these
planes
,
you
must
elevate
Perpendicules
from
all
the
Angles
,
and
set
on
the
side
a
line
of
elevation
M
N
,
upon
the
which
we
must
set
the
measure
for
the
Travers
,
as
O
,
shall
be
for
the
Bars
below
,
P
,
for
the
bars
of
the
seat
.
And
Q
shall
be
for
the
backs
of
the
Chairs
.
All
being
disposed
thus
,
we
must
from
the
Angles
of
the
plane
draw
parallels
to
the
base
,
unto
the
line
of
Elevation
,
and
at
the
section
to
elevate
Perpendicules
,
which
shall
give
the
measures
,
as
we
have
said
of
other
figures
heretofore
.
All
the
lines
of
the
sides
ought
to
draw
to
the
point
accidentall
of
the
plane
:
For
example
,
in
the
chair
of
the
midst
,
all
the
sides
ought
to
draw
to
the
point
G
,
which
is
the
point
of
the
plane
,
as
I
make
it
to
be
seen
in
the
figure
.
Of
Moveables
lying
or
thrown
upon
the
Ground
.
FRom
the
same
Plane
of
the
Chairs
aforegoing
,
which
are
upon
their
feet
,
it
is
easie
to
make
these
which
are
cast
upon
the
Ground
.
We
must
raise
Perpendiculars
from
all
the
Angles
of
the
Plane
,
and
give
to
the
Side
lying
the
same
Measures
,
as
to
the
side
upright
:
For
example
,
having
rais'd
Perpendiculars
from
all
the
Angles
of
the
Plane
,
we
shall
have
the
bredth
M
,
which
is
in
the
Chair
lying
upon
its
side
,
which
draweth
to
the
point
K
;
we
must
double
this
Measure
M
,
which
will
give
O
for
the
Barre
below
of
the
Chair
,
and
the
Perpendicules
elevated
from
the
Plane
,
will
give
the
Barr
of
the
Seat
P
;
from
which
drawing
to
the
point
K
,
we
shall
divide
the
other
Perpendiculars
of
the
front
at
the
place
that
it
ought
,
for
to
make
the
same
Barrs
appear
from
all
the
sides
whence
they
may
be
seen
;
for
the
height
of
the
back
of
the
Chair
,
there
is
but
only
to
give
to
it
the
same
Measure
that
the
Seat
hath
of
height
:
And
for
the
back
of
that
in
the
midst
,
you
must
double
the
Diagonal
on
the
Plane
,
and
take
notice
where
it
divideth
the
Rays
or
Ascents
lying
R
S.
the
rest
is
clear
enough
.
The
two
other
Pieces
which
are
under
the
feet
upwards
are
very
easie
to
make
:
the
one
draweth
to
the
point
of
sight
T
,
the
other
to
the
point
of
distance
V
X
,
the
line
of
Elevation
is
Y
Z.
The
Order
for
to
elevate
these
is
the
same
,
as
to
make
them
upon
their
feet
,
that
is
to
say
,
that
we
must
raise
these
Perpendiculars
from
the
Angles
of
the
Plane
,
and
from
the
same
Angles
to
draw
to
the
line
of
Elevation
,
which
will
give
the
Measures
which
we
must
give
to
every
Ascent
,
and
the
place
for
the
Travers
,
as
well
above
as
below
.
For
to
set
Altars
into
Perspestive
.
THE
Order
of
Altars
,
is
the
same
with
that
of
the
frames
of
a
long
Table
:
that
which
is
more
in
this
,
is
the
Round
of
the
midst
,
the
Borders
of
the
Table-cloth
,
and
the
Laces
which
shall
be
found
in
their
place
,
doing
that
which
followeth
.
First
,
for
the
body
of
the
Altar
,
which
we
see
in
front
there
is
no
difficulty
:
for
having
given
to
it
the
height
and
length
,
there
is
nothing
but
to
draw
from
all
the
points
above
the
base
,
to
the
point
of
sight
E
,
and
from
the
sections
that
these
points
shall
give
to
the
line
of
the
bottom
of
the
Altar
,
you
must
raise
Perpendicules
for
the
Round
of
the
midst
,
it
is
made
with
the
Compass
.
The
rest
is
clear
enough
within
the
Figure
.
For
to
make
an
Altar
on
the
side
,
we
must
set
the
bredth
and
height
,
which
we
should
give
it
at
the
place
where
we
would
begin
it
,
as
is
A
B
the
bredth
,
and
B
D
the
height
.
Then
from
B
D
and
C
to
draw
to
the
point
of
sight
E
,
seeing
that
B
F
is
the
length
of
the
body
of
the
Altar
,
and
that
we
would
give
the
same
to
this
,
we
must
from
the
point
F
draw
to
the
distance
G
,
and
take
notice
where
we
shall
divide
the
Ray
B
E
,
and
from
the
section
elevate
a
little
Perpendicular
,
until
that
it
touch
the
Ray
D
at
the
point
H
,
and
from
H
to
make
a
little
Parallel
,
which
shall
give
I
at
the
Ray
C
,
and
then
we
shall
have
the
upper
part
of
the
Altar
C
D
H
I
:
for
to
have
these
two
laces
which
are
on
one
part
,
and
the
other
of
the
Round
:
the
points
K
L
will
give
them
upon
the
Ray
B
E
,
by
drawing
them
to
the
distance
G
,
and
M
will
give
the
bredth
of
the
Borders
of
the
Table-cloth
;
and
having
taken
the
measure
B
M
,
we
must
bring
it
to
D
,
which
will
give
O
,
for
the
bredth
of
the
Border
of
the
Table-cloth
on
high
As
concerning
the
Round
,
I
will
not
repeat
that
,
for
I
have
spoke
of
it
elsewhere
,
where
any
may
have
learned
,
how
it
is
set
into
Perspective
,
it
is
enough
that
we
know
,
that
from
all
the
divisions
we
must
draw
to
the
distance
G
:
And
at
the
sections
of
the
Ray
B
to
raise
Perpendicules
;
then
to
take
these
same
Measures
,
and
transport
them
from
B
unto
O
,
as
are
P
;
And
from
all
these
Measures
to
draw
to
the
point
of
sight
E
,
and
to
observe
where
they
shall
divide
the
occult
Perpendiculars
,
for
to
make
by
these
points
a
crooked
line
,
which
shall
give
the
Rounds
in
Perspective
.
If
instead
of
these
laces
,
and
of
the
Round
,
there
were
an
Embroidery
,
we
should
use
the
same
Order
for
to
abbreviate
it
In
the
Figure
below
I
have
made
the
same
Altar
without
line
,
and
adorned
with
a
Cross
and
two
Candlesticks
;
for
to
finde
the
place
of
these
Candlesticks
,
we
must
prolong
the
line
of
the
corner
of
the
Altar
,
as
is
Q
R
;
then
from
the
distance
G
draw
a
line
by
the
corner
of
the
Altar
T
,
and
to
continue
it
until
that
it
divide
that
Q
R
;
and
this
line
Q
R
shall
be
the
length
of
the
Altar
,
equal
to
B
F
of
the
first
figure
,
upon
the
which
we
shall
set
the
Measures
of
the
Cross
and
of
the
Candlesticks
,
as
are
V
for
the
Cross
,
and
S
for
the
Candlesticks
;
from
all
these
points
S
V
we
must
draw
to
the
distance
G
,
and
take
notice
that
at
the
sections
of
the
Ray
Q
E
,
we
must
draw
little
Parallels
,
which
we
shall
divide
by
the
Ray
S
E
,
and
will
give
the
squares
above
the
Altar
X
for
the
Cross
.
We
must
leave
the
square
for
the
foot
,
and
from
the
midst
of
the
square
elevate
the
Cross
;
for
to
finde
the
Measure
of
the
Arms
of
the
Cross
,
we
must
from
the
corners
of
the
square
raise
the
occult
Perpendiculars
,
as
it
is
mark'd
Y
,
and
draw
to
the
point
of
sight
E
for
the
Candlesticks
Of
this
square
we
must
make
a
Round
;
and
observe
where
it
shall
divide
the
Diagonal
,
for
to
elevate
these
Perpendicules
,
which
shall
give
the
bredth
of
the
Basons
,
from
the
which
we
must
draw
to
the
point
of
sight
E
,
from
the
middle
square
or
round
foot
of
the
Candlestick
,
we
must
elevate
a
Perpendicular
for
the
Body
of
the
Candlestick
,
and
for
the
Taper
which
we
shall
make
as
high
as
we
will
:
for
to
proportion
it
,
we
must
from
the
top
of
the
first
draw
to
the
point
of
sight
E
,
the
rest
hath
already
been
said
:
the
Figure
will
cause
us
to
remember
the
Orders
.
Of
Merchants
Shops
in
Perspective
.
ORdinarily
Merchants
Shops
are
compassed
about
with
Shelves
or
Boxes
,
for
to
lay
there
and
keep
their
Merchandize
.
The
Rule
or
Order
for
to
make
these
Boxes
,
is
as
it
were
the
same
with
that
of
the
doors
and
windows
:
For
example
,
if
instead
of
the
thickness
of
the
Wall
,
in
the
order
of
the
windows
;
You
set
in
this
the
board
A
B
from
the
point
B
,
you
must
draw
to
the
point
of
sight
C
:
For
the
under
part
,
or
bottom
of
the
Boards
,
from
the
point
B
,
having
set
upon
the
base
the
distances
,
and
the
measures
of
the
Boards
,
or
ascents
E
F
G
,
you
must
from
these
3
points
draw
to
the
points
of
distance
D
,
which
shall
give
upon
the
Ray
B
,
the
section
H
I
K
,
for
to
raise
the
Perpendiculars
there
.
For
to
have
the
boards
a
cross
,
we
must
set
such
a
number
,
as
we
will
give
upon
the
board
A
B
,
or
only
upon
the
first
Perpendicule
B
O
,
as
are
the
measures
L
M
N
O
,
from
the
which
points
we
must
draw
to
the
point
of
sight
C
,
and
we
shall
have
the
boxes
in
the
section
of
the
Perpendicules
at
the
points
P
;
Then
from
the
same
section
P
,
we
must
draw
little
parallels
to
the
base
,
which
shall
give
the
corner
of
the
box
,
by
separating
the
side
from
the
upper
part
,
or
the
under
.
For
the
boxes
in
the
Front
,
there
is
nothing
but
to
draw
Rays
from
the
points
,
or
measures
E
F
,
and
at
the
section
of
the
line
of
the
hollow
K
Q
,
to
raise
Perpendiculars
R
S
;
And
for
the
Travers
to
draw
parallels
from
all
the
divisions
which
shall
be
found
upon
the
Perpendicule
K
,
as
are
P.
1.
P.
2.
P.
3.
P.
4.
For
the
boxes
of
the
other
side
,
where
there
are
ascents
in
square
for
to
uphold
the
boards
,
we
shall
have
their
breadth
,
drawing
to
the
point
of
sight
C
,
the
measures
T
G
,
and
for
to
have
their
plane
,
or
square
,
we
must
from
the
measures
A
E
F
,
draw
to
the
distance
V
,
which
shall
give
upon
the
Ray
T
C
,
the
section
,
X
Y
Q
,
by
the
which
we
must
draw
little
parallels
,
until
that
we
divide
the
Ray
T
G
,
at
the
point
Z.
and
from
the
Angles
of
these
little
squares
to
raise
Perpendicules
which
shall
be
the
ascents
:
as
we
see
clearly
in
the
figure
.
The
figure
below
sheweth
a
Shop
;
already
to
receive
such
moveables
;
as
one
would
put
there
,
and
to
furnish
the
Boxes
with
that
which
you
shall
please
.
For
a
Library
,
we
must
fill
them
with
Books
.
For
an
Apothecary
with
little
Boxes
,
and
Pots
.
For
a
Mercer
,
with
bundles
of
stuffs
.
In
short
,
for
all
that
you
would
,
according
to
their
occasions
.
Of
the
out-side
of
Buildings
.
HItherto
we
have
spoken
of
all
that
belongeth
to
the
in
side
of
houses
,
buildings
Churches
,
&c.
Now
we
will
give
some
orders
for
the
out-side
.
Many
of
the
Rules
and
Orders
,
that
we
have
given
for
the
in-side
of
Houses
,
may
serve
for
the
out-side
.
For
example
,
the
Rule
which
is
for
to
set
the
doors
and
the
windows
,
in
what
place
one
would
within
,
the
Wall
is
sufficient
alone
for
the
out-side
of
all
sorts
of
buildings
,
seeing
that
on
the
out-side
of
the
house
;
there
appeareth
no
other
thing
then
doors
and
windows
.
But
if
they
be
enriched
with
Ornaments
,
we
have
also
given
,
how
they
ought
to
be
set
into
Perspective
,
if
any
have
forgot
them
they
may
have
recourse
thither
.
When
there
are
Windows
in
front
,
as
A
,
and
that
one
would
set
them
in
a
return
;
which
have
the
same
measures
,
we
must
transport
these
measures
upon
the
base
,
as
are
B
B
B
,
equal
to
A
A
A
,
to
draw
them
to
the
point
of
distance
C
,
and
to
take
notice
where
they
shall
divide
the
Ray
D
E
,
at
the
points
F
,
and
from
these
points
to
raise
Perpendiculars
which
shall
be
the
ascents
of
the
windows
in
the
Return
.
For
the
Travers
,
we
must
continue
those
of
the
window
in
Front
,
unto
the
Perpendicular
D
,
which
shall
be
the
points
I
,
which
we
must
draw
to
the
point
of
sight
E
,
for
to
divide
the
Perpendicules
F
,
and
to
give
the
cross
bars
to
the
window
of
the
Return
.
When
there
shall
be
a
greater
number
of
Windows
,
there
shall
be
nothing
else
to
do
,
but
to
continue
their
Rays
,
for
to
give
them
the
same
measure
and
height
of
the
crosses
,
as
is
to
be
seen
on
the
other
side
,
at
the
house
which
hath
2
windows
,
by
the
means
of
the
same
Rays
For
the
breadth
or
thickness
of
the
Jawmbs
,
and
crosses
of
the
windows
in
Front
,
we
must
set
it
upon
one
of
the
Travers
,
as
it
is
at
that
below
K
H
,
and
from
the
corner
of
the
window
K
,
draw
to
the
point
of
sight
E
,
and
from
the
point
H
to
the
distance
C
,
for
the
window
A.
And
to
the
distance
L
,
for
that
of
the
other
side
,
and
at
the
section
of
these
two
last
lines
,
we
must
raise
a
Perpendicular
H
M
:
And
then
from
all
the
corners
of
the
window
draw
to
the
point
of
sight
And
from
the
sections
or
points
Q
,
which
they
shall
give
upon
this
Perpendicule
H
M
,
we
must
draw
parallels
,
which
shall
be
the
thicknesses
of
the
Crosses
,
or
Travers
:
The
thickness
of
the
Jawmbs
of
the
midst
N
,
shall
be
taken
drawing
from
the
corner
N
,
to
the
point
of
sight
:
And
where
we
shall
divide
the
thicknesses
of
the
Travers
at
the
point
Q
,
to
raise
a
Perpendicular
Q
R.
For
the
thickness
of
the
windows
in
Return
,
you
must
set
it
at
the
corner
of
the
Wall
,
upon
the
Perpendicule
D
,
as
is
the
distance
I
O
,
and
from
the
points
O
,
to
draw
to
the
point
of
sight
E
Then
to
make
little
parallels
from
all
the
corners
of
the
windows
as
S
T
,
which
shall
divide
the
Ray
O
,
and
shall
give
the
thickness
at
the
point
S.
These
rules
serve
for
all
sorts
of
windows
,
be
they
high
or
low
.
In
the
figure
below
,
we
may
see
a
door
abridged
by
the
order
that
we
have
given
elsewhere
:
as
also
all
that
is
there
,
is
easie
enough
to
understand
and
practice
by
the
instructions
afore-going
.
For
to
set
the
Roofs
of
Houses
in
Perspective
.
THE
Roofs
are
different
in
height
,
according
to
that
whereof
they
are
made
:
those
of
slate
are
the
most
right
;
their
ordinary
Measure
is
the
Triangle
Equilateral
,
that
is
to
say
,
that
the
bending
of
the
Roof
is
equal
to
the
bredth
of
the
house
,
as
one
may
see
by
the
little
Figure
that
I
have
set
the
lowest
,
that
C
A
or
C
B
is
equal
to
A
B
Others
set
this
br●d●h
A
B
,
for
the
middle
top
D
C
,
which
is
the
highest
,
but
that
is
not
so
ordinary
,
as
this
D
C
:
for
the
flat
Tyle
,
they
allow
but
the
two
thirds
of
the
height
of
those
of
Slate
,
or
of
the
bredth
of
the
house
,
as
one
may
see
A
E
B
:
for
the
Tha●ch
,
which
is
a
Covering
commonly
used
,
they
allow
but
the
half
of
the
bredth
,
as
if
A
F
B
And
for
the
hollow
Tyle
,
they
allow
only
a
third
of
the
bredth
for
the
descent
,
as
is
A
9
B
Before
we
pass
any
farther
,
we
must
know
that
which
I
call
the
middle
Top
,
are
Pieces
elevated
Perpendicularly
upon
the
Beams
which
bear
the
Ridg
where
all
the
rafters
do
meet
,
as
is
G
H
The
rafters
are
pieces
of
wood
that
give
the
descent
of
the
Roof
,
as
is
H
I.
The
other
Pieces
which
are
set
in
the
corner
,
and
which
go
unto
the
middle
Top
,
are
called
Stays
,
and
are
ordinarily
longer
then
the
Rafters
,
as
is
H
K.
Three
sorts
of
Roofs
are
in
use
,
Pavilions
,
Pynions
,
and
Appentis
,
or
Pent-house
like
The
Pavillions
have
four
sides
,
the
Pinions
have
but
two
,
and
the
Appentis
but
one
;
for
to
make
a
Pavillion
in
Perspective
,
we
must
know
the
place
of
the
Balls
or
middle
tops
,
for
to
draw
the
stays
thither
:
the
which
hath
made
me
make
this
Geometrical
Plane
L
M
N
O
,
for
to
shew
that
of
the
bredth
of
the
house
L
N
,
we
must
make
a
square
L
M
N
P
,
from
which
we
shall
draw
two
Diagonals
,
which
shall
divide
themselves
at
the
point
Q
:
some
set
the
Ball
at
this
point
Q
,
but
that
is
too
much
advanced
,
and
maketh
this
bending
of
the
end
lie
too
flat
:
it
hath
more
comeliness
when
it
is
straighter
;
wherefore
we
must
advance
it
towards
the
wall
L
N
,
by
the
third
part
of
the
distance
Q
R
,
which
shall
be
the
point
S
,
and
by
this
point
S
we
must
draw
a
Perpendicule
upon
the
line
N
P
,
which
shall
be
T.
Then
to
transport
these
Measures
L
T
and
T
M
,
upon
the
base
,
and
draw
them
to
the
point
of
distance
,
which
is
here
farther
off
then
ordinary
,
and
to
observe
where
they
shall
divide
the
Ray
V
;
and
from
the
sections
to
elevate
Perpendicules
unto
the
height
of
the
wall
,
which
shall
give
the
points
X
,
from
which
me
must
draw
Parallels
to
the
base
,
unto
the
other
Ray
I.
Then
from
the
midst
of
the
wall
Y
,
to
draw
to
the
point
of
sight
,
for
to
divide
those
Parallels
at
the
point
Z
,
and
from
these
points
to
elevate
the
Balls
;
for
to
give
the
height
to
these
Balls
,
we
must
know
wherewith
we
would
cover
them
,
and
according
to
that
to
give
them
the
Measure
that
we
have
spoken
of
,
supposing
that
it
be
of
Slates
;
we
must
of
the
bredth
of
the
wall
make
a
Triangle
equilateral
1
,
2
,
3.
And
from
the
point
3
to
draw
to
the
point
of
sight
,
and
to
divide
the
Ball
at
the
point
4.
At
which
point
4
we
must
draw
lines
from
the
corners
of
the
House
,
which
will
give
the
shape
to
the
Pavillion
For
the
Roofs
with
Pinions
there
is
not
so
much
to
order
,
we
must
only
of
the
bredth
of
the
wall
5
,
6
,
make
a
Triangle
equilateral
5
,
6
,
7.
and
as
much
on
the
other
end
of
the
wall
,
which
shall
give
the
point
8.
Then
to
joyn
this
7
and
8
,
the
Roof
will
have
its
shape
and
its
measure
.
The
Figures
on
the
other
side
do
shew
the
same
thing
,
without
being
confused
with
lines
:
This
projecting
which
goeth
beyond
the
Roof
,
is
made
according
as
one
will
.
This
House
on
the
Floor
is
covered
with
a
Pavillion
,
which
is
made
by
the
same
Orders
as
that
on
the
side
.
In
this
Figure
where
are
the
Letters
,
I
have
set
the
Horizon
on
very
high
,
for
to
make
the
upper
part
of
the
houses
to
be
seen
,
and
to
give
the
more
easiness
to
understand
the
Order
;
but
as
this
is
seldom
met
with
,
I
have
set
the
other
Figure
above
,
where
the
Horizon
is
low
,
as
it
is
ordinarily
,
which
nevertheless
is
not
therefore
any
other
Rule
for
to
make
the
Roof
,
then
that
below
,
as
one
may
see
by
the
Figure
.
The
rest
of
the
Roofs
in
Perspective
.
IN
the
figure
aforegoing
,
we
have
set
the
Roofs
with
small
Pinacles
view'd
in
front
,
to
which
we
must
give
the
Triangle
equilateral
for
their
height
,
when
we
do
make
them
of
slate
:
If
they
make
them
of
other
things
,
as
of
Tile
or
Thatch
we
must
take
their
measures
at
the
little
figure
below
.
For
to
set
this
fashion
of
Roofs
in
return
we
must
set
upon
the
base
from
the
foundation
of
the
house
,
the
breadth
that
it
hath
as
is
A
B
;
and
of
this
breadth
to
frame
a
Triangle
according
to
the
height
that
we
would
give
to
the
Roof
,
as
to
this
,
which
hath
a
Triangle
equilateral
,
whereof
C
D
,
is
the
height
which
must
be
set
Perpendicularly
at
the
first
corner
of
the
house
,
at
the
whole
height
of
the
Wall
as
is
E
F.
Then
to
take
the
breadth
of
the
house
C
,
which
is
the
midst
of
A
B
,
and
to
draw
it
to
the
distance
,
and
where
it
shall
divide
the
Ray
A
,
at
the
point
G
,
to
raise
a
Perpendicule
;
then
you
must
from
the
point
F
draw
to
the
point
of
sight
X
,
and
the
section
that
shall
be
made
of
the
Perpendicule
H
,
shall
be
the
point
of
the
Pinacle
,
to
which
you
must
draw
from
the
corners
of
the
house
E
I
,
if
one
would
have
there
any
advancings
,
he
may
set
them
there
at
his
pleasure
as
we
may
see
on
the
other
side
K.
For
the
sloping
we
must
only
prolong
the
line
where
one
would
set
the
top
of
the
Roof
,
as
is
here
the
line
L
M
,
and
to
give
it
such
a
bending
as
we
would
.
To
this
,
there
is
as
much
of
the
height
M
N
,
as
the
house
hath
of
breadth
N
O
,
if
from
the
points
M
O
,
we
draw
to
the
point
of
sight
X
,
we
shall
divide
the
Perpendicule
of
the
Hollow
at
the
point
P
Q.
which
we
must
joyn
with
a
right
line
,
which
shall
finish
the
framing
of
the
Roof
.
The
figures
of
the
other
side
make
the
house
covered
to
be
seen
after
these
fashions
.
The
figures
above
are
only
to
make
it
seen
,
that
we
must
always
keep
the
same
order
,
although
the
Horizons
change
.
I
have
set
a
Church
within
the
floor
;
which
is
covered
with
Pinacles
,
and
the
wings
of
the
two
bendings
,
which
have
only
the
simple
draught
.
There
is
also
a
Pavillion
seen
by
one
end
,
of
which
we
have
spoken
in
the
figure
preceeding
.
For
to
set
a
street
into
Perspective
.
IT
might
suffice
to
see
the
figure
,
for
to
know
the
order
thereby
which
is
very
easie
,
we
must
only
make
a
plane
of
single
little
squares
by
the
ordinary
way
,
and
to
take
one
square
,
or
2
or
3
for
the
bredth
,
or
length
of
every
house
;
And
upon
this
breadth
which
we
shall
take
,
to
set
the
measures
of
the
Doors
and
Windows
,
for
to
have
thereby
the
abridgement
,
by
drawing
to
the
point
of
distance
A
,
as
are
the
Measures
B
C
D
E
,
and
F.
The
first
Angle
of
every
house
may
serve
for
the
line
of
elevation
,
as
we
at
the
first
house
the
Angle
G
for
the
Roofs
;
we
have
said
already
,
how
they
ought
to
be
set
.
When
we
would
have
streets
going
a
cross
,
we
need
only
to
leave
1.
2.
or
3
little
squares
,
without
elevating
any
thing
,
even
as
are
H
and
I.
The
figure
below
is
to
shew
that
when
one
would
advance
,
or
draw
back
the
houses
;
we
ought
only
to
advance
,
or
draw
back
their
elevation
,
upon
the
plane
of
the
squares
,
as
L
,
is
more
advanced
by
one
square
then
K
,
and
M
more
advanced
then
L
,
and
so
of
others
,
and
for
the
rest
to
follow
the
Method
which
we
have
given
the
figure
above
,
to
that
below
.
That
the
Objects
afar
off
shew
not
the
Thickness
.
HE
that
practiseth
this
Art
shall
be
advertised
,
that
the
objects
neer
to
the
Horizon
,
that
is
to
say
very
much
distant
,
must
not
shew
the
Thickness
being
view'd
in
the
front
,
For
example
,
the
houses
,
A
B
C
D
,
ought
not
to
have
thickness
at
the
Windows
,
and
at
the
Door
;
But
only
a
single
draught
:
The
reason
of
this
is
that
the
Rays
which
part
from
the
Object
,
unite
themselves
in
the
Eye
with
those
that
are
Collaterals
.
I
would
have
brought
the
demonstration
of
this
,
if
I
had
beleeved
that
it
would
have
served
,
but
as
it
is
not
Necessary
for
my
design
,
and
that
it
would
be
unprofitable
,
I
have
let
it
alone
,
remembring
my self
,
that
I
promised
at
the
beginning
of
the
Book
that
I
would
not
give
any
,
seeing
that
I
have
to
do
with
many
persons
,
which
would
be
in
trouble
to
understand
them
.
For
the
Buildings
viewed
by
the
Angle
.
OF
these
two
buildings
view'd
by
the
Angle
,
that
of
the
first
figure
is
made
in
the
same
manner
,
as
we
have
said
of
the
little
squares
,
view'd
by
the
Angle
;
and
at
the
beginning
of
the
elevations
of
other
pieces
view'd
in
like
manner
.
But
to
avoid
the
trouble
to
run
back
to
the
one
,
and
to
the
other
:
I
will
say
,
that
for
to
make
these
buildings
,
we
must
always
set
the
measures
upon
the
base
,
and
draw
them
to
the
point
of
distance
;
and
at
their
sections
to
raise
Perpendiculars
,
and
the
first
Angle
shall
serve
for
the
line
of
elevation
:
For
example
,
this
body
of
an
house
hath
for
his
breadth
A
B
,
and
for
its
length
B
C
,
which
is
the
double
of
its
breadth
A
B
,
from
th●se
points
A
B
,
we
must
draw
to
the
point
of
distance
D
,
and
from
B
C
,
to
the
point
of
distance
E
,
from
their
sections
B
F
,
and
G
,
we
must
raise
Perpendicules
which
shall
serve
for
the
corners
of
the
house
.
For
the
measures
of
the
doors
and
the
windows
they
must
be
set
upon
the
base
between
the
letters
A
B
,
and
B
C
,
and
drawing
from
all
these
points
to
the
points
of
distances
D
E
,
we
must
take
notice
,
where
the
B
D
,
or
B
E
,
shall
be
divided
,
for
to
elevate
there
the
ascents
of
the
windows
.
The
Perpendicule
of
the
first
Angle
B
,
must
serve
for
the
line
of
elevation
,
which
shall
give
the
Travers
and
height
of
the
windows
,
all
the
rest
is
intelligible
enough
.
For
the
figure
below
it
is
the
same
order
,
with
that
of
the
Chairs
without
order
which
is
,
that
having
made
the
plane
Geometrical
,
we
must
set
it
into
Perspective
,
as
the
irregular
pieces
.
Then
to
set
the
Rule
at
every
bending
of
the
plane
,
and
to
observe
where
the
Horizon
shall
be
divided
,
for
to
make
a
point
there
,
to
which
we
must
draw
,
as
if
it
were
the
point
of
sight
of
each
side
of
the
building
,
each
side
having
its
particular
point
:
For
example
,
the
plane
being
set
in
Perspective
,
the
side
H
I
,
giveth
upon
the
Horizon
the
point
K
,
to
which
we
must
draw
all
the
Rays
of
this
side
:
The
other
side
I
L
,
must
also
have
its
point
within
the
Horizon
,
but
our
paper
is
too
short
for
to
make
it
be
seen
.
These
2
points
being
found
,
we
must
place
there
the
Rule
,
and
make
an
occult
line
to
pass
by
the
other
side
of
the
building
parallel
upon
the
plane
to
that
which
hath
given
the
point
within
the
Horizon
;
and
to
continue
it
unto
the
base
,
as
from
the
point
K
by
the
corner
L
,
unto
M
;
and
by
the
corner
H
,
unto
N.
Then
to
set
between
N
I
,
the
number
of
the
windows
which
must
be
on
the
side
H
I
,
and
between
I
,
and
M
,
to
set
the
measures
of
them
that
we
would
have
on
the
side
I
L
:
All
these
measures
being
upon
the
base
,
we
must
draw
them
to
the
points
that
we
have
found
,
and
do
altogether
the
same
,
as
in
the
figure
above
.
For
to
set
Alleys
of
Trees
in
Perspective
.
ALthough
that
by
the
orders
fore-going
one
might
draw
sufficient
instructions
for
to
set
Alleys
of
Trees
in
Perspective
,
yet
I
did
believe
that
it
would
not
be
unprofitable
,
to
give
a
particular
order
therein
,
which
might
make
the
method
more
easie
.
If
one
would
have
but
one
Rank
of
Trees
on
each
side
of
the
Perspective
,
there
will
be
no
need
to
make
a
plane
of
little
squares
,
he
may
only
do
,
as
I
have
said
in
the
fourth
advice
Fol.
17.
But
when
one
would
make
a
company
of
Alleys
to
appear
,
it
seemeth
to
me
,
that
he
shall
do
very
well
to
frame
with
occult
lines
a
pavement
of
little
squares
with
the
Oaks
;
even
as
it
hath
been
taught
in
the
planes
Fol.
31.
And
from
the
Diagonal
of
little
squares
to
raise
Perpendicules
,
as
one
may
see
A
B
;
If
one
desire
the
Trees
to
be
farther
of
,
or
nearer
the
one
to
the
other
,
he
must
encrease
or
diminish
upon
the
base
the
distances
of
the
squares
.
When
one
shall
have
given
such
height
as
he
would
to
the
trunk
of
the
first
Tree
,
as
is
A
C
,
from
the
point
C
,
he
must
draw
to
the
point
of
sight
D
,
to
the
end
that
all
the
Trunks
of
the
other
Trees
may
not
pass
the
Ray
C
D
,
the
first
Tree
A
B
,
maketh
it
to
be
seen
,
that
between
2
right
lines
one
may
give
to
the
Trees
such
compass
as
he
shall
find
good
,
and
that
they
ought
not
to
be
drawn
by
the
Rule
.
The
figure
below
is
ordered
as
that
above
,
there
is
no
difference
,
but
only
that
above
giveth
the
squares
Right
,
or
in
Front
,
and
this
giveth
them
view'd
by
the
Angle
,
that
is
to
say
,
that
from
the
measures
upon
the
base
we
must
always
draw
to
the
points
of
distances
E
F
,
and
from
the
little
squares
to
raise
Perpendicules
,
and
to
do
the
rest
as
we
have
said
heretofore
.
One
may
within
the
same
Perspective
,
where
some
Alleys
should
be
drawn
to
the
points
of
distances
,
set
also
those
that
should
draw
to
the
point
of
sight
;
as
one
may
see
by
this
of
the
midst
,
which
draweth
to
the
point
G
,
which
is
the
point
of
sight
,
and
the
others
draw
to
the
points
E
F
,
which
are
the
points
of
distances
.
For
Gardens
in
Perspective
.
I
Have
given
in
the
Treatise
of
Planes
,
the
Method
to
abbreviate
,
and
set
into
Perspective
the
Plane
of
a
Garden
with
its
Compartments
,
by
an
Order
sufficiently
easie
;
supposing
that
you
have
the
Plane
.
But
as
I
avoid
these
Geometrical
Planes
,
because
there
is
need
of
too
much
time
for
to
make
them
,
I
have
set
these
here
,
by
the
which
we
shall
know
,
that
having
made
a
Plane
of
squares
,
we
may
take
as
much
or
little
as
we
will
for
the
squares
of
the
Garden
,
as
are
here
A
B
,
which
have
each
three
squares
on
every
side
:
and
the
squares
that
remain
shall
serve
for
the
Alleys
C.
He
that
would
make
some
Compartment
within
the
squares
of
the
Garden
,
he
must
use
the
little
squares
of
each
square
,
dividing
them
,
and
giving
them
such
a
figure
as
he
would
have
,
so
as
we
may
see
the
little
square
A
B
:
and
on
the
other
side
D
E
:
the
hedge-Rows
and
Arbors
are
placed
opposite
to
each
other
,
and
of
the
bredth
of
the
Alleys
.
The
little
Squares
with
Borders
.
WHEN
one
would
set
Borders
to
the
squares
,
he
must
set
at
the
corner
the
heights
and
bredths
that
he
would
give
them
.
And
from
these
Measures
to
draw
to
the
point
of
sight
I.
For
example
,
in
the
figure
below
F
G
is
the
height
and
bredth
of
the
Borders
of
the
little
square
H
,
from
the
corners
of
this
little
square
F
G
,
we
must
draw
to
the
point
of
sight
I
,
and
do
all
the
rest
as
it
hath
been
said
several
times
.
For
the
Arbo●s
,
we
must
from
the
Angles
of
the
squares
of
the
Alley
,
elevate
the
Ascents
or
Perpendiculars
O.
All
the
rest
is
done
,
as
in
the
Arches
view'd
by
the
side
,
fol.
60.
The
little
wood
which
is
at
bottom
is
made
by
elevating
Perpendiculars
from
all
the
Angles
of
a
Pavement
of
little
squares
,
&c.
For
to
elevate
and
set
in
Perspective
Fortifications
.
I
Will
not
repeat
here
the
Order
of
Abridging
,
and
setting
the
Planes
of
all
sorts
of
Fortifications
in
Perspective
;
that
which
we
have
spoken
thereof
fol.
39.
is
plain
enough
.
For
to
elevate
them
,
there
is
no
more
difficulty
then
in
one
single
wall
;
but
there
needs
more
time
by
reason
of
the
multitude
of
Angles
,
which
we
must
always
bring
to
the
line
of
Elevation
,
for
to
take
there
the
heights
,
that
they
ought
to
have
,
so
as
we
have
said
elsewhere
many
times
,
speaking
of
other
Works
.
The
little
line
of
elevation
is
divided
into
four
Parts
;
I
he
first
from
1
unto
2
is
the
height
of
the
Parapet
of
the
way
covered
;
from
2
unto
3
is
the
height
of
the
Rampart
;
from
3
unto
4
is
the
height
of
the
Parapet
of
the
Rampart
.
And
from
5
unto
1
is
the
depth
of
the
Trench
.
For
to
make
the
designs
of
Perspective
.
THere
is
not
so
excellent
a
Master
,
which
hath
not
some
design
in
such
pieces
,
as
he
would
willingly
attain
to
:
If
this
be
ordinary
almost
in
all
sciences
,
it
is
necessary
in
this
,
more
then
in
any
other
,
by
the
great
substitution
of
points
and
of
lines
,
which
we
must
therein
exactly
observe
,
and
without
which
nothing
can
be
done
,
which
may
content
those
that
have
any
understanding
therein
.
Seeing
that
one
is
obliged
in
some
manner
,
to
make
designs
,
we
must
search
out
that
which
may
help
to
make
them
exactly
,
that
may
be
possible
:
and
as
every
one
knoweth
that
all
the
length
of
these
works
,
is
to
draw
lines
parallel
,
and
Perpendiculars
,
having
then
searched
the
Invention
,
as
well
by
experience
,
as
in
the
Authours
,
to
be
able
to
make
them
readily
:
I
have
found
nothing
which
can
help
us
in
that
,
but
the
board
and
the
square
,
which
Viator
hath
left
us
in
his
Works
.
All
those
that
would
pass
the
time
in
designing
,
ought
to
have
one
from
the
which
they
shall
draw
the
delight
and
benefit
which
experience
will
make
them
to
understand
.
Although
that
the
Figure
giveth
sufficient
understanding
,
how
it
ought
to
be
,
and
the
manner
of
using
it
,
I
did
believe
that
I
ought
to
give
a
more
clear
understanding
thereof
.
This
Plank
or
Board
A
B
C
D
,
ought
to
be
perfectly
by
the
rule
or
square
,
of
a
Foot
and
half
long
,
of
fifteen
inches
broad
,
and
half
an
inch
thick
,
that
the
Wood
be
good
,
very
dry
,
and
well
united
,
one
may
past
a
sheet
of
Paper
on
it
,
for
to
make
it
more
smooth
and
to
help
the
Pen.
The
square
E
F
,
is
a
Rule
of
a
foot
and
half
long
,
as
the
board
,
an
inch
broad
,
and
of
thickness
2
lines
,
which
is
helved
at
the
right
Angle
within
another
frame
of
a
Rule
G
H
,
eight
inches
long
,
one
inch
broad
,
and
three
quarters
of
an
inch
thick
;
for
to
draw
lines
,
they
hold
this
latter
Rule
G
H
,
closed
against
the
board
A
B
C
D
,
and
the
other
Rule
E
F
is
assuredly
strait
,
if
so
be
the
board
and
the
Rule
be
well
ordered
.
When
one
would
work
,
we
must
fasten
the
leaf
of
Paper
I
K
L
M
upon
the
board
,
with
4
little
bits
of
Wax
N
O
P
Q
,
and
then
from
one
only
point
,
you
may
draw
lines
,
with
assuredness
that
they
will
be
right
.
And
when
you
would
have
Perpendiculars
,
set
the
handle
of
the
Rule
G
H
,
on
the
side
C
D
,
the
Rule
E
F
shall
be
Perpendicular
to
C
D.
For
my
part
I
find
that
this
easeth
exceedingly
,
and
that
without
this
invention
,
you
must
always
have
the
hand
at
the
Compass
.
There
is
no
further
need
of
substitution
,
but
for
the
visual
Rays
,
and
there
are
also
those
that
use
a
Rule
pierced
at
one
end
,
which
they
fasten
with
a
Needle
to
the
point
of
sight
,
but
this
is
too
much
intangling
,
I
would
not
counsel
any
to
use
it
,
one
may
as
soon
do
it
with
the
common
Rule
,
and
so
is
not
in
danger
to
spoil
any
thing
.
R.
Is
the
common
Rule
.
T.
A
common
Compass
.
V.
Another
Compass
which
beareth
the
Ink
,
for
to
make
circular
Lines
.
See
here
are
all
the
Instruments
that
one
hath
need
of
,
for
to
make
the
designs
of
Perspective
.
For
to
draw
little
Perspectives
into
great
,
and
great
into
little
.
SEeing
that
designs
are
made
in
small
,
with
more
facility
then
in
great
,
it
is
credible
that
they
will
be
made
therein
always
,
the
which
hath
made
me
resolve
to
give
the
Method
of
setting
small
designs
into
great
upon
Cloth
.
The
Painters
use
ordinarily
Squares
or
Checquers
,
that
is
to
say
,
that
they
divide
the
small
designes
and
the
clothes
,
where
they
must
be
painted
into
the
same
number
of
squares
,
and
set
proportionally
;
that
which
is
within
one
square
of
the
design
,
into
the
square
of
the
Cloth
which
answereth
to
it
;
some
do
like
well
of
this
Order
.
But
here
is
another
,
which
in
my
judgement
,
is
more
easie
,
more
facile
,
and
more
assured
;
we
must
have
a
skale
proportionate
to
the
less
design
,
and
another
skale
proportionate
to
the
bigger
.
When
one
would
make
a
design
,
the
first
thing
that
he
resolveth
on
,
is
the
skale
which
must
give
all
the
Measures
of
all
the
other
pieces
of
the
design
.
For
example
,
in
the
less
design
A
,
the
skale
B
C
,
of
five
little
parts
,
(
which
one
may
take
for
feet
Royal
)
hath
been
made
the
first
upon
this
skale
;
they
have
taken
the
Horizon
,
the
height
and
distance
of
the
Trees
,
the
bredth
of
the
Alleys
,
&c.
For
to
fet
this
small
into
great
,
observe
how
we
must
proceed
.
First
,
we
must
know
,
if
the
Perspective
must
have
the
natural
Horizon
,
that
is
to
say
,
that
the
bottom
of
the
Picture
being
on
the
Ground
,
the
Horizontal
line
be
at
the
height
of
our
eye
,
which
is
about
five
feet
Royal
;
This
being
,
there
must
be
five
little
parts
which
are
between
B
C
,
to
make
a
skale
of
five
feet
Royal
F
G
,
that
having
taken
all
the
Measures
at
the
little
one
,
we
may
transport
them
,
and
take
upon
the
great
one
,
as
I
am
about
to
say
.
The
two
Measures
of
Proportion
or
skales
,
being
ordered
,
as
I
have
now
said
;
the
first
thing
that
one
doth
,
is
to
take
upon
the
lesser
design
with
a
pair
of
Compasses
;
the
distance
of
the
base
D
unto
the
Horizon
E
,
and
to
carry
this
opening
of
the
Compass
D
E
,
upon
the
lesser
skale
B
C
,
and
to
take
notice
what
number
of
Parts
it
shall
give
,
as
he
doth
give
5
,
we
must
then
take
as
many
parts
upon
the
great
skale
F
G
,
and
set
them
on
the
one
part
and
other
of
the
Picture
,
or
great
Design
,
beginning
at
the
bottom
of
the
Cloth
H
H
,
and
they
shall
end
in
I
I
,
from
these
points
I
I
we
must
draw
a
Packthread
whited
or
blacked
,
this
line
I
I
shall
mark
the
Horizon
in
the
great
Picture
;
Then
to
take
the
distance
or
sinking
K
L
,
of
the
lesser
design
,
which
is
the
foot
of
the
House
;
and
to
carry
it
upon
the
lesser
skale
R
C
,
for
to
see
how
many
parts
we
shall
have
,
and
to
take
the
same
number
upon
the
great
skale
F
G
,
and
to
set
that
which
we
shall
finde
upon
the
edge
of
the
Cloth
H
M
,
H
M
,
which
we
must
tringle
about
,
as
the
Horizon
for
to
have
the
sinking
of
the
second
Tree
;
In
the
less
design
,
we
must
take
the
distance
N
O
,
and
carry
it
upon
the
lesser
skale
B
C
,
and
take
as
many
parts
upon
the
great
scale
F
G
,
as
we
shall
have
found
in
the
less
.
N
O
giveth
two
parts
of
the
lesser
,
we
must
take
two
of
the
great
one
,
which
will
give
H
P
,
which
we
must
tringle
,
as
we
have
said
:
We
shall
use
in
like
manner
all
the
Parallels
to
the
base
,
as
are
the
other
Trees
,
the
Windows
,
the
Roofs
of
the
Houses
,
&c.
For
the
Plumb
lines
or
Perpendiculars
to
the
base
,
it
is
the
same
Method
,
there
is
nothing
but
to
change
the
side
for
to
mark
them
,
which
is
,
that
in
stead
of
marking
on
the
side
of
the
Cloth
,
as
we
have
done
,
we
must
mark
above
and
below
.
For
example
,
for
to
have
the
two
Cotners
of
the
house
at
bottom
;
we
must
take
with
the
Compasses
upon
the
lesser
design
Q
R
,
and
carry
this
opening
upon
the
scale
B
C
,
we
shall
finde
about
7
parts
and
an
half
;
we
shall
take
as
many
parts
upon
the
great
scale
F
G
,
which
shall
give
H
S
T
S
,
which
we
must
tringle
and
do
so
with
all
the
other
Perpendiculars
,
whether
building
Trees
,
Hedge-Rows
,
&c.
For
to
finde
the
visual
Rays
,
which
are
the
lines
that
go
to
the
point
of
sight
V
:
at
this
point
V
we
must
fasten
a
pack-thread
or
thread
,
with
a
pin
bended
,
for
fear
of
making
the
hole
too
great
,
this
thread
or
pack-thread
must
be
of
the
length
of
the
Picture
,
for
to
be
able
to
tringle
and
draw
all
the
Rays
very
exactly
;
For
example
,
for
to
have
the
two
Rays
of
the
bredth
of
the
Trees
,
which
are
in
the
less
design
D
X
,
we
must
take
this
design
D
X
,
and
to
carry
it
upon
the
lesser
scale
B
C
,
and
to
take
upon
the
great
F
G
,
in
proportion
to
that
which
we
shall
have
found
in
the
less
which
will
give
H
Y
,
the
which
points
H
Y
we
shall
tringle
with
the
Pack-thread
of
the
point
V
;
for
to
have
also
the
Ray
of
Hedge-Rows
,
we
must
take
the
diffance
D
Z
,
and
carry
it
upon
the
scale
B
C
,
and
take
as
many
parts
upon
the
great
scale
F
G
,
which
will
give
H
I
,
which
we
must
tringle
with
the
pack-thread
from
the
point
V
,
&c.
All
that
is
in
Perspectives
falleth
ordinari●y
under
these
three
sorts
of
lines
,
Parallels
,
Perpendiculars
,
and
Rays
v●sual
,
which
having
been
made
easie
to
make
upon
the
cloth
,
we
shall
less
fear
the
pains
of
setting
the
less
designs
into
great
;
for
to
set
the
designs
of
great
into
small
,
we
must
only
change
the
Orders
,
that
is
to
say
,
that
we
must
take
the
measures
first
upon
the
great
scale
,
and
diminish
them
proportionally
upon
the
less
,
as
if
the
Horizon
of
the
great
design
were
of
5
parts
of
the
great
s●ale
.
I
would
take
5
parts
of
the
lesser
scale
,
for
the
height
of
the
Horizon
of
the
less
design
,
and
so
of
all
the
rest
.
Orders
to
facilitate
the
Vniversal
manner
of
the
Siour
G.
D.
L.
AS
all
those
for
whom
I
labour
,
have
not
perhaps
a
sufficient
ground
for
to
be
clear
into
this
order
,
or
Universal
manner
;
I
believed
that
the
Author
would
permit
me
to
make
it
easie
to
them
,
as
much
as
I
shall
be
able
,
that
they
may
draw
benefit
thereby
.
Wherefore
I
shall
set
these
two
figures
,
which
will
cause
to
remember
that
which
I
have
already
said
,
in
the
2.
3.
4.
and
5.
advice
,
which
are
for
the
understanding
of
this
order
,
there
having
shewed
to
take
all
the
measures
upon
the
base
,
and
that
as
many
Rays
as
d●vide
the
Diagonal
C
,
are
as
many
small
squares
in
the
sinking
of
the
picture
,
to
which
squares
they
give
such
a
greatness
as
they
will
.
That
we
may
not
go
to
seek
so
far
,
let
us
look
on
the
first
figure
where
the
base
is
A
B
,
the
point
of
sight
G
,
the
points
of
distances
E
F
,
I
divide
this
base
into
12
equal
parts
;
each
of
which
I
shall
make
to
be
about
a
foot
,
and
from
all
these
divisions
,
I
shall
draw
to
the
point
of
sight
,
which
shall
be
as
many
Rays
,
whereof
A
and
B
are
the
last
.
Now
I
say
that
he
that
would
have
a
line
,
which
should
appear
sunk
a
foot
in
the
Picture
,
that
he
must
draw
from
the
first
division
●
D
to
the
point
of
distance
F
,
and
where
this
line
D
F
,
shall
divide
the
Ray
E
G
,
that
shall
be
the
point
for
to
draw
the
line
sunk
a
foot
in
the
picture
,
if
we
would
have
one
of
3
feet
sinking
,
we
must
take
upon
the
base
3
of
these
parts
,
and
from
the
third
to
draw
also
to
the
distance
F
;
and
we
shall
have
at
the
section
of
the
Ray
B
G
;
the
place
for
to
draw
this
line
.
So
that
if
from
the
point
C
,
we
draw
to
the
point
F
,
where
this
line
C
F
,
shall
divide
B
G
,
this
shall
be
a
line
sunk
of
6
feet
,
If
of
the
other
6
parts
that
remain
A
C
,
we
make
24
,
dividing
each
into
4
,
and
that
we
leave
not
to
make
each
part
to
avail
a
foot
,
there
will
be
●4
feet
from
A.
to
C.
In
such
manner
as
if
we
require
a
line
;
which
should
appear
sunk
18
feet
in
the
Picture
,
I
should
reckon
from
A
,
18
little
parts
,
and
from
the
18
I
would
draw
to
the
distance
E
,
which
would
give
me
by
the
section
of
the
Ray
A
C
,
the
point
for
to
draw
this
line
;
if
one
would
that
it
should
be
sunk
24
feet
,
we
must
take
A
C
,
and
draw
from
C
,
to
E
,
and
where
this
line
should
divide
A
G
,
at
the
point
H
,
we
shall
draw
H
I
,
which
will
appear
of
24
feet
of
sinking
in
the
picture
.
According
to
the
Perspective
,
this
line
H
I
,
is
equal
to
that
A
G
,
and
containeth
as
many
feet
or
parts
,
so
that
if
one
draw
from
the
point
I
,
to
the
point
E
,
the
section
of
this
line
I
E
,
at
the
Ray
A
G
,
shall
be
for
to
draw
a
line
K
L
sunk
of
48
feet
;
If
from
this
we
draw
further
to
the
distance
E
,
we
shall
have
the
section
of
the
Ray
A
G
,
yet
a
line
removed
24
feet
more
then
the
others
.
And
if
one
would
have
a
line
sunk
30
feet
,
we
must
from
the
point
A
,
reckon
6
small
parts
,
and
from
the
sixth
draw
to
the
point
of
sight
G
,
and
take
notice
where
we
shall
divide
the
line
H
I
,
as
here
at
the
point
M.
Then
from
the
point
M
,
to
draw
to
the
distance
E
,
and
this
line
M
E
,
shall
divide
the
Ray
A
G
,
where
we
must
draw
this
line
N
,
if
it
were
of
40.
We
should
from
A
,
reckon
16
,
and
do
all
the
same
if
,
it
were
60
,
we
should
from
A
,
reckon
12
,
and
from
12
,
draw
to
the
point
of
sight
G
,
unto
the
line
K
L
,
which
should
be
the
point
O
,
Then
from
O
;
to
draw
to
the
distance
E
,
and
from
the
section
of
the
Ray
A
G
,
shall
be
for
to
draw
this
line
.
For
the
second
figure
.
BY
that
which
I
have
spoken
,
it
is
easie
to
find
a
point
for
such
a
sinking
as
one
would
have
.
There
remaineth
to
shew
how
we
may
find
it
within
,
or
without
the
Ray
A
G
,
or
B
C
,
for
this
the
line
B
C
,
shall
serve
as
a
scale
of
six
feet
,
the
one
of
which
I
shall
divide
into
twelve
inches
,
that
I
may
there
find
the
half
,
the
third
,
and
the
4th
of
a
foot
.
All
being
thus
ordered
.
If
one
require
of
me
a
point
which
appeareth
of
17
feet
long
,
and
of
a
foot
and
half
within
the
Ray
A
G.
I
will
draw
from
the
17th
part
of
the
base
to
the
point
of
distance
E
,
and
where
the
Ray
A
G
,
shall
be
divided
in
P
,
I
will
draw
a
line
P
Q
,
now
when
one
requireth
a
foot
and
half
within
the
Ray
A
G
,
I
will
take
with
a
Compass
upon
the
same
line
P
Q
,
but
on
the
side
B
C
,
a
foot
6
inches
,
which
I
will
carry
from
P
,
unto
R.
And
this
point
R
,
shall
be
the
point
which
hath
been
demanded
.
And
if
one
would
have
one
yet
at
29
feet
distance
within
the
Picture
,
and
seven
and
an
half
beyond
the
Ray
A
G.
We
must
draw
from
C
,
to
the
point
E.
and
where
it
shall
divide
A
G
,
to
draw
a
line
which
shall
be
of
24
feet
,
then
from
A.
taking
five
little
parts
,
to
draw
them
to
the
point
of
sight
G
,
until
that
we
divide
this
line
at
the
point
S
,
and
from
this
point
S
,
to
draw
to
the
d
stance
E
Where
the
Ray
A
G
shall
be
divided
,
we
must
draw
a
line
T
V
,
seeing
they
require
7
feet
and
an
half
beyond
the
Ray
A
,
we
must
upon
the
same
line
T
V
,
but
on
the
side
B
C
,
take
7
parts
and
6
inches
with
a
Compa●s
,
and
carry
them
from
the
point
T.
to
the
point
X
And
this
point
X
,
shall
be
the
point
that
one
desireth
,
And
so
of
all
others
,
at
such
a
distance
and
removal
,
as
one
would
have
.
Of
a
general
manner
for
to
exercise
Perspective
,
without
setting
the
Point
of
distance
out
of
the
Picture
,
or
Field
of
the
Work
by
the
Sieur
G
D
L.
THIS
Order
obligeth
us
to
make
a
Geometrical
Plane
,
or
at
least
a
device
of
Measures
,
as
well
for
th●
Plane
,
as
for
the
Elevation
;
that
by
the
one
,
or
by
the
other
,
it
may
be
brought
to
set
into
Perspective
I
will
take
for
the
object
or
subject
the
same
Example
of
the
Author
,
which
is
a
Cage
squared
,
covered
with
a
Point
;
or
a
Building
covered
like
a
Pavillion
or
Tent
,
to
the
which
we
shall
give
the
Measures
by
the
means
of
a
Scale
.
Having
then
made
the
plane
of
this
Cage
m
,
i
,
l
,
k
,
which
I
have
set
on
the
top
of
the
figure
,
it
must
be
,
th●
at
such
a
distance
as
one
w●u●d
have
,
that
the
Obj●ct
seeme
recoyld
within
the
Picture
,
as
it
is
here
of
17
feet
;
we
mak●
a
line
a
,
b
,
which
shall
be
the
base
or
the
bottom
of
the
Picture
,
which
we
shall
place
according
to
the
aspect
,
th●●
the
object
ought
to
be
seen
.
Then
from
the
two
ends
of
this
line
a
,
b
,
we
must
draw
two
lines
Parallels
the
o●
to
the
other
,
and
undeterminate
;
thrt
is
to
say
,
it
is
no
matter
if
they
divide
the
plane
,
nor
in
what
place
,
●
are
a
g
,
b
g
,
upon
the
one
of
these
lines
,
as
here
this
a
g
,
we
must
make
little
Parallels
to
the
line
a
b
,
which
ma●
go
unto
the
Angles
of
the
plane
,
and
by
the
means
of
the
scale
,
to
see
how
far
each
Angle
of
the
plane
shall
be
r●moved
from
this
line
a
g.
the
which
shall
be
marked
near
to
each
line
.
Now
from
the
place
,
which
one
sh●
choose
for
to
view
the
Picture
,
which
is
here
the
point
c
,
at
five
feet
near
to
b.
We
must
make
a
Perpendicular
〈◊〉
a
b
,
which
shall
be
the
line
c
t
,
to
this
line
c
,
t
,
we
must
give
as
many
little
parts
of
the
scale
as
we
would
have
〈◊〉
be
removed
for
to
view
the
Picture
,
which
is
for
this
24
feet
,
and
at
the
end
of
these
24
feet
,
which
is
the
poin●
t
,
to
raise
a
small
Perpendicule
of
the
height
of
the
eye
,
which
shall
be
the
line
c
t
,
of
four
feet
and
an
half
.
The
Cloth
,
the
Wall
,
or
the
Paper
,
being
ordered
for
to
set
the
plane
in
perspective
,
and
upon
the
plane●
make
the
Elevation
;
We
must
divide
the
bottom
of
the
picture
,
or
the
base
A
B
,
into
as
many
,
parts
as
that
a
b●●
the
plane
;
this
having
12
thereof
.
We
must
divide
the
great
A
B
into
12
,
which
will
be
of
value
each
a
foo●
Above
the
points
A
B
we
must
set
the
height
of
the
line
s
,
t
,
which
is
of
four
feet
and
an
half
.
Take
then
with
th●
Compasses
four
parts
and
an
half
of
those
which
are
upon
the
line
A
B
,
and
carry
them
perpendicularly
upo●
the
points
A
B
,
which
shall
give
the
points
E
F
and
draw
the
line
E
F
parallel
to
A
B
,
and
this
line
shall
b●
the
Horizon
.
Seeing
that
in
the
plane
the
point
C
,
which
is
the
place
for
to
view
the
Picture
,
is
removed
●i●
parts
from
b
,
we
must
reckon
as
many
parts
from
B
,
and
from
the
fifth
C
,
Elevate
a
Perpendicule
to
A
B
,
which
sh●
divide
the
Horizon
at
the
point
G
,
which
shall
be
the
point
of
sight
,
to
which
we
must
draw
the
Rays
A
G
,
B
G
which
shall
represent
the
Parallels
of
the
p●ane
a
g
,
b
g
,
for
the
point
of
distance
,
it
shall
be
the
point
F
,
and
by
reason
that
the
line
c
,
t
,
hath
24
feet
,
must
take
six
parts
of
the
l●ne
A
B
,
which
shall
be
A
D
,
and
divide
them
ea●●
into
4
,
and
these
24
parts
shall
serve
for
a
scale
,
for
the
depths
,
or
removalls
;
being
sufficient
for
to
let
them
out
infinitely
.
And
the
six
parts
that
remaine
between
B
D
,
shall
be
the
Scale
which
shall
furnish
the
Measures
of
these
according
as
the
lines
drawn
from
the
points
found
by
the
plane
,
shall
divide
the
Rays
drawn
to
the
point
of
s●●
G
;
For
as
this
Scale
,
is
a
pyramide
,
whereof
B
D
,
is
the
Base
the
Measures
diminish
in
proportion
as
they
are
sunk
have
divided
the
one
of
these
parts
into
Inches
for
to
finde
there
all
the
Measures
,
as
they
are
upon
the
plane
.
With
the
Scale
or
Removalls
we
finde
the
points
of
the
plane
,
and
with
that
of
the
Measures
the
length
that
〈◊〉
lines
ought
to
have
.
aswell
for
the
plane
,
as
for
the
Elevation
.
How
for
to
finde
the
plane
in
Perspective
,
we
must
observe
all
the
Measures
of
the
Geometrical
plane
the
〈◊〉
Angle
of
the
planer
,
m
,
is
removed
7
feet
from
the
point
a
,
upon
the
line
a
,
g
;
Wherefore
I
will
reckon
17
pa●
begining
at
A
;
and
from
the
seventeenth
,
I
will
to
the
point
F
,
dividing
the
Ray
A
G
,
at
the
point
R.
from
this
p●
R
,
we
must
draw
a
parallel
to
the
Base
;
and
by
reason
that
the
Plane
m
,
is
within
the
Ray
a
g
,
a
foot
and
an
h●●
we
must
upon
the
same
line
R
but
on
the
side
B
D
,
take
part
and
an
half
for
to
carry
within
the
Ray
A
G
,
which
shall
be
the
point
M
,
representing
the
Angle
of
the
plane
M
;
for
〈◊〉
Angle
l
;
which
is
removed
26
feet
from
the
point
a.
we
must
from
the
point
D
,
which
is
24
feet
from
the
pe●
A
,
draw
to
F
,
and
where
the
Ray
A
G
,
shall
be
divided
at
the
pointy
,
draw
a
Parallel
.
Now
as
it
is
about
〈◊〉
feet
,
that
this
line
y
,
is
enough
removed
;
we
must
draw
from
the
second
part
of
the
Scale
to
the
point
G
,
a●
where
this
Ray
shall
divide
the
Parallel
y.
at
the
point
Q
,
we
must
draw
Q
F
,
which
shall
give
upon
A
G
,
〈◊〉
point
H
,
from
which
point
H
,
we
must
draw
a
parallel
to
A
B
,
and
upon
the
same
line
H
,
but
on
the
side
B
take
the
Measures
for
to
g●ve
13
feet
and
an
half
;
from
the
point
H
unto
the
point
L.
For
the
point
k
,
which
is
removed
29
feet
from
A
,
we
must
from
the
fifth
part
of
the
Scale
A
D
,
draw
to●
point
G
,
and
where
this
Ray
shall
divide
the
Parallel
y
,
at
the
point
O
,
to
draw
O
F
,
for
to
have
upon
A
G
,
〈◊〉
point
N.
Then
from
the
point
N.
to
draw
a
Parallel
for
to
take
on
the
side
B
D
,
7
feet
and
an
half
,
〈◊〉
we
must
Carry
out
of
the
Ray
A
G
,
that
is
to
say
,
from
N
to
K.
For
the
point
i.
removed
38
feet
from
the
point
a.
we
must
upon
the
Scale
A
D
,
take
14
parts
,
〈◊〉
from
the
14
draw
a
Ray
to
the
point
G
,
which
shall
divide
the
parallel
the
point
S.
And
from
the
point
S
,
to
d●
to
F
,
which
shall
divide
the
Ray
A
G
,
at
the
point
T
,
removed
38
feet
from
the
point
A
:
by
reason
t●
the
Parallel
y
is
of
24
,
to
the
which
having
joyned
14.
they
make
38.
at
the
point
T.
And
by
reason
that
Angle
i
,
is
4
feet
and
an
half
within
the
Ray
A
G
,
we
must
upon
this
Parallel
T
,
but
on
the
side
D
B
,
tak●
feet
and
an
half
,
and
Carry
them
from
the
point
T
;
to
the
point
I.
For
to
frame
the
plane
we
must
joyn
by
right
lines
,
these
4
points
M
I
,
K
I
,
and
from
their
Angles
raise
p●●pendicules
as
M
,
st
,
L
,
ff
,
K
,
fr
,
and
I
,
sp
.
The
which
shall
have
Each
17
feet
,
as
is
marked
in
the
plane
by
〈◊〉
●
ne
X
,
and
from
the
ends
of
these
perpendiculars
,
to
draw
two
Diagonals
,
st
,
sp
,
ff
fr
,
which
shall
divide
themsel●●
in
Z
,
and
upon
this
point
Z
,
to
elevate
a
perpendicular
Z
Ae
,
of
13
feet
and
an
half
.
Then
to
draw
lines
〈◊〉
all
the
four
corners
sl
.
ff.
sp
,
and
fr
,
to
the
point
Ae
,
and
the
Cage
shall
be
framed
in
perspective
.
If
one
would
〈◊〉
it
descend
within
the
ground
one
foot
,
we
must
adjoyn
one
foot
under
every
point
of
the
plane
;
and
joyn
th●
together
with
lines
.
For
to
give
justly
the
distance
removed
,
the
Point
remaining
in
the
Picture
,
THose
that
would
use
this
common
manner
must
know
,
that
the
number
of
feet
that
we
shall
take
upon
the
base
,
ought
to
have
respect
to
the
distance
that
they
shall
have
determined
of
.
For
to
cause
my
Proposition
to
be
understood
,
I
will
set
in
the
first
figure
two
distances
,
the
one
of
six
feet
,
the
other
of
twelve
,
which
have
respect
the
one
to
the
other
,
by
reason
that
dividing
into
two
each
of
the
six
parts
,
we
shall
have
twelve
.
Let
us
suppose
then
that
the
line
A
B
is
divided
into
twelve
parts
,
and
that
from
all
these
parts
,
one
hath
drawn
Rays
to
the
point
of
sight
C
,
let
us
take
now
the
half
of
these
divisions
A
D
,
and
draw
to
the
point
E
,
which
is
the
distance
of
6
feet
;
it
is
certain
that
the
section
of
the
Ray
A
C
,
shall
be
the
abridgement
of
the
squares
view'd
six
feet
distant
.
If
from
the
point
D
we
draw
to
the
point
F
,
which
is
the
distance
of
twelve
feet
,
this
line
D
F
dividing
the
Ray
A
C
,
shall
give
the
abridgement
of
six
little
squares
view'd
twelve
feet
distance
.
He
that
would
have
the
abridgement
of
twelve
squares
,
view'd
twelve
feet
distant
,
he
must
from
the
point
B
,
which
is
the
whole
base
,
draw
to
the
point
F
;
and
at
the
section
of
the
Ray
A
C
to
the
point
H
,
shall
be
that
which
is
required
:
or
else
from
the
point
I
to
draw
I
F
,
which
shall
give
the
same
point
H
,
and
the
line
H
K
shall
be
sunk
twelve
little
squares
viewed
at
12
feet
distance
.
We
see
in
this
that
12
little
squares
viewed
at
12
feet
distance
,
do
meet
in
the
same
line
H
K
,
that
six
squares
viewed
at
six
feet
distance
,
and
all
the
lines
of
six
squares
,
that
the
section
of
the
Diagonal
D
G
hath
given
,
do
reflect
themselves
by
two
and
two
to
those
,
which
the
Diagonal
D
F
hath
given
,
the
reason
why
the
Diagonal
D
F
hath
given
two
lines
for
one
of
those
D
G
,
is
that
the
distance
is
doubled
.
If
it
were
trebled
it
would
give
three
,
and
four
if
it
were
four-fold
.
Now
for
to
finde
on
the
side
B
D
,
the
same
sections
,
and
the
same
number
of
little
squares
,
as
on
the
side
D
A
,
without
the
point
of
distance
be
out
of
the
picture
,
we
must
only
divide
into
two
each
of
the
six
equal
parts
which
are
between
B
D
,
which
will
make
12
parts
,
and
from
their
divisions
to
draw
occult
lines
to
the
point
of
sight
C
;
and
if
one
draw
Parallels
to
the
base
,
by
all
the
sections
that
the
Diagonal
maketh
of
all
these
Rays
he
shall
have
12
squares
of
sinking
in
the
same
line
,
and
if
the
distance
were
of
twelve
feet
,
although
that
G
be
but
six
feet
of
distance
:
the
reason
of
this
is
,
that
by
multiplying
the
Rays
we
multiply
the
squares
,
and
multiplying
the
squares
we
remove
the
distance
:
see
then
how
having
made
twelve
parts
of
six
,
which
were
between
B
D
,
there
ariseth
twelve
little
squares
,
which
make
the
same
sinking
that
the
distance
at
twelve
feet
distant
.
And
he
that
would
have
the
distance
at
24
feet
,
he
must
divide
still
into
two
,
each
of
the
parts
between
B
D
,
which
would
make
24
parts
,
and
from
the
24th
.
to
the
point
D
,
to
draw
the
line
D
G
the
section
that
it
would
make
of
the
Ray
B
C
at
the
point
K
,
would
be
the
sinking
of
the
24
feet
.
In
the
second
figure
,
I
have
set
upon
the
line
L
M
the
same
Measures
as
upon
A
B
of
the
first
figure
,
and
on
the
side
M
N
,
the
same
sinking
,
and
the
same
distance
as
on
the
side
A
D
,
which
giveth
the
line
H
K
,
to
the
end
that
we
may
see
,
that
he
which
would
draw
the
fifth
part
,
as
Q
G
,
or
from
the
seventh
as
R
G
,
that
he
should
not
have
the
true
sinking
which
is
at
K
:
for
R
G
would
not
sink
enough
,
and
Q
G
would
sink
too
much
,
although
from
these
5
or
7
parts
,
there
would
be
made
twelve
or
twenty
four
.
Wherefore
we
must
observe
to
take
always
a
Number
,
which
may
be
multiplied
by
the
distance
,
as
here
the
distance
of
six
may
serve
for
12
,
18
,
24
,
30
,
36
,
42
,
48.
and
so
an
infinite
number
by
six
.
The
distance
of
5
may
serve
for
10
,
15
,
20
,
25
,
30
,
&c.
The
distance
of
eight
,
may
serve
for
16
,
24
,
32
,
40.
48
,
&c.
We
cannot
fail
doing
thus
,
for
supposing
that
the
point
of
distance
could
not
be
nearer
to
the
point
of
sight
then
G
is
near
to
C
,
it
follOweth
that
if
G
is
at
6
,
at
7
,
8
,
or
at
10
feet
from
the
point
C
,
that
the
half
of
the
base
hath
the
same
number
,
the
which
number
we
must
divide
proportionably
to
the
removal
,
which
we
will
give
it
.
For
example
,
if
there
be
eight
feet
from
N
to
L
,
and
that
I
would
have
the
distance
of
32
feet
without
that
G
go
out
from
his
place
,
I
will
divide
each
of
the
eight
parts
,
which
is
the
half
of
the
base
as
L
N
into
4
,
and
4
times
8
will
be
32
Rays
,
so
the
abridgements
of
the
square
should
be
at
32
feet
of
distance
.
All
these
little
divisions
remain
not
after
the
Picture
is
made
,
there
are
none
but
the
principal
divisions
of
feet
,
which
they
draw
to
the
point
of
sight
,
and
the
abridgements
,
that
is
to
say
,
the
Parallel
to
the
base
which
remain
always
.
A
very
sine
Invention
,
for
to
make
naturally
Perspectives
without
keeping
the
Rules
.
HAving
set
down
all
the
Rules
,
that
we
must
keep
for
to
make
exactly
Perspectives
:
I
would
set
also
this
Invention
,
and
the
following
,
for
to
make
thereby
perfectly
fair
ones
and
very
exact
without
being
obliged
for
to
use
any
one
rule
therefore
This
shall
serve
for
those
that
love
Panting
,
and
take
the
pleasure
to
use
it
;
without
being
willing
to
take
the
pains
to
open
the
Compass
,
nor
to
take
the
Rule
for
to
draw
a
line
;
for
in
this
order
,
we
shall
not
need
neither
the
one
nor
the
other
.
And
nevertheless
we
may
make
very
fair
Perspectives
,
either
of
Buildings
,
of
Gardens
,
or
Landskips
.
Before
we
proceed
to
the
order
,
we
must
know
,
that
the
principal
piece
and
necessary
for
this
invention
,
is
a
great
lease
of
Glass
very
clear
,
enclosed
in
a
frame
of
Wood
well
smooth'd
and
thin
,
which
I
have
marked
with
A
:
at
the
bottom
of
the
figure
,
this
frame
must
slide
between
two
pieces
of
Wood
,
an
Inch
and
an
half
thick
,
the
which
must
be
fastned
to
the
end
of
a
board
,
which
is
of
the
breadth
of
the
Frame
,
as
B
C
sheweth
,
fit
for
to
receive
the
Frame
A.
The
breadth
of
this
board
B
D
,
shall
be
of
a
foot
C.
At
the
midst
of
the
fore-part
of
this
board
,
we
must
make
one
or
more
square
holes
E
,
for
to
fasten
there
a
little
Iron
Rod
or
Wire
,
as
a
Rule
pierced
all
along
,
whereby
to
raise
it
,
or
let
it
down
at
the
top
of
this
Rule
F
,
there
shall
be
Round
of
3
or
4
Inches
of
Diameter
,
without
thickness
,
as
it
might
be
of
white
Lattin
,
the
which
must
have
a
little
hole
in
the
midst
,
as
it
were
for
a
piece
to
go
through
,
all
these
things
put
into
one
,
make
the
piece
G
Although
the
figure
sheweth
the
order
,
and
how
we
must
use
this
piece
G
,
yet
I
will
not
cease
to
tell
,
how
we
must
proceed
therein
.
Having
then
placed
this
piece
G
,
before
that
which
one
would
draw
,
he
shall
look
through
the
little
hole
of
the
spectacle
F
,
if
one
can
discover
upon
the
Glass
all
that
he
would
that
should
be
there
:
if
any
thing
come
not
there
,
you
must
put
the
spectacle
nearer
to
the
Glass
;
until
that
he
do
see
there
,
that
which
he
desireth
The
piece
being
so
setled
,
we
must
mark
upon
the
Glass
,
all
that
shall
be
seen
there
,
looking
through
the
hole
F
,
which
doth
here
,
that
which
the
point
of
sight
doth
in
other
Orders
,
it
being
most
certain
,
that
all
that
shall
be
marked
upon
the
leaf
of
Glass
,
having
the
eye
at
the
little
hole
of
the
spectacle
shall
be
found
perfectly
in
the
Rules
of
the
Perspective
.
Every
one
knoweth
how
we
must
withdraw
that
which
shall
be
designed
;
wherefore
I
shall
leave
that
,
for
to
say
that
one
may
mark
upon
the
Glass
with
the
Pen
and
Ink.
and
after
that
all
is
done
,
to
moisten
a
little
the
other
side
of
the
Glass
for
to
refresh
the
Ink
and
to
set
on
the
side
,
which
we
shall
have
traced
,
a
Paper
somewhat
moist
,
and
then
to
pass
the
hand
upon
it
;
and
the
Paper
will
take
,
all
that
which
was
marked
upon
the
Glass
.
If
one
will
,
they
may
also
use
a
Pensil
,
and
colours
according
as
every
one
shall
think
good
,
it
is
enough
that
one
know
the
invention
to
use
it
,
for
to
retract
that
which
they
will
:
For
it
is
as
easie
to
retract
a
Pallace
as
a
Countrey-House
,
or
a
Chamber
,
seeing
that
it
is
nothing
but
to
set
ones
self
in
a
place
,
where
there
may
see
that
which
they
would
design
,
and
to
bring
the
spectacle
near
the
Glass
,
when
there
shall
be
ne●d
,
by
the
means
of
holes
,
which
are
in
the
Board
.
A
Painter
may
also
use
this
for
to
retract
figures
,
at
such
a
posture
,
as
he
shall
have
given
them
,
for
to
retract
after
the
embossing
.
In
a
word
,
for
all
that
he
shall
judge
,
be
assured
,
that
the
use
will
render
many
things
easie
that
were
hard
before
.
Another
pretty
Invention
for
to
exercise
the
Perspective
,
without
knowing
it
.
THis
Invention
is
found
to
be
as
pretty
,
as
the
former
,
and
some
do
esteem
it
more
;
by
reason
that
the
other
obligeth
to
design
twice
:
the
first
upon
the
Glass
:
the
second
to
retract
that
which
one
hath
done
there
:
and
in
this
,
we
design
but
once
,
and
as
exactly
as
the
other
.
I
will
not
set
down
the
framing
of
this
instrument
,
it
having
no
difference
from
that
which
I
have
now
given
,
but
only
that
instead
of
a
leaf
of
Glass
,
we
must
set
there
a
frame
,
divided
by
little
squares
,
with
threads
very
slender
,
as
the
figure
sheweth
it
,
the
which
I
shall
call
a
Lettice
;
for
the
number
of
the
squares
,
I
leave
that
to
the
discretion
of
every
one
,
I
shall
say
only
that
we
must
not
make
them
too
great
,
for
to
work
more
exactly
,
nor
too
little
for
fear
of
being
confused
.
For
the
order
,
there
is
need
,
that
this
piece
H
,
be
placed
in
such
manner
,
that
one
may
see
by
the
hole
of
the
spectacle
I
,
all
that
we
would
design
;
if
the
design
,
which
we
desire
to
make
,
must
be
greater
then
the
frame
,
or
then
the
Lettice
is
,
or
as
others
will
,
the
Checker-board
,
we
must
make
the
squares
of
linnen-Cloth
or
of
Paper
,
greater
then
that
of
the
frame
,
and
if
it
be
lesser
,
we
must
make
the
squares
lesser
,
but
we
must
always
make
squares
for
to
carry
in
each
square
of
its
paper
,
or
of
the
Cloth
,
that
which
we
shall
see
within
the
squares
of
the
frame
,
looking
upon
it
by
the
spectacle
I
,
and
if
all
shall
be
represented
proportionably
,
the
design
will
be
as
just
for
the
Perspective
,
as
if
one
had
used
Rules
and
the
Compass
.
I
have
set
the
two
figures
,
for
to
cause
to
be
seen
how
this
piece
H
,
must
be
placed
for
to
use
it
in
designing
upon
a
Table
,
and
when
one
would
paint
,
by
the
one
and
the
other
manner
,
we
may
make
more
exactly
all
sorts
of
Perspectives
,
counterfeit
Pictures
,
and
draw
to
the
life
.
I
doubt
not
but
many
will
say
,
that
this
method
is
not
new
,
and
that
there
is
not
a
Painter
,
that
knoweth
not
how
to
enlarge
and
diminish
Pictures
,
using
this
Checker-board
,
that
is
true
,
but
I
beleive
that
not
any
one
hath
ever
used
the
spectacle
,
which
is
the
secret
for
to
make
every
thing
in
its
perfection
.
ORDERS
FOR
TO
FIND
THE
NATURAL
SHADOVVS
AS
WELL
BY
THE
SUN
AND
BY
A
TORCH
AS
BY
A
CANDLE
AND
A
LAMP
.
The
Original
of
Shadows
.
FOr
to
define
the
natural
Shadow
,
we
say
not
that
it
is
an
entire
Privation
of
light
;
for
that
would
be
to
say
a
perfect
obscurity
,
where
we
should
see
as
little
the
objects
as
their
shadows
,
but
we
understand
a
diminution
of
Light
,
caused
by
the
interposition
of
some
body
which
is
not
transparent
,
the
which
receiving
the
Sun
,
or
the
clearness
which
should
cast
it self
upon
the
plane
where
it
is
set
,
giveth
there
a
shadow
of
its
shape
,
for
the
light
being
Comunicative
of
it self
,
produceth
it self
upon
all
that
which
is
not
hidden
from
it
,
&
Extendeth
it self
upon
all
that
is
plain
and
united
:
but
if
it
meet
which
the
least
Elevation
,
this
hinderance
causeth
it
to
make
a
Shadow
,
which
rendreth
upon
the
Plane
the
forme
and
figure
of
that
which
is
Enlightned
.
The
diversity
of
lights
,
maketh
a
diversity
of
shadows
for
if
the
body
that
enlightneth
is
greater
then
that
which
is
enlightned
the
shadow
will
be
lesser
then
the
body
if
they
be
equall
,
the
shadow
will
be
equall
to
the
Body
enlightned
:
but
if
the
light
be
lesser
then
the
Object
,
the
shadow
will
still
be
more
and
more
the
greater
.
For
to
understand
this
the
better
,
we
will
make
the
three
figures
following
,
which
shall
serve
us
as
a
foundation
,
for
the
Rules
which
we
shall
give
.
The
first
sheweth
that
the
Body
of
light
A
B
,
being
much
greater
then
the
Enlightned
C
D
,
it
Enlightneth
more
then
the
half
of
the
Object
,
the
which
maketh
it
to
give
a
shadow
with
a
Point
and
frame
it
into
a
Pyramide
,
whereof
the
Sun
is
the
Base
.
This
truth
is
shewed
in
the
Ecliepse
of
the
Moon
,
which
is
seldom
wholly
Covered
with
the
shadow
of
the
earth
,
which
nevertheless
exceedeth
it
in
greatness
forty
times
,
by
reason
that
the
Sun
,
which
is
the
body
full
of
light
,
is
an
hundred
sixty
six
times
,
and
more
,
greater
then
the
Earth
,
which
it
enlightneth
more
then
the
half
;
and
by
consequencee
causeth
to
give
a
shadow
to
it
in
a
point
.
The
second
,
having
the
body
of
light
F
G
,
equal
in
greatness
to
the
enlightned
H
I
,
it
enlightneth
the
half
of
the
Object
,
and
giveth
its
shadow
parallel
H
I
K
L.
The
third
maketh
appear
,
that
the
lightsome
body
,
or
the
light
M
,
being
less
then
that
which
is
enlightned
N
O
,
is
not
enlightned
by
the
half
,
the
which
causeth
a
shadow
unto
it
,
N
O
P
Q
,
which
enlargeth
it self
according
as
it
is
removed
,
from
the
object
,
and
maketh
a
Pyramide
,
whereof
the
light
is
the
point
.
Of
the
difference
of
Shadows
.
BY
that
which
I
have
spoken
in
the
Leaf
aforegoing
,
we
must
conclude
,
that
one
and
the
same
Object
may
give
divers
shapes
of
shadows
or
projections
,
although
that
it
be
enlightned
of
the
same
side
;
by
reason
that
the
Sun
giveth
it
of
one
fashion
,
the
Torch
of
another
,
and
the
Day
doth
not
frame
it
.
The
Sun
rendreth
always
the
shadow
equal
to
the
object
,
that
is
to
say
,
by
parallel
,
as
the
first
figure
sheweth
it
.
I
shall
teach
in
the
Leaves
following
,
how
we
ought
to
use
this
method
,
and
to
give
to
every
object
the
natural
shadow
,
which
the
Sun
would
cause
it
to
have
;
All
Painters
,
Gravers
and
others
may
,
if
they
please
,
observe
these
Rules
,
when
they
would
make
any
thing
pleasing
,
and
not
to
take
the
Rule
of
the
Candle
,
or
Torch
,
for
this
;
as
divers
have
done
.
The
shadow
of
the
Torch
is
not
given
by
parallels
,
but
by
Rays
,
which
issue
from
the
same
Center
,
that
which
causeth
the
shadow
is
never
equal
to
the
body
,
but
more
large
,
and
is
greater
always
according
as
it
is
removed
,
the
which
may
be
seen
in
the
second
figure
,
where
the
shadow
is
larger
then
in
the
first
,
although
that
the
Cubes
of
the
one
and
the
other
be
of
equal
breadth
and
height
.
See
then
how
one
should
be
much
deceived
if
one
should
make
the
shadow
of
a
Torch
,
like
as
that
of
the
Sun
,
and
of
the
Sun
,
as
that
of
the
Candle
,
seeing
that
the
difference
is
so
notable
.
There
is
a
third
sort
of
shadow
,
which
is
neither
of
the
Sun
,
nor
of
a
Torch
,
but
only
caused
by
a
fair
Day
,
the
which
having
not
strength
enough
for
to
frame
the
figure
,
rendreth
only
a
confused
blackness
at
the
object
,
as
in
the
third
figure
.
Now
this
hath
no
Rule
,
wherefore
every
one
giveth
it
,
and
practiceth
it
according
to
his
fancy
,
All
these
shadows
as
well
of
the
Sun
,
as
of
the
Torch
,
and
of
the
Day
,
ought
to
be
more
dark
then
the
parts
of
the
objects
which
are
not
enlightned
,
as
A
,
it
not
so
dark
as
B
,
by
reason
that
A
receiveth
the
reflection
of
the
clearness
,
which
is
about
it
:
and
B
,
hath
not
the
reflection
that
A
,
which
is
in
obscurity
.
We
must
observe
also
,
that
the
part
of
the
shadow
most
distant
from
the
object
,
is
also
more
dark
,
then
the
part
nearer
as
G
,
is
darker
then
H
,
by
reason
that
A
cannot
communicate
that
little
reflection
which
it
receiveth
unto
G
,
as
it
doth
to
H.
1.
Figure
2.
Figure
3.
Figure
For
to
finde
the
shape
of
the
Shadows
.
WE
shall
observe
at
the
beginning
of
this
Book
,
that
the
Definition
of
Perspective
is
to
give
upon
a
Plane
perpendicular
to
the
Horizon
,
the
Representation
of
Objects
which
are
upon
the
Ground
,
or
upon
a
Plane
Horizontal
:
And
for
shadows
,
it
is
altogether
contrary
;
seeing
that
one
supposeth
a
Body
elevated
upon
the
Plane
,
the
which
being
enlightned
,
casteth
its
shadow
upon
the
same
Plane
,
as
we
see
,
that
the
Body
A
giveth
upon
the
Plane
the
shadow
B
;
for
to
finde
the
shadows
we
must
suppose
two
things
,
the
Light
and
a
Body
:
The
Light
,
although
it
be
contrary
to
it
,
it
is
that
nevertheless
which
giveth
it
its
Being
,
and
the
Body
or
the
Object
giveth
it
its
shape
and
its
figure
.
I
shall
not
discourse
here
but
of
shadows
,
for
I
suppose
that
we
have
learned
to
set
the
Bodies
or
Objects
into
Perspective
.
For
to
understand
these
shadows
more
easily
,
and
render
the
Orders
following
more
easie
;
we
must
mark
that
we
must
make
use
of
two
points
:
the
one
of
the
foot
of
the
light
,
which
ought
always
to
be
taken
upon
the
Plane
where
the
Object
is
placed
;
and
the
other
of
the
Torch
or
lightsom
Body
;
seeing
that
the
Rule
is
general
for
the
Sun
and
for
the
Torch
,
with
this
only
difference
,
that
the
shadow
of
the
Sun
is
given
by
Parallel
,
and
that
of
the
Torch
by
the
Ray
of
the
same
Center
.
We
will
begin
with
that
of
the
Torch
,
seeing
that
it
will
help
the
better
to
comprehend
that
of
the
Sun
,
which
shall
follow
.
We
say
then
for
example
,
That
if
one
would
have
the
shadow
of
the
Cube
A
,
as
we
see
B
,
that
we
must
from
the
point
O
,
foot
of
the
light
,
draw
lines
by
all
the
Angles
of
the
Plane
of
the
Object
,
as
here
by
the
plane
of
the
Cube
O
D
,
O
E
,
O
F
,
O
G
:
Then
you
must
draw
other
lines
from
the
point
of
the
light
of
the
Torch
by
all
the
same
Angles
elevated
,
and
to
continue
these
lines
until
that
they
divide
the
other
lines
drawn
from
the
point
O
:
for
example
,
having
from
the
point
O
drawn
the
line
passing
by
the
Angle
of
the
Plane
D
;
if
one
draw
from
the
point
C
,
a
line
passing
by
the
same
Angle
elevated
;
this
shall
divide
the
other
at
the
point
H
,
and
the
point
H
shall
be
the
shadow
of
this
Angle
.
If
from
the
point
C
,
we
do
the
same
by
all
the
Angles
elevated
,
we
shall
divide
the
lines
of
the
Plane
,
at
the
points
H
I
K
L
,
the
which
points
we
must
joyn
with
right
lines
,
and
we
shall
have
the
shadow
of
the
Cube
,
as
is
to
be
seen
at
the
Figure
above
,
and
more
clearly
at
that
below
.
Of
Shadows
taken
from
the
Sun
.
THE
Sun
,
that
glorious
lightsom
body
,
being
far
greater
then
the
whole
Globe
of
the
Earth
,
as
I
have
already
said
in
the
beginning
of
this
Treatise
,
should
make
all
its
shadows
in
point
,
seeing
that
he
doth
always
enlighten
more
then
the
half
.
In
pursuit
of
this
demonstration
we
should
conclude
,
that
all
the
shadows
of
the
Sun
ought
to
be
less
then
the
Body
that
is
opposed
unto
it
,
and
to
diminish
as
it
removeth
it self
far
off
:
which
would
be
true
,
if
there
were
any
correspondency
of
the
Body
enlightned
,
to
the
Body
enlightning
:
but
all
the
Objects
which
are
upon
Earth
,
are
so
small
a
thing
in
respect
of
this
great
light
,
that
the
diminution
of
their
shadows
is
unperceivable
by
our
eyes
,
which
acknowledged
them
all
equal
,
that
is
to
say
,
that
they
are
neither
larger
nor
streighter
,
then
the
Bodies
that
give
them
their
shape
;
for
this
reason
,
we
give
all
the
shadows
caused
by
the
Sun
by
Parallels
,
as
we
have
seen
at
the
second
Figure
of
this
Treatise
.
It
followeth
from
all
this
discourse
,
that
for
to
have
the
shadow
of
what
body
soever
it
be
,
being
opposed
to
the
Sun
,
we
must
draw
a
line
from
above
this
great
light
,
which
may
fall
plumb
at
the
place
where
one
would
take
the
foot
of
the
light
;
and
from
this
place
to
draw
an
occult
line
by
one
of
the
Angles
of
the
Plane
of
the
Object
,
and
another
of
the
Sun
by
the
same
Angle
elevated
,
and
the
section
of
these
two
lines
shall
shew
how
far
the
shadow
must
go
,
all
the
other
lines
shall
be
drawn
Parallel
unto
these
.
For
example
,
for
to
take
the
shadow
of
the
Cube
A
,
the
Sun
being
at
B
,
we
must
from
under
the
Sun
C
,
which
is
as
the
foot
of
the
light
,
draw
a
line
which
toucheth
an
Angle
of
the
Plane
,
as
C
D.
Then
from
the
o●her
Angles
E
,
to
draw
Parallels
to
this
;
for
to
finde
the
end
of
the
shadow
,
we
must
draw
a
line
from
the
Sun
B
,
passing
by
the
Angle
elevated
F
,
which
shall
divide
the
line
C
D
in
G.
Then
drawing
a
Parallel
to
this
by
the
Angle
H
,
it
will
divide
the
line
E
at
the
point
I
,
and
we
shall
have
the
shadow
of
the
Cube
D
G
L.
He
that
would
cause
the
shadows
to
cast
before
,
or
in
any
other
way
;
he
must
determine
the
place
of
the
Sun
,
and
the
point
underneath
,
to
draw
the
lines
of
an
Angle
,
and
make
all
other
lines
parallel
to
that
,
as
you
may
see
by
the
figure
below
,
without
repeating
the
Practick
,
which
is
the
same
as
that
above
.
The
Shadows
of
the
Sun
are
equal
to
the
Objects
of
the
same
height
,
although
that
they
be
removed
the
one
from
the
other
.
EXperience
teacheth
us
,
that
many
stiles
,
or
elevations
of
the
same
height
;
removed
the
one
from
the
other
,
cease
not
to
give
their
shadows
equal
in
the
same
time
,
I
say
in
the
same
time
,
for
they
do
lengthen
or
shorten
themselves
,
according
as
the
Sun
cometh
near
,
or
retireth
himself
,
the
which
he
doth
every
moment
,
seeing
that
he
never
standeth
still
.
Wherefore
when
one
desireth
to
cause
the
shadow
of
some
object
to
cast
,
we
must
determine
of
the
place
of
the
Sun
and
the
point
under
it
,
to
draw
from
thence
the
two
occult
lines
which
give
the
term
of
the
shadow
,
as
here
the
Hedge-row
A
,
giveth
the
point
of
its
shadow
in
B
,
and
if
from
the
point
B
,
you
draw
to
the
point
of
sight
C
,
this
line
B
C
shall
be
as
well
the
shadow
of
the
Hedge-row
D
,
as
of
that
A
,
and
of
all
those
that
should
be
in
the
same
line
unto
the
point
of
sight
,
and
you
must
hold
for
a
maxime
,
that
the
shadows
do
always
keep
the
same
point
of
sight
with
the
objects
.
Following
this
experience
,
that
the
objects
of
the
same
height
do
give
the
shadows
equal
,
if
one
would
give
the
shadow
to
the
Hedge-rows
E
F
,
which
are
of
the
same
height
with
A
D
;
we
must
only
take
with
a
Compass
the
distance
A
B
,
and
carry
it
to
the
foot
of
the
Hedge-Row
E
,
for
to
have
E
G
;
and
from
this
point
G
,
to
draw
to
the
point
of
sight
C
,
and
to
make
always
the
same
Practice
,
even
when
these
Alleys
were
prolonged
infinitely
.
But
if
the
light
come
from
the
bottom
,
or
from
before
,
as
in
the
figure
below
,
must
we
change
the
Order
?
No
,
we
most
only
set
forward
or
draw
back
the
foot
,
or
that
under
the
Sun
,
and
draw
lines
from
the
one
and
from
the
other
by
an
Angle
,
as
are
H
and
I
,
which
shall
give
the
bound
of
the
shadow
of
the
Hedge-Row
K
,
to
the
point
L
;
and
from
this
point
L
we
must
draw
to
the
point
of
sight
M
:
Then
from
all
the
Angles
of
the
Plane
of
the
Palissades
,
we
must
draw
Parallels
to
the
line
H
,
unto
the
Ray
L
M
,
and
we
shall
have
the
natural
shadows
of
the
same
Palissades
or
Hedge-Rows
.
Of
the
Shadows
when
the
Sun
is
directly
opposite
to
the
Eye
.
AS
often
as
the
Sun
is
before
our
eyes
,
that
is
to
say
,
above
the
point
of
sight
;
the
sides
of
the
shadow
that
it
shall
cause
shall
be
parallels
,
as
are
all
the
visual
Rays
;
wherefore
the
point
of
sight
shall
serve
always
for
the
foot
of
the
light
;
And
the
other
Ray
,
which
shall
determine
the
shadow
,
shall
be
taken
from
the
center
of
the
Sun
.
For
example
,
when
we
would
find
the
shadow
of
the
Cube
A
,
we
must
by
the
Angles
of
its
plane
B
C
,
draw
Rays
to
the
point
of
sight
D
,
as
are
B
E
,
C
F.
Then
from
the
center
of
the
Sun
G
,
draw
also
two
Rays
,
which
shall
divide
those
at
the
point
K
L
,
passing
by
the
ends
of
the
lines
elevated
from
the
angles
B
and
C
,
which
are
H
and
I
:
In
such
manner
as
the
shadow
of
this
Cube
shall
be
B
K
L
C.
The
shadows
of
the
two
other
pieces
M
and
N
,
shall
be
taken
by
the
same
order
,
and
so
of
all
the
others
,
which
may
there
be
met
withall
.
It
cometh
into
my
mind
,
that
one
might
be
troubled
,
if
instead
of
a
Cube
,
there
were
a
Pyramide
:
by
reason
that
the
Ray
of
the
midst
of
the
plane
of
the
Pyramide
,
and
the
Ray
of
the
Sun
,
that
passeth
by
the
point
,
made
but
one
line
,
and
by
consequence
can
terminate
nothing
for
to
take
the
shadow
from
the
point
of
this
Pyramide
.
When
this
shall
happen
,
we
must
from
an
Angle
of
the
plane
,
as
is
here
O
,
draw
a
Ray
to
the
point
of
sight
P
,
which
shall
make
O
Q
:
And
from
the
same
Angle
O
,
elevate
a
Perpendicular
O
S
,
then
from
the
point
of
the
Pyramide
T
,
make
a
parallel
to
the
base
,
until
that
it
divide
the
Perpendicular
O
S
,
at
the
point
V
:
We
must
make
the
Ray
of
the
Sun
to
pass
by
this
point
V
,
and
continue
it
until
that
it
divide
the
Ray
O
Q
,
at
the
point
X
,
from
this
point
X
,
we
must
make
a
parallel
to
the
base
,
unto
the
Ray
of
the
midst
of
the
Pyramide
,
which
shall
be
divided
at
the
point
Y
,
the
bound
of
the
shadow
:
We
must
draw
to
this
point
Y
,
from
the
Angles
Z
and
O
,
and
the
Triangle
Z
Y
O
,
shall
be
the
shadow
of
the
Pyramide
.
These
Walls
,
which
are
at
the
bottom
of
the
one
and
the
other
figures
,
take
their
shadows
as
we
have
said
of
the
Cube
A.
For
to
give
the
shadow
of
the
Objects
pierced
by
the
light
.
WHEN
the
Object
is
square
,
or
of
a
right
line
,
we
must
from
the
point
A
from
under
the
Sun
,
draw
lines
Parallels
from
all
the
Angles
of
the
Plane
:
Then
from
the
midst
of
the
Sun
B
,
draw
a
line
to
the
Angle
the
far●hest
removed
C
,
which
shall
divide
the
line
A
at
the
point
D
,
and
to
draw
from
the
point
D
to
the
point
of
sight
E
,
until
that
it
finde
the
last
line
of
the
Plane
F
:
for
to
have
the
rest
of
the
shadows
,
we
must
draw
Parallels
to
the
line
B
C
D
,
by
the
corners
G
H
I
,
by
reason
that
the
Sun
enlightneth
two
faces
,
and
maketh
the
shadow
larger
,
as
is
to
be
seen
in
the
first
figure
,
that
G
C
and
H
I
are
the
Diagonals
of
these
square
Pieces
enlightned
on
two
sides
;
and
where
these
lines
drawn
by
C
G
and
H
I
shall
divide
the
line
A
,
we
must
draw
to
the
point
of
sight
E
,
and
we
shall
have
all
the
Projection
,
or
the
shadow
of
the
Object
.
If
it
be
a
Round
,
as
in
the
second
figure
,
we
must
make
the
Round
by
the
Order
of
the
Arches
on
the
side
,
as
fol.
62.
and
63
by
elevating
the
Perpendiculars
,
and
when
the
Round
shall
be
framed
with
its
thicknesses
,
we
must
from
the
foot
of
all
these
Perpendiculars
draw
Parallels
to
the
base
,
as
L
K
,
then
to
take
for
the
under-part
of
the
Sun
L
,
which
is
the
Parallel
of
the
midst
of
the
Round
.
Then
from
the
midst
of
the
Sun
M
,
to
draw
a
line
passing
by
the
upper
part
of
the
Round
N
,
and
to
continue
until
that
it
divide
this
Parallel
L
,
at
the
point
O
,
which
shall
be
the
bound
of
the
shadow
.
The
empty
part
of
this
Round
shall
be
found
,
drawing
a
Parallel
to
N
O
from
the
point
P
,
which
is
the
upper
part
of
the
Round
opposite
to
the
Sun
,
until
that
it
divide
the
line
I
O.
The
rest
of
the
Round
shall
be
found
drawing
also
a
little
Parallel
to
N
O
from
the
point
R
,
which
shall
give
S.
All
the
rest
of
the
Rounds
are
found
by
making
parallels
to
N
O
,
by
all
the
points
of
the
Round
of
the
Perpendicules
,
which
we
must
continue
until
that
they
divide
the
Parallels
to
the
base
,
so
as
I
have
made
that
of
the
midst
L
O
,
I
had
marked
them
all
with
points
;
but
I
am
such
an
enemy
of
confusion
,
that
this
hath
caused
me
to
omit
them
.
The
Shadows
take
the
shape
of
the
Planes
where
they
are
cast
.
HItherto
I
have
given
the
shadows
within
a
Plane
united
,
being
assured
that
he
which
shall
understand
them
well
,
shall
not
have
any
difficulty
to
practise
these
here
,
and
the
others
that
follow
;
because
that
it
is
all
the
same
Rule
,
and
that
one
only
direction
shall
suffice
for
to
make
to
understand
,
how
these
shadows
do
raise
and
abase
themselves
according
as
they
finde
their
Planes
.
For
to
make
it
appear
,
that
these
shadows
are
found
by
the
same
Rule
that
the
former
,
is
it
not
sertain
that
he
which
should
draw
a
line
from
under
the
Sun
A
,
passing
by
the
Plane
of
this
Gate
B
,
and
that
from
the
Sun
C
,
one
should
draw
another
by
the
top
of
the
Gate
D
,
that
these
lines
would
divide
themselves
out
of
our
paper
,
and
would
give
the
bound
of
the
shadow
,
so
as
I
have
said
of
others
?
But
the
wall
E
hindring
the
line
A
B
to
prolong
it self
,
as
it
would
do
if
the
Plane
were
united
,
obligeth
it
to
raise
it self
as
we
see
E
G
:
wherefore
it
is
that
the
Ray
of
the
Sun
C
,
which
ought
to
go
very
far
to
seek
the
line
A
B
,
divideth
it
against
the
wall
at
the
point
G
,
and
there
marketh
the
shape
,
or
the
shadow
of
this
Gate
,
whereof
the
Top
draweth
to
the
point
of
sight
H.
The
shadow
of
this
piece
K
easteth
its
self
with
its
whole
length
K
I
,
passing
over
this
other
piece
I
;
and
we
must
mark
,
that
the
shadow
keepeth
always
its
length
,
although
that
it
meet
with
something
between
two
:
and
it
must
be
,
that
the
shadow
which
passeth
over
something
,
observeth
the
figure
and
the
forme
of
the
same
thing
:
as
here
the
shadow
M
and
N
,
keepeth
the
shape
of
the
Piece
L.
Although
that
I
have
made
the
Sun
to
appear
in
the
other
figures
,
we
must
not
think
that
he
should
be
so
near
the
Objects
;
it
hath
bin
only
for
to
give
to
understand
,
that
the
Rays
do
come
from
thence
,
whenas
he
is
in
this
height
:
but
nevertheless
,
out
of
the
Piece
,
as
in
this
second
Figure
,
which
yet
ceaseth
not
,
have
the
line
from
under
the
Sun
A
B
,
and
that
of
the
Ray
of
the
Sun
C
,
by
reason
that
we
ought
always
to
suppose
them
for
to
finde
the
bound
of
the
shadow
.
The
shadow
of
the
Piece
O
is
found
,
by
continuing
the
line
A
B
,
and
making
it
to
ascend
the
steps
,
and
raise
it self
against
the
wall
,
until
that
the
Ray
C
,
passing
by
the
corner
of
the
Piece
,
divideth
it
at
the
point
S
,
then
from
the
point
S
to
draw
to
the
point
of
sight
T
For
to
finde
the
shadow
of
the
Piece
P
,
we
must
remember
that
which
I
said
at
the
beginning
of
this
Treatise
,
that
we
must
always
suppose
the
foot
of
the
light
upon
the
Plane
where
the
Object
is
placed
,
and
so
the
Ray
C
,
dividing
the
little
line
A
B
,
sheweth
how
far
the
shadow
of
the
little
piece
P
ought
to
go
,
which
must
be
drawn
to
the
point
of
sight
T.
The
Piece
V
giveth
its
shadow
all
along
,
although
it
descend
into
a
Pit
;
the
shadow
of
the
wall
R
is
found
by
the
same
Order
that
the
others
,
as
also
the
lines
A
B
,
and
●he
Ray
C
,
cause
it
to
be
seen
.
For
to
find
the
shadow
of
the
Objects
,
when
they
have
more
breadth
above
then
below
.
WHEN
one
would
have
the
projection
below
,
or
shadow
of
Figures
,
whereof
the
upper
part
hath
more
breadth
or
length
then
the
lower
,
how
these
two
figures
ought
to
be
.
They
make
ordinarily
a
plane
,
from
which
they
raise
the
Perpendiculars
A
B.
The
plane
being
made
,
we
must
from
under
the
Sun
draw
a
line
as
I
have
already
said
,
and
from
all
the
Angles
of
the
plane
draw
parallels
to
that
,
then
to
draw
one
from
the
Sun
C
,
passing
by
one
of
the
Angles
of
the
Object
,
as
D
,
until
that
it
divide
the
line
of
the
plane
of
the
same
Angle
A
,
so
that
it
make
the
line
D
E
at
the
point
F
,
and
to
draw
E
and
F
,
at
the
point
of
sight
G
;
which
shall
give
the
shadow
of
the
square
above
the
Object
,
then
drawing
from
the
point
of
the
figure
H
,
to
the
point
F
and
L
,
we
have
the
whole
shadow
of
this
Pyramide
turned
down-wards
.
We
may
see
well
,
that
the
projection
,
or
the
shadow
of
this
cross
below
is
made
by
the
same
Order
,
which
I
will
not
repeat
that
I
may
not
be
troublesome
,
For
to
find
the
shadow
of
Objects
elevated
from
the
Ground
.
THis
order
will
be
rendred
easy
by
that
which
I
have
newly
given
,
seeing
that
in
the
one
and
in
the
other
,
we
need
only
to
find
the
plane
,
and
from
this
plane
to
draw
lines
,
parallels
to
those
under
the
Sun
by
all
the
Angles
,
then
from
the
same
Angles
of
the
Objects
,
elevated
into
the
Air
,
to
draw
also
lines
for
to
divide
those
which
are
drawn
from
the
plane
,
and
to
find
the
bound
of
the
shadows
,
as
I
have
here
already
said
many
times
in
the
figures
foregoing
.
The
which
maketh
me
believe
,
that
any
one
shall
easily
understand
all
that
I
can
make
of
the
shadows
taken
from
the
Sun
,
without
that
there
be
any
need
of
other
explications
for
the
figures
,
seeing
that
they
are
sufficiently
intelligible
,
and
all
made
by
the
Rules
which
one
may
have
learned
by
others
heretofore
.
But
as
every
figure
hath
always
some
particular
observation
,
it
will
not
be
besides
the
purpose
to
give
notice
thereof
,
to
the
end
there
may
be
nothing
,
which
may
not
be
easily
understood
.
I
say
then
,
that
in
the
first
figure
,
I
have
only
made
use
of
the
plane
A
B
C
D
,
for
to
find
the
shadows
of
the
objects
E
and
F
,
by
reason
that
they
are
both
upon
the
same
line
,
and
of
the
same
height
.
In
the
second
,
we
must
observe
that
the
piece
of
wood
G
,
casting
its
shadow
upon
the
Wall
H
;
this
shadow
maketh
the
same
figure
that
the
Corniche
I
,
which
is
below
,
the
which
is
seen
also
at
the
Staff
K
,
set
against
the
same
Wall
H.
For
to
find
the
shadow
of
the
board
L
,
we
must
remember
the
order
afore-going
of
the
Objects
broader
above
then
below
:
for
having
drawn
the
Perpendicule
M
,
where
it
shall
divide
the
Ray
N
O
,
we
must
draw
the
line
from
under
the
Sun
M
P
,
then
from
the
board
elevated
L
,
to
draw
a
line
,
which
divideth
M
P
,
and
this
section
shall
be
the
bound
of
the
shadow
.
The
shadow
of
the
Boul
Q
,
shall
be
found
also
,
making
two
Perpendiculars
to
fall
,
of
which
we
must
frame
the
plane
:
Then
by
the
Center
of
this
plane
,
to
draw
the
line
from
under
the
Sun
R
,
and
from
the
Sun
a
Tangent
,
as
Q
S
,
until
that
we
divide
the
line
R
,
at
the
point
T
,
and
also
another
V
,
which
divideth
the
same
R
,
and
this
distance
T
V
,
shall
be
the
greatness
of
the
shadow
of
the
boul
.
For
to
find
the
shadow
at
the
Sun
in
all
sorts
of
Figures
.
THE
shadow
of
these
Figures
is
found
by
the
same
Orders
of
other
bodies
,
that
is
to
say
,
by
parallels
,
as
well
of
them
from
under
the
Figure
,
as
of
those
that
come
from
the
Sun
;
with
this
only
difference
,
that
the
shadow
of
the
bodies
,
or
objects
,
is
found
by
the
help
of
their
plane
,
and
that
the
figures
have
none
thereof
,
but
instead
of
these
planes
,
we
must
,
from
the
aspect
whereby
we
see
the
Figure
,
draw
a
line
by
the
under
part
,
and
upon
this
line
make
to
fall
perpendicularly
,
that
which
is
most
remarkable
in
the
figure
,
for
to
help
to
find
the
shadow
,
and
then
this
line
from
below
,
shall
serve
as
for
a
plane
.
For
example
,
the
figure
being
naked
,
or
cloathed
,
and
without
a
Cloak
,
as
the
first
that
turneth
the
back
to
us
:
We
must
from
under
its
feet
A
,
draw
a
line
to
the
point
of
sight
B
,
and
upon
this
line
A
B
,
make
to
fall
occult
lines
from
all
the
points
which
can
help
to
find
the
true
shadow
:
as
from
the
hand
C
,
to
make
to
fall
a
Plumb-line
,
which
shall
divide
the
line
A
B
at
the
point
D
,
and
from
the
Elbow
E
,
to
make
one
fall
to
the
point
F
,
and
yet
another
from
the
head
G
,
which
shall
give
the
point
H
,
from
all
these
points
D
F
H
,
from
the
feet
of
the
figure
,
and
from
the
end
of
his
Staff
I.
We
must
draw
parallels
to
the
base
.
Then
the
height
of
the
Sun
being
determined
of
,
we
must
draw
a
line
,
as
K
,
passing
by
the
fore-part
,
touching
the
brim
of
the
Hat
G
,
and
to
continue
the
same
,
until
that
it
divide
the
line
H
,
at
the
point
L
,
which
shall
be
the
end
of
the
shadow
.
And
also
from
the
brim
behind
his
Hat
M
,
to
draw
a
parallel
to
K
G
L
,
until
that
it
divide
also
the
line
H
,
at
the
point
N
,
these
points
N
L
,
shall
be
the
shadow
of
the
Hat
.
We
must
draw
a
parallel
by
the
point
C
,
until
that
it
divide
the
line
D
,
at
the
point
O.
This
point
O
shall
be
the
shadow
of
the
hand
,
which
holdeth
the
Staff
:
Wherefore
drawing
from
this
point
O
,
to
the
point
I
,
this
line
O
I
,
shall
be
the
shadow
of
the
Staff
:
We
must
also
draw
a
parallel
to
the
point
E
,
which
shall
divide
F
;
at
the
point
P
,
and
shall
be
the
shadow
of
the
Elbow
,
and
so
of
all
the
places
that
one
would
,
as
of
the
Knees
,
upon
the
parallels
,
which
pass
under
the
feet
;
and
from
all
these
points
to
mark
the
shadow
of
the
whole
figure
:
the
little
figure
Q
,
hath
taken
its
shadow
by
the
same
order
.
I
have
not
marked
all
the
points
,
nor
the
parallels
for
to
avoid
confusion
.
When
they
are
cloathed
at
length
,
for
to
find
the
shadows
of
the
figures
,
we
must
,
as
I
have
said
draw
from
under
their
feet
,
a
line
to
the
point
of
sigh●
R
,
as
this
S
R
,
and
from
the
bottom
of
the
garment
on
the
one
side
and
the
other
,
draw
two
parallels
to
the
base
,
as
T
V
,
and
between
T
V
,
another
X
,
which
is
the
midst
of
the
figure
.
Then
from
the
top
of
the
Head
,
to
draw
a
line
Y
,
which
shall
be
for
the
Ray
of
the
Sun
,
which
we
must
continue
,
until
that
it
divide
the
line
X
,
at
the
point
Z
,
and
this
point
Z
shall
h●●
the
bound
,
where
the
shadow
must
end
,
the
rest
of
the
shadow
shall
be
drawn
between
the
two
parallels
T
V
,
and
if
any
thing
flow
over
,
as
the
two
folde
✚
,
and
*
,
we
must
draw
them
by
parallel
to
Y
X
,
untill
that
they
divide
the
Ray
V
,
as
we
see
that
the
✚
,
giveth
the
shadow
of
the
Elbow
,
and
the
*
,
giveth
that
of
the
folds
of
the
Cloak
.
For
to
finde
with
facility
the
shadows
by
the
Sun
.
IF
I
would
here
set
down
the
shadows
of
all
the
Objects
which
may
be
given
,
it
were
to
take
in
hand
a
design
without
end
,
for
the
Objects
may
be
given
infinitely
:
for
besides
the
great
number
that
there
is
of
them
,
each
would
suffice
to
make
a
Book
,
seeing
that
it
may
be
turned
,
bended
,
and
lie
down
in
divers
manners
,
each
having
its
shadow
different
.
But
this
labour
would
be
very
unprofitable
seeing
that
every
one
may
make
those
which
shall
please
him
,
so
that
he
remember
well
two
or
three
Rules
which
he
must
keep
,
as
I
have
shewed
in
the
Orders
of
the
shadows
taken
from
the
Sun
;
where
two
sorts
of
lines
give
the
means
to
finde
all
the
shadows
which
may
be
;
the
one
coming
from
under
the
Sun
passing
by
the
Plane
:
the
other
which
parteth
from
the
Sun
by
the
upper
part
of
the
Object
,
and
goeth
to
divide
this
other
line
,
where
the
shadow
must
go
:
but
as
these
lines
must
be
each
Parallels
:
that
is
to
say
,
those
from
under
the
Sun
Parallels
between
themselves
,
and
those
of
the
Sun
also
Parallels
between
themselves
.
I
believed
that
I
should
oblige
,
I
gave
an
Invention
to
draw
them
readily
the
one
and
the
other
.
I
have
said
elsewhere
,
how
we
should
draw
Parallels
to
the
base
,
by
the
means
of
a
Board
well
squared
,
as
this
here
A
,
and
of
a
Rule
as
B
,
the
which
shall
serve
to
draw
lines
from
under
the
Sun
,
when
it
meeteth
directly
opposite
to
the
face
of
the
Object
,
as
may
be
the
line
C
D
;
but
if
it
enlighten
by
the
Angle
,
we
must
use
another
instrument
,
as
that
marked
E
,
which
is
a
Rule
fastned
to
the
End
of
another
piece
of
Wood
well
squared
,
and
hollowed
of
one
side
and
the
other
,
in
such
manner
that
the
Rule
F
G
,
may
move
with
force
,
to
the
end
that
having
taken
a
line
bended
as
H
D
,
one
may
therby
make
one
which
may
be
Parallel
to
it
,
which
is
I
K
with
this
false
square
or
Grashoper
,
it
is
so
as
the
Workmen
call
it
E
F
G
;
this
Instrument
doth
abbreviate
exceedingly
,
when
one
would
make
shadows
of
the
Sun
,
for
there
is
not
a
line
,
and
of
what
inclination
soever
it
be
,
whereof
one
may
not
draw
Parallels
.
The
use
will
make
us
to
know
its
profitableness
.
But
for
the
shadow
by
the
Torch
and
the
Candle
,
it
is
of
no
use
at
all
,
by
reason
that
all
the
lines
are
drawn
from
one
Center
.
The
Shadows
taken
from
a
Torch
,
from
the
Candle
,
and
from
a
Lamp
;
are
found
by
one
and
the
same
Order
.
I
Have
already
said
,
that
for
to
finde
the
shadows
,
we
must
necessarily
have
two
points
,
the
one
from
the
foot
of
the
Torch
,
or
of
the
Candle
,
or
of
the
Lamp
,
which
ought
always
to
be
found
upon
the
Plane
,
where
the
Object
is
set
:
the
other
from
the
flame
of
one
of
these
lights
.
From
the
first
point
,
which
is
the
foot
of
the
Torch
,
the
bottom
of
the
Lamp
or
of
the
Candle
,
we
must
draw
Rays
by
all
the
Angles
of
the
plane
of
the
Object
,
of
which
one
would
have
the
shadow
:
And
the
second
point
,
which
is
the
flame
,
will
give
other
Rays
,
which
passing
by
the
Angles
from
the
top
of
the
Objects
,
will
go
to
divide
these
lines
drawn
from
the
plane
,
and
to
mark
where
the
shadow
must
end
it self
:
I
shall
shew
this
by
example
,
using
the
same
Letters
,
for
these
three
lights
,
in
which
it
shall
be
easie
to
see
,
that
it
is
all
the
same
order
,
in
the
one
,
as
in
the
other
,
with
this
only
difference
,
that
the
foot
of
the
Torch
,
or
of
the
Taper
is
set
below
,
and
that
it
must
suppose
in
others
that
they
set
it
there
.
I
say
then
,
that
if
one
would
have
the
shadows
B
,
of
the
Cubes
A
,
that
we
must
from
the
point
O
,
foot
of
the
light
,
draw
lines
by
all
the
Angles
of
the
planes
of
these
Cubes
,
as
O
D
,
O
E
,
O
F
,
O
G
,
Then
from
the
point
C
,
which
is
the
light
,
or
the
fire
of
these
Luminaries
,
draw
other
lines
,
which
must
pass
by
the
Angles
of
the
objects
elevated
,
and
continue
these
lines
,
until
that
they
divide
the
other
lines
drawn
from
the
point
O.
For
example
,
having
drawn
a
line
from
the
point
O
,
passing
by
the
Angle
of
the
plane
D
,
if
one
draw
from
the
point
C
,
another
line
passing
by
the
same
Angle
elevated
P
,
this
of
the
point
C
being
continued
,
shall
divide
the
first
of
the
corner
D
,
at
the
point
H
,
and
this
point
H
,
shall
be
the
shadow
of
this
Angle
D
P.
If
from
the
point
C
,
we
do
the
same
by
all
the
Angles
elevated
,
we
shall
divide
the
lines
of
the
Angles
of
the
plane
,
at
the
points
H
I
K
L
,
the
which
points
H
I
K
L
,
we
must
joyn
with
right
lines
;
and
we
shall
have
the
shadow
of
the
Cubes
,
as
is
to
be
seen
in
the
three
figures
,
By
this
example
,
it
is
easie
to
see
,
that
it
is
all
the
same
order
,
in
the
one
as
is
in
the
others
.
In
the
leaf
following
,
it
shall
be
taught
to
find
the
under
parts
or
the
feet
of
the
Candles
and
Lamps
.
Of
the
foot
of
the
light
.
SEeing
that
the
Order
for
to
finde
the
shadows
for
the
Torch
,
for
the
Candle
at
for
the
Lamp
,
is
altogether
the
same
in
the
one
as
in
the
other
,
as
we
have
sai
but
now
.
There
will
be
no
more
need
to
set
down
distinctions
in
the
Order
following
:
for
when
I
shall
set
a
Torch
,
one
may
set
a
Candle
or
Lamp
in
the
place
,
by
reason
that
the
flame
of
the
one
hath
the
same
effect
with
that
of
the
other
:
wherefore
from
henceforth
,
I
will
use
the
word
of
light
for
all
three
.
For
the
foot
of
these
lights
,
which
must
be
upon
all
the
Planes
,
where
they
set
the
Objects
,
they
shall
be
found
by
this
Method
.
Having
a
Torch
lighted
within
a
Chamber
,
whether
we
shall
set
it
in
a
corner
on
the
side
,
or
in
the
midst
as
this
,
it
must
be
,
that
all
the
Parts
of
the
Chamber
,
or
of
the
Hall
,
as
the
Boards
above
and
below
,
the
sides
and
the
bottom
have
a
point
that
serve●h
for
the
foot
of
the
light
:
that
from
this
point
we
may
draw
by
all
the
Angles
of
the
Plane
of
the
Object
,
of
which
we
would
have
the
shadow
,
as
I
shall
shew
in
the
leaf
following
,
contenting
my self
to
shew
in
this
,
how
we
must
finde
this
point
which
I
call
the
foot
of
the
light
.
The
Torch
being
placed
in
A
,
this
point
A
,
is
the
foot
of
the
light
,
and
B
the
fire
or
the
light
of
the
Torch
;
this
fire
or
light
B
remaineth
firm
and
never
changeth
,
but
the
foot
must
be
found
on
all
sides
.
For
to
have
the
foot
of
the
light
at
the
wall
on
the
side
C
,
we
must
from
the
point
A
draw
a
Parallel
to
the
base
;
until
that
it
divide
the
Ray
D
E
at
the
point
F
,
and
from
the
point
F
to
raise
a
Perpendicular
F
G
;
Then
from
the
point
B
,
which
is
the
fire
,
to
draw
another
Parallel
to
the
base
until
that
it
divide
F
G
at
the
point
H
,
and
this
point
H
shall
be
the
foot
of
the
light
,
as
if
the
Torch
were
lying
,
by
reason
that
its
fire
remaineth
always
at
the
point
B.
For
to
finde
this
foot
of
light
at
the
Board
above
,
we
must
from
the
point
G
draw
a
Parallel
to
the
base
as
G
I
,
and
from
the
point
B
to
make
a
Perpendicule
to
G
I
,
which
shall
give
the
point
K
,
which
shall
be
the
point
of
the
foot
of
the
light
,
as
if
the
Torch
were
turned
upside
down
.
For
to
finde
it
on
the
other
side
of
the
Hall
,
we
must
make
the
same
Order
as
on
the
side
C
,
and
we
shall
have
the
point
L.
For
to
finde
the
foot
of
the
light
at
the
bottom
of
the
Hall
,
we
must
from
the
point
H
draw
to
the
point
of
sight
O
,
until
that
we
divide
the
Perpendicule
E
at
the
point
M
;
then
from
this
point
M
to
make
a
Parallel
to
the
base
,
which
shall
divide
the
Torch
at
the
point
N
,
this
point
shall
be
the
foot
of
the
light
for
the
bottom
of
the
Hall
.
The
foot
of
the
Candle
is
found
by
the
same
Order
,
as
that
of
the
Torch
,
taking
the
midst
of
the
foot
of
the
Candlestick
for
the
foot
of
the
light
;
but
when
it
is
a
P●ated
Candlestick
,
or
an
Arm
set
against
a
wall
,
it
must
be
that
the
Arm
or
the
Branch
of
the
Candlestick
,
determine
the
line
,
or
shall
be
the
foot
of
the
light
.
For
example
,
in
the
Plate
P
,
we
must
by
the
branch
Q
draw
a
Perpendicular
to
the
base
,
as
R
S
;
then
from
the
fire
T
to
make
a
small
Parallel
to
the
base
,
which
shall
divide
R
S
at
the
point
V
,
which
shall
be
the
foot
of
the
light
for
this
side
,
the
point
X
shall
be
it
for
the
board
below
,
the
point
Y
for
the
board
above
,
and
Z
for
the
bottom
of
the
Hall
or
Chamber
.
For
the
Lamp
,
it
is
the
place
where
it
is
fastned
,
which
determineth
its
foot
,
as
here
*
,
from
which
place
they
draw
a
Parallel
to
the
base
unto
the
first
Ray
,
and
altogether
the
same
as
at
the
Torch
,
and
at
the
Candl●
.
For
to
find
the
shadows
by
a
Torch
,
on
all
the
sides
of
a
Chamber
,
THe
shadows
taken
from
the
Sun
,
draw
always
towards
the
Earth
,
by
reason
that
this
Star
,
communicateth
not
its
brightness
except
it
be
above
our
Horizon
:
and
by
consequence
elevated
above
all
the
objects
,
which
causeth
that
their
shadow
always
descendeth
.
But
it
is
not
so
with
the
Torch
;
nor
with
the
Candle
,
or
with
the
Lamp
,
the
which
one
may
set
above
or
below
,
or
on
the
side
of
the
objects
,
which
rendreth
their
shadows
on
all
parts
,
as
we
have
said
.
The
Figure
aforegoing
will
help
to
find
the
shadows
of
the
Objects
,
set
on
every
side
of
a
Chamber
,
for
having
found
the
Foot
of
the
Light
,
as
I
have
newly
spoken
,
there
is
no
more
difficulty
,
seeing
that
this
is
all
the
same
order
,
as
the
Cube
of
the
141
F
O
,
whither
we
may
have
recourse
:
but
that
we
go
not
to
search
so
far
:
I
shall
say
,
that
for
to
have
the
shadow
of
the
Table
,
upon
the
which
the
Torch
is
passed
we
must
from
the
point
A
;
the
foot
of
the
Torch
,
draw
Rays
by
all
the
feet
of
the
Table
C
,
then
from
the
point
of
the
light
B
,
draw
lines
by
the
corners
from
upon
the
Table
I
,
until
that
they
divide
the
Rays
C
,
at
the
points
O
,
which
shall
be
the
bounds
of
the
shadow
of
the
Table
.
The
shadow
of
the
piece
D
,
shall
be
found
drawing
from
the
point
A
,
by
all
the
Angles
of
the
plane
,
unto
the
Angle
of
the
Wall
E
,
and
from
this
Angle
to
raise
them
Perpendicularly
:
Then
from
the
point
of
the
light
B
,
to
draw
lines
by
the
top
of
this
piece
D
,
by
observing
the
Angles
correspondent
to
the
lines
of
the
plane
,
and
we
shall
have
the
shadow
F
,
of
the
figure
,
or
of
the
piece
D.
The
shadows
of
all
the
other
pieces
shall
be
found
by
the
same
order
:
Wherefore
I
shall
quote
only
the
foot
of
the
light
,
seeing
that
the
fire
shall
be
always
the
point
B.
For
to
find
the
shadow
of
the
piece
G
,
the
point
L
,
is
the
foot
of
the
light
.
For
to
find
the
shadow
of
the
piece
N
,
the
point
H
,
is
the
foot
of
the
light
.
For
to
find
the
shadows
of
the
pieces
I
and
M
,
the
point
K
,
is
the
foot
of
the
light
.
The
second
Figure
.
HAving
found
the
foot
of
the
light
on
all
the
sides
of
the
Chamber
as
I
have
said
in
the
foregoing
leaf
;
one
may
have
the
shadows
of
the
objects
in
what
place
soever
they
be
;
by
the
order
that
I
have
given
.
For
by
example
,
having
found
the
foot
of
the
light
Q
,
and
its
fire
P.
We
must
for
to
have
the
shadow
of
the
piece
R
,
draw
Rays
from
the
point
Q
,
which
pass
by
the
plane
of
the
peice
R
,
and
to
continue
them
infinitely
,
but
because
that
they
meet
with
the
bottom
of
the
Chamber
,
or
the
Wall
T
,
we
must
at
the
meeting
of
the
Angle
S
,
elevate
all
these
lines
;
Then
from
the
point
P
,
draw
other
lines
,
by
the
top
of
the
same
piece
R
,
which
shall
go
to
divide
those
of
the
plane
,
and
to
mark
the
place
of
the
shadow
upon
each
of
them
,
taking
care
that
the
Angles
have
reference
to
the
lines
drawn
on
the
plane
.
This
order
is
so
general
,
and
universal
,
that
he
which
shall
well
understand
only
how
to
take
the
shadow
of
a
Cube
,
shall
find
no
difficulty
to
find
the
shadow
of
any
object
whatsoever
it
be
.
Wherefore
having
given
this
order
of
the
Cube
at
the
141
fol
and
this
above
which
is
altogether
the
same
,
I
believe
I
have
sufficiently
instructed
how
to
give
all
the
shadows
,
without
being
obliged
to
use
repetitions
in
all
the
other
figures
which
follow
,
where
I
shall
only
quote
the
point
for
the
foot
of
the
light
.
For
to
find
the
shadow
of
the
piece
V
,
the
point
X
,
is
the
foot
of
the
light
.
For
to
find
the
shadow
of
the
piece
Y
,
the
point
Z
,
is
the
foot
of
the
light
.
For
to
find
the
shadow
of
the
piece
✚
,
the
point
&
,
is
the
foot
of
the
light
,
and
P
,
the
fire
or
the
light
,
for
all
the
pieces
of
this
second
figure
.
2
Figure
The
shadow
by
a
Torch
of
a
Pyramide
upright
,
and
another
upside
down
.
THIS
Pyramide
upright
,
giveth
its
shadow
by
a
Torch
,
as
if
it
were
by
the
Sun
,
by
reason
that
in
the
one
and
the
other
,
there
is
but
one
line
only
,
upon
the
which
they
determine
a
point
●n
which
is
for
the
point
of
the
Pyramide
:
For
example
,
having
made
the
Plane
B
C
D
E
,
and
drawn
two
Diagonals
for
to
finde
the
midst
of
the
Plane
F
,
we
must
raise
a
Perpendicule
F
A
,
then
to
draw
from
these
four
points
B
C
D
E
,
to
the
point
A
,
and
the
Pyramide
shall
be
framed
;
for
to
finde
its
shadow
,
we
must
from
the
foot
of
the
light
G
,
draw
one
line
only
passing
by
the
point
F
,
and
prolong
it
infinitely
.
Then
from
the
fire
or
light
of
the
Torch
H
,
draw
another
line
by
the
top
of
the
Pyramide
A
,
and
continue
it
until
that
it
divide
G
F
,
at
the
point
I
,
which
shall
be
the
bound
for
the
shadow
of
the
Pyramide
,
which
shall
be
finished
,
drawing
C
to
I
,
and
E
to
I
,
for
this
Triangle
C
I
E
,
shall
be
the
shadow
of
the
Pyramide
A.
For
to
have
the
shadow
of
this
Pyramide
over-turn'd
,
we
must
cause
Perpendiculars
to
fall
from
the
square
above
,
and
to
frame
the
Plane
below
thereby
,
as
we
have
said
at
that
of
the
Sun
fol.
138.
this
Plane
being
framed
,
we
must
from
the
foot
of
the
light
G
,
draw
lines
by
all
these
Angles
.
Then
from
the
point
H
,
which
is
the
fire
,
draw
also
others
by
the
Angles
of
the
square
above
,
which
dividing
those
of
the
Plane
,
shall
mark
the
place
of
the
shadow
as
we
have
said
in
other
Orders
of
the
Torch
.
The
shadow
of
a
Cross
.
HAving
set
a
Cross
in
the
shadows
of
the
Sun
,
it
seemed
to
me
necessary
also
to
set
one
in
the
shadow
of
a
Torch
,
to
the
end
that
by
that
and
by
this
,
we
might
know
the
difference
of
the
one
from
the
other
.
The
Order
is
seen
enough
,
seeing
that
we
have
already
taught
at
the
137
fol
,
to
finde
the
Plane
;
and
that
the
rest
is
as
in
other
Orders
of
the
Torch
.
For
to
finde
the
shadow
of
Round
Objects
,
by
a
Torch
.
HAving
made
the
fore-going
figure
,
it
came
into
my
mind
,
that
one
might
be
in
trouble
,
if
there
should
be
Bowles
,
Cups
,
Viols
,
Flagons
,
or
other
round
pieces
(
which
have
Ordinarily
more
breadth
above
then
below
)
of
the
which
we
would
have
the
shadow
by
a
Torch
;
by
reason
that
such
pieces
seem
more
difficult
then
the
squares
,
although
that
in
effect
,
it
be
all
the
same
Order
there
being
nothing
but
to
reduce
the
square
into
round
so
as
I
,
have
taught
in
the
fol.
19.
20.
28.
29
and
86
:
Where
we
shall
see
all
the
Orders
for
to
set
the
Planes
of
round
pieces
into
Perspective
;
the
which
being
known
,
all
the
rest
is
very
easy
to
understand
.
I
have
said
already
at
fol.
138
,
how
we
must
finde
the
Plane
of
a
Bowle
,
and
by
this
Plane
,
to
have
justly
the
greatness
of
the
shadow
by
the
Sun
:
But
as
this
of
the
Torch
is
different
from
that
;
I
believed
it
to
be
necessary
to
set
that
also
down
here
by
reason
that
it
doth
facilitate
the
Order
of
all
the
other
Rounds
.
For
the
shadow
of
this
Bowle
,
I
say
then
,
that
having
made
its
Roundness
with
a
Compass
,
which
is
the
the
Circle
A
,
and
draw
his
Diameter
B
C
,
that
we
must
under
this
Circle
make
a
line
Parallel
to
B
C
,
which
toucheth
the
Circle
at
the
point
H
,
then
from
the
ends
of
the
Diameter
B
C
,
to
Cause
Perpendiculars
to
fall
upon
this
line
underneath
,
as
B
D
,
and
C
E
,
of
the
which
points
D
E
,
we
shall
frame
the
ordinary
way
the
Plane
D
E
F
G
,
whereof
the
diameter
F
G
,
shall
divide
this
D
E
,
at
the
point
H
;
This
Plane
D
E
F
G
,
shall
serve
for
to
finde
shadow
of
this
Bowle
A.
For
after
having
drawn
from
the
Foot
of
the
Light
I
,
lines
which
touch
this
plane
on
the
one
side
and
other
,
as
are
the
lines
I
K
and
I
L
;
And
also
another
line
passing
by
the
midst
of
the
plane
H
,
which
shall
be
the
line
I
H
M.
We
must
afterwards
draw
other
lines
from
the
Light
of
the
Candle
N
,
which
touching
the
Bowle
shall
go
to
divide
these
lines
of
the
Plane
,
as
from
the
point
N
,
to
draw
a
line
,
which
toucheth
the
Bowle
between
A
and
B
,
and
divideth
the
line
I
H
,
at
the
point
M
,
which
shall
be
the
end
of
the
shadow
:
for
to
have
the
beginning
of
this
shadow
we
must
from
the
same
point
N
,
draw
another
line
which
toucheth
the
fore-part
of
the
Bowle
,
and
divideth
also
the
line
I
H
,
at
the
point
Q
:
this
distance
Q
M
,
shall
be
the
length
of
the
shadow
,
for
its
bredth
,
we
must
also
from
the
point
N
,
draw
two
lines
by
the
ends
of
the
Diameter
of
the
Bowle
Z
Z
,
and
they
shall
divide
the
lines
I
K
,
at
the
point
R
,
and
this
I
L
,
at
the
point
S.
Wherfore
if
R
S
,
be
the
bredth
of
the
shadow
,
and
Q
M
,
the
length
,
we
have
only
to
joyn
these
fower
letters
of
Crooked
lines
,
which
shall
give
an
Ovall
,
for
the
shadrw
of
the
Bowle
A
I
have
a
little
Extended
my self
for
to
facilitate
the
shadow
of
this
Bowle
,
by
reason
that
I
believe
this
only
Order
sufficient
for
to
finde
the
shadow
of
other
Rounds
,
as
of
the
Figure
V
,
the
which
having
two
breadths
unequall
,
ought
to
have
a
Plane
of
two
Circles
.
And
that
below
X
,
which
hath
three
differences
,
obligeth
to
make
a
Plane
of
three
Circles
;
The
one
for
the
Neck
of
the
Viol
,
or
Flagon
,
the
other
for
its
Belly
and
the
other
for
the
foot
:
all
these
Planes
are
made
as
of
the
Bowle
.
I
believe
that
it
not
necessary
to
use
Repe●itions
.
The
figure
being
able
to
teach
of
it self
.
Of
the
shadow
upon
many
Planes
Parallels
.
THE
first
Plane
,
that
is
the
Ground
,
where
the
Chair
A
is
placed
,
the
second
Plane
is
the
upper
part
of
the
Table
,
which
is
Parallel
to
the
first
Plane
,
and
either
above
or
below
the
Table
:
it
might
also
have
one
,
or
two
,
or
more
of
these
Planes
,
upon
which
we
shall
finde
the
foot
of
the
light
;
for
to
finde
the
shadows
of
the
Object
,
which
should
be
there
.
For
example
,
the
foot
of
the
light
it
is
C
,
and
the
fire
B
;
from
these
points
C
B
,
we
must
draw
lines
by
the
under-part
,
and
the
upper
of
the
Object
D
,
for
to
have
its
shadow
E
,
upon
the
Table
E.
But
to
have
the
shadow
of
the
Chair
A
,
which
is
upon
the
Ground
,
we
must
find
upon
the
same
ground
the
foot
of
the
light
which
is
upon
the
Table
the
point
C
,
the
Order
following
teacheth
this
.
We
must
from
the
point
of
distance
,
which
is
here
out
of
the
Paper
,
draw
a
line
by
the
foot
of
the
Table
F
;
then
from
the
corner
upon
the
Table
G
,
to
make
a
Perpendicular
G
to
fall
,
which
shall
divide
the
line
F
at
the
point
H
,
and
from
this
point
H
to
draw
a
Parallel
H
I
,
which
is
equal
to
the
upper
part
of
the
Table
,
and
which
ought
to
facilitate
to
finde
that
which
we
seek
:
for
having
from
the
point
of
sight
K
,
drawn
a
Ray
passing
by
the
foot
of
the
light
C
,
unto
the
end
of
the
Table
L
;
we
must
from
this
point
L
,
let
fall
a
Perpendicular
upon
H
I
,
which
shall
give
the
point
M
;
from
which
point
M
we
must
draw
a
Ray
to
the
point
of
sight
K
;
and
upon
this
Ray
M
K
must
be
the
point
of
the
foot
of
the
light
,
which
shall
be
found
easily
,
making
a
Perpendicular
to
fall
from
the
point
C
,
the
which
dividing
the
Ray
M
K
,
shall
give
the
point
N
for
the
foot
of
the
light
.
This
point
N
being
found
,
there
is
no
more
difficulty
to
finde
the
shadow
of
this
Chair
A
,
because
that
it
is
all
the
same
Order
as
of
other
Objects
,
which
we
have
seen
in
the
leaves
aforegoing
;
that
is
to
say
,
that
we
must
from
the
foot
of
the
light
N
,
draw
lines
by
all
the
Angles
of
the
Plane
of
this
Chair
,
and
from
the
light
B
,
to
draw
other
lines
by
the
upper
part
of
the
same
Chair
,
which
divide
those
of
the
Plane
,
and
shall
mark
where
the
shadow
ought
to
go
:
the
figure
will
make
it
known
,
that
all
is
to
be
ordered
as
I
have
said
elsewhere
.
The
second
Figure
.
I
Do
not
set
down
this
second
Figure
,
for
that
I
have
any
particular
thing
,
nor
different
from
that
above
.
But
only
to
refresh
the
Memory
of
that
which
I
have
said
in
the
beginning
,
that
all
the
Objects
cast
their
shadows
diversly
,
and
according
as
they
are
set
about
the
light
,
as
we
see
that
which
is
upon
the
Table
giveth
its
shadow
,
according
as
it
is
enlightned
,
that
is
to
say
,
directly
,
either
on
the
right
or
on
the
left
:
that
which
is
found
by
the
ordinary
Orders
of
the
foot
of
the
light
P
,
and
of
its
fire
or
light
O
,
the
most
part
of
these
Objects
are
broader
above
then
below
,
wherefore
we
must
make
their
Planes
,
as
I
have
said
in
those
folio's
where
I
have
spoken
of
the
like
figures
.
The
shadow
of
boarded
Floores
by
a
Torch
.
I
Have
not
set
this
figure
in
the
shadows
taken
from
the
Sun
,
by
reason
that
this
light
is
above
all
the
Objects
that
are
in
the
World
,
and
by
consequence
cannot
give
a
shadow
,
which
supposeth
the
Light
,
or
the
Light-some-body
under
the
Object
.
One
might
object
to
me
that
Experience
causeth
it
to
be
seen
every
day
,
that
when
the
Rays
of
the
Sun
enter
within
an
Hall
,
or
a
Chamber
:
the
shadow
of
the
Floores
and
of
other
things
cease
not
to
appear
;
To
which
I
answer
,
that
then
this
shadow
,
or
these
shadows
,
is
not
,
or
are
not
of
the
Sun
,
but
caused
by
the
great
Brightness
of
the
Sun
;
and
such
shadows
might
not
be
given
by
Parallels
,
as
those
of
the
Sun
,
but
by
Rays
from
one
and
the
same
Center
;
as
those
of
a
Torch
,
taking
the
Window
where
the
Sun
passeth
,
or
the
place
where
it
giveth
,
for
the
point
of
the
light
,
and
to
do
for
such
shadow
,
as
I
am
saying
of
the
shadow
of
a
Torch
.
The
Orders
aforegoing
which
oblige
to
make
Planes
and
to
draw
lines
by
all
the
Angles
,
for
to
finde
the
bound
of
the
shadows
,
would
be
too
long
for
this
,
and
the
great
Number
of
lines
,
which
one
must
draw
there
,
would
make
this
figure
very
difficult
,
by
reason
of
the
Number
of
Beames
and
Joysts
which
there
are
met
with
:
the
which
made
me
seek
the
Means
to
abridge
it
,
for
to
make
is
easie
in
the
practise
,
without
going
forth
of
Rules
and
Maximes
of
Art
Having
made
the
floore
in
Perspective
,
as
it
is
taught
in
the
55th
or
57
fol.
And
placed
the
Candle
,
the
Torch
,
or
the
Lampe
,
in
what
place
we
would
.
We
must
search
by
the
means
of
the
foot
of
the
light
,
the
place
where
the
fire
ought
to
to
be
,
or
to
speak
more
truly
,
the
which
we
shall
use
in
stead
of
the
fire
,
for
from
this
point
to
lines
,
which
pass
under
the
Object
,
and
mark
out
the
bound
of
the
shadows
.
For
to
have
this
point
of
fire
,
the
light
being
at
B
,
we
must
from
the
foot
of
the
light
C
,
draw
a
Parallel
to
the
Base
D
E
,
untill
that
it
cut
the
Ray
E
F
,
at
the
point
G
,
from
this
point
G
,
we
must
elevate
a
Perpendicule
G
L.
Then
from
the
fire
of
the
Torch
B
,
draw
a
Parallel
to
D
E
,
which
shall
divide
the
Perpendicular
G
L
,
at
the
point
L
,
and
this
point
L
,
shall
serve
for
the
point
of
fire
,
which
shall
give
the
place
and
the
length
of
the
shadow
.
For
Example
,
having
to
finde
the
shadow
of
the
Beame
A
,
we
must
from
the
point
L
,
make
a
line
to
pass
under
the
Angle
which
is
towards
us
as
H
,
and
see
where
this
line
L
H
,
shall
divide
the
first
Joyst
,
at
the
point
I
,
for
this
shall
be
the
place
where
the
shadow
of
the
Beame
endeth
:
from
this
point
I
,
we
must
draw
a
parallel
I
K
,
and
marke
upon
the
Joysts
the
place
of
the
shadow
O
,
for
the
shadow
of
the
space
of
the
Joysts
,
ir
will
be
found
by
drawing
also
a
line
from
the
point
L
,
by
the
Angle
of
the
first
Joyst
M
,
which
shall
divide
the
Angle
of
the
Hollow
at
the
point
N
,
from
this
point
N
,
making
a
Parallel
N
P
,
we
shall
have
all
the
shadow
marked
Q
,
for
the
Beame
A.
For
to
finde
the
shadow
of
Joysts
,
besides
that
of
the
Beame
,
we
must
only
draw
a
line
of
fire
B
,
by
the
Angle
S
,
untill
that
it
divide
the
Bottome
of
the
Floore
at
the
point
T
,
do
the
same
to
all
the
other
Joysts
,
and
you
shall
finde
the
shadow
longer
at
the
farther
distance
from
the
fire
.
Having
marked
upon
one
Beame
all
the
points
T
,
we
must
from
the
point
of
sight
R
,
draw
lines
by
each
of
these
points
,
and
we
shall
have
justly
between
all
the
other
Beams
,
the
shadow
of
the
Joysts
as
is
to
be
seen
at
the
points
V.
The
figure
below
is
the
same
with
that
above
,
with
this
difference
,
that
this
is
shadowed
and
that
the
former
is
not
,
by
reason
that
the
shadow
would
have
hindred
to
see
the
letters
and
the
small
lines
.
There
is
more
in
this
,
the
shadow
of
the
Iawmbs
of
this
Gate
,
which
must
be
taken
from
the
foot
of
the
light
as
is
to
be
seen
in
X
and
Y.
For
to
finde
the
shadow
by
the
foot
of
the
light
.
IF
the
Objects
be
Perpendiculars
to
the
base
,
and
more
elevated
then
the
fire
of
the
Candle
A.
We
ought
only
to
draw
lines
from
the
foot
of
this
light
B
,
by
the
Angles
most
advanced
of
the
Objects
,
as
are
C
D
of
the
Screen
,
and
from
the
Angle
of
the
wall
E
,
the
which
lines
B
C
,
B
D
,
and
B
E
,
shall
make
the
place
of
the
shadow
at
the
meeting
of
the
Angles
,
which
the
Shuts
of
the
Screen
make
with
the
floor
,
and
also
the
return
of
the
wall
at
the
points
G
,
from
which
points
G
we
must
elevate
Perpendiculars
at
the
base
G
R
,
which
shall
finish
the
shadows
which
the
Candlestick
A
giveth
The
reason
of
this
is
,
that
the
line
A
B
,
is
parallel
to
the
lines
C
H
,
D
I
,
K
,
and
E
L
,
the
which
maketh
that
,
in
what
part
soever
the
fire
be
upon
the
line
A
B
,
whether
on
high
,
or
in
the
midst
,
or
all
below
,
it
shall
give
always
the
like
shadow
.
We
must
observe
,
that
this
Order
is
not
good
but
in
Pieces
,
which
are
more
elevated
then
the
fire
,
as
these
here
;
for
when
those
shew
the
upper
part
,
as
the
Object
M.
we
must
use
the
Orders
aforegoing
,
by
drawing
lines
from
the
points
of
the
feet
,
and
of
the
fire
of
the
light
Of
the
Shadow
doubled
.
WHEN
two
lights
meet
in
the
same
subject
or
object
,
it
is
of
necessity
that
two
shadows
meet
there
,
because
that
each
day
or
each
light
produceth
its
own
with
proportion
,
I
say
,
with
proportion
;
for
if
these
Fires
lights
be
equal
,
at
the
same
distance
:
It
is
certain
that
the
shadows
shall
be
equal
;
but
if
there
be
the
least
disproportion
,
as
if
the
one
of
these
lights
be
a
little
greater
then
the
other
,
or
that
these
fires
be
a
little
greater
then
the
other
,
or
that
these
fires
,
although
equal
,
be
more
or
less
advanced
the
one
then
tho
other
from
the
object
;
these
shadows
shall
be
different
;
for
example
,
the
object
O
,
being
enlightned
with
two
Candles
;
the
one
near
P
,
the
other
farther
off
Q
;
it
is
most
assured
,
that
the
shadow
of
the
Candle
P
,
shall
be
much
stronger
then
that
of
the
Candle
Q
,
as
is
to
be
seen
in
the
figure
.
The
Orders
of
these
shadows
,
are
no
other
,
then
those
that
I
have
given
,
as
well
so
the
Sun
as
the
Torch
For
the
Shadow
of
Figures
by
a
Torch
.
IT
is
to
be
believed
,
that
my
counsel
will
be
followed
that
one
should
not
turn
over
the
leaf
for
to
learn
the
order
which
followeth
;
before
they
understand
and
remember
well
,
that
which
went
before
Wherefore
supposing
that
one
understands
well
the
order
,
that
I
have
given
at
139
fol.
for
to
find
the
shadow
by
the
Sun
,
for
all
the
figures
of
such
postures
as
they
may
be
:
I
have
nothing
to
say
for
these
,
seeing
that
the
line
below
,
which
I
make
to
serve
for
the
plane
,
and
all
the
other
measures
are
taken
jn
one
,
as
in
the
other
.
But
because
that
the
Torch
doth
not
render
an
equal
shadow
in
breadth
to
the
body
that
giveth
its
shape
,
as
doth
the
Sun
:
We
must
take
this
advice
,
which
is
,
that
instead
of
drawing
the
llnes
parallels
,
that
one
to
the
other
,
as
they
are
in
the
shadows
taken
from
the
Sun
,
we
must
draw
them
all
from
the
same
point
,
as
from
a
Center
;
that
is
to
say
,
that
all
the
lines
,
which
are
drawn
by
the
plane
,
must
be
drawn
from
the
foot
of
the
light
A
,
and
those
above
,
and
about
the
figure
must
be
drawn
from
the
point
of
fire
B
,
in
like
manner
as
in
all
the
other
orders
of
the
Torch
,
the
which
maketh
me
leave
the
rest
,
that
would
be
but
tedious
repetitions
,
seeing
that
the
figure
expresseth
it
of
its
self
.
Of
the
divers
dispositions
and
heights
of
shadows
by
the
Torch
.
THe
shadows
taken
by
the
Sun
,
do
cast
themselves
always
on
the
same
side
,
and
have
ordinarily
one
and
the
same
disposition
:
it
being
impossible
that
the
Sun
should
cause
at
the
same
time
,
to
cast
the
shadow
of
one
body
towards
the
West
,
and
of
another
towards
the
East
,
it
is
very
true
that
it
doth
this
every
day
,
the
one
in
the
morning
,
and
the
other
in
the
evening
,
but
in
one
and
the
same
hour
,
it
will
never
do
it
naturally
.
The
which
is
done
without
failing
,
by
the
Torch
,
the
Candle
,
or
the
Lamp
:
for
in
what
place
soever
you
set
one
of
these
lights
,
if
there
be
many
bodies
about
them
,
they
will
cast
their
shadow
diversly
,
that
is
to
say
,
that
the
one
will
cast
it
to
the
East
,
the
other
to
the
West
,
this
to
the
North
,
that
to
the
South
:
in
short
on
every
side
according
as
the
bodies
shall
be
ordered
about
the
light
,
the
foot
of
the
which
marked
A
,
serveth
them
for
a
Center
,
whether
all
these
shadows
draw
,
and
the
fire
B
,
marketh
where
they
must
end
,
although
diversly
,
by
reason
that
the
nearest
,
have
their
shadow
shortest
,
and
those
that
are
farther
off
,
cast
it
more
at
length
,
Although
that
the
second
figure
hath
not
the
light
in
the
midst
,
yet
the
order
of
these
shadows
ceaseth
not
to
be
kept
,
as
we
see
that
they
all
draw
to
the
foot
of
the
light
C
,
and
that
they
are
bounded
by
the
point
of
fire
D.