YRLE UNIVERSITY LIBRRRY

P39002005913778B

YALE UNIVERSITY
LIBRARY

The
EDWIN J. BEINECKE, '07
FREDERICK W. BEINECKE, '09 S
WALTER BEINECKE, '10
FUND

THE
ART O F
DRAWING IN PERSPECTIVE
MADE EASY.

THE

R

O F

DRAWING IN PERSPECTIVE
MADE EASY
To thofe who have no previous Knowledge of
the Mathematics.
By JAMES FERGUSON, F.R.S.
Sluflrated with Platss.

LONDON:
Printed for W. Strahan ; and T. Cadell in the Strand.
MDCCLXXV.

775

P R E F A C E.
T N my infirm ftate of health, a fitua-
¦*- tion that is very apt to affedl the
mental faculties, I thought my late
book of Mechanical Exercifes would
have been the lafl I Ihould ever pub-
lifli. But, as I have been conftantly
accuftomed to an adtive life, and to
coniider idlenefs as an infupportable
burden, I have, of late, amufed my-
felf at intervals, as my ufual bufinefs
would permit, with ftudying Per/pec-
five J which is an art that every one
who makes drawings, were it but for
plates (efpecially offoUd figures) in
books, fhould be acquainted wftb.
And indeed I drew the figures which
a are

vi PREFACE.
are now engraved ftff this Book, with
no other view than to inftruft others
verbally by, who came to me to learn
fomething of that Iwrancli of fcience,
•without having the leaft thought of
ever laying them before the Public.
But, upon fliewing thefe draJwings
accidentally to fome friends, they ex-
prefied their defire that I ihould write
a defcription of the rules by which
they were delineated. I complied
with their defire, and it is entirely
owing to their partiality to me, that- 1
have confented to this publication^
I need not obferve how requ^fite
it is "for painters who put groupes
of figures togethervbut alfo for thofe
who draw landfcapes, or figures of
machines and engines for books, to
5 know

P RE FACE. . vjl
know the rules of Perfpe<a:ive. The
want of this branch of knowledge is
the reafoh why we not only fee very
bad and diftorted figures of machines
and engines in printed books, but alfo
why wie fee many hiftorical paintingsi
in which the different pidlures of men,
womjen, hillsi houfes, birds, and beaftsi
are put together without any regard
to what painters call keeping ; which is
the fame thing as repfefenting'^ohje&iS
in the fame manner that they appear
to the ^ eye, at different diftances
from it.
I fhall only mention two inftances
in the works of one of the greateft
painters that ever exifted; — I mean
the celebrated Raphael Urbin. ,
Every man isfenfible, that, if he
ihouid ftand by the fea-fide, and look
a 2 at

viii PREFACE.
at a boat with men in it at fome dif^
tance, he could not diftinftly fee the
features of thofe men, much lefs the
wrinkles and marks of the mufcles
in their faces or bare arms. And if
he were in a boat, at fome diftance
from the land, he could not perceive
the eyes and beaks of fowls on the
fiiore. Yet fo it is, that, in one of the fa
mous Cartons of Raphael, reprefent-
ing the. miraculous draught of fiffies,
the men in each of the, two boats ap
pear of full fize, the features of their
faces ftrongly marked ; and the boats
are reprefented fofmall, and the men
fo big, that any one of them appears
fufiicient to fink either of the boats by
his own bare weight : and the fowls
on the fliore are likewife drawn fo
big,

PREFACE. ix
big, as to feem very near the eye of
the obferver ; who could not pofiibly,
in that cafe, diftinguilh the features
of the men in the diftant boats. Or,
fuppofing the obferver to be in either
of the boats, he could not fee the eyes
or beaks of the fowls on the Ihore.
The other inftance is of a very ca
pital miftake in Raphael's hiftorical
pifture of our Saviour's transfigura
tion on the Mount ; where he is re
prefented with thofe who were then
with him, almoft as large as the reft
of his difciples at the foot of the
Mount, with the father and mother
of the boy whom they brought to be
cured: and the mother, though on
her knees, is more than half as tall
as the Mount is high. So that the
Mount appears only of the fize of a
little

^ PREFACE.
little hay-riek, with a fevr people on
its top, and a' greater i^u«3tbeS'. at its
bottom on the ground : iu which cafe^
a fpe<5tator at a little diftanec could as
well- diftinguifli the features of thpffe
on the top as of thofe on the ground.
But.upon any large eminence^ deferv-
ing the name of a Mount, that would
be quite iiftpoffible. — My only i?€afon
for mentioning thefi@ extraordinary
particulars, is to ihew, how neceflary
it is for painters to be well acquaiilted
with the rules of PerfpecStive.'
- I am far from €onfidering the fol
lowing Work as a complete fyftem
of PerfpeSlive, for that would require
a very large volume. But I think I
may venture to fay, that, when the
learner is fully mafter of what is there
contained, he will not find any great
difiiculty

P R E F A C E. xi
difficulty in proceeding to what length
h€ pleafes in the attainment of this
feienc6, without any further aflft-
ance. — Or, if he ihould grow tired,
and be weary of going on according
to the rules, he may make ufe of the
Perfpe^ive Machine defcribed and
delineated at the end of this fmall
tradl, by which he may draw every
thing equally eafy that he fees before
him, without knowing any rule at
all. But I hope there are very few
who will have recourfe to fuch an
unfcientific method.
It is very probable, that thofe who
already underftand Perfpeftive, if they
take the trouble of reading this fmall
Treatife, may think I have been ra
ther too vprbofe in moft of my defcrip-
tions. I only requeft of fuch to con-
fider,

xii PREFACE.
fider, that I ^ never wrote any thing
for thofe who are well fkilled in the
few branches of fcience whereof I
have treated j but only for t^ofe who
wifli to attain a moderate knowledge
of theih; and to fuch, I think, every
thing ought to be made as plain and
eafy, and be as minutely defcribed,
as is poffible.

Perfpedtive

Peflpedlive made Eafy^

c M A P. h
Ti}e Theory of PERSPEctivEi
I. T^ERSPECTIVE is the art of
Jl^ drawing the refemblances or
pictures of objedts oil a plane
furface, as the objedts themfelves ap
pear to the eye.^  Thus, fuppofe a
perfon at a window looks through an
upright pane of glafs at any obje(5t
beyond it* and, keeping his head
fteady, draw's the figure of the objedt
B upon

s PERSPECTIVE
upon the glafs, with a black lead
pencil', asif the point of the pencil
touched the objedt itfelf ; he would
then ha^e a tTue reprefentation of the
obj^dl in perfpedive, as it appears to
his eve.
In order to this, two things are ne-
ceiFary : firft, thatj the glafs be laid
over with ftrong gum-water, which,
wh ^ n "d r 7, Will - ht. fit " for d rawing
upon, and will retain the traces of the
pencil : - and, fecohdly, that he, looks
through a frfiail hole in a tllin plate
of metal, fiS:ed about a footiirom the
glafs, between it and his eye, and that
he keeps hh eye cloife tO the hole ;
otherwife he might ftiift the pofition
of his head, and con fequently make
a fatfe delineation of the objedt. Having

MADE EASY. 3
Having traced out the figure of the
objedt, he may go over it again with
pen and ink ; and, when that is dry,
put a flieet of paper upon it, and trace
it thereon with a pencil: then, taking
away the paper,, and laying it on a
table, he may finifh the pidture, by
giving it the colours, lights, and
Ihades, as he fees them in the objedt
itfelf; and then he wilL have a true
refemlplance of the objedt. r;
2. TJie nearer that any objedt is to
the ey6, the bigger it appears : the
farther from the eye, fo much the
lefs, both in height and breadth.
3. All objedts become vifible by the
rays of light which flow from them
into the eye. Thefe rays pafs through
the pupil, and fall upon the retina,
B 2 which

4 PERSPECTIVE
which is a fine expanfion of the optic
nerve, interwoven like net-work in
the back-part or bottom of the eye ;
and there the rays form a pidture of
the objedt, whofe apparent bulk de
pends upon the fize of fuch pidture,
fo formed upon the retina*
In Fig. I. of Plate I. let PbdcaP be
the eye, P the pupil, or round black
opening in the middle or fore- part of
the eye, through which the rays of
light enter, and proceed to the retina
or back-part bcday where they are
intercepted, and form the pidtures of
the objedts from which they flow.
Every point of the objedt throws off
rays of light in all manner of ftraight-
lined diredtions ; and therefore, every
vifible point of an objedt will fend
fome rays through the pupil into the
eye;

MADE EASY. .5
eye ; and thefe rays, falling upon the
retina, will form all the correfpond-
ing points of the pidture or image of
the objedt thereon. The rays are co
loured according to the colours of the
objedts they flow from, and give the
like colours to its pidture formed in
the eye.
4. To ihew that the pidtures of ob
jedts are thus formed upon the retina,
take the eye of a iheep or bullock,
newly killed, and cut off all the opake
part from the outfide of the back of
the eye, till the tranfparent retina ap
pears : then hold up the eye between
your own eye and any objedt, with
the fore-part of the eye toward the
objedt, and you will fee a fine inverted
pidture of the objedt on the retina,
having all the colours of the objedt
itfelf. B 3 S'^^

6 PERSPECTIVE
5. In Fig. I. let AeB be an objedt,
whofe diftance from the eye is P e.
A ray APa from the top of the ob
jedt, paffing through the pupil P of
the eye, and going on to the retina,
forms the pidture or image of the
point A thereon, at a\ and a ray BPb,
from the foot of the objedt, paffing
through the pupil P, and going on to
the retina, forms the image of the
point ^ at ^ on the retina. — All the
intermediate points of the objedt, from
A to By fend rays of light into the
eye, which form all the intermediate
points of the image between a aijd b
in the eye. So that the image Of the
objedt is inverted in the eye ; and its
whole length is included between the
points a and h on the retina. Thofe
who want to know why we fee the
objedts themfelves in an inverfe pofi tion

-MAPI: EASY. f
tion to that of their pidtures \n rh^
eye, muft read vvhat optical writers
h^ve faid on that fubjedt.
Let the fame objedt be placed twice
as far from the eye, as at CD; ibfn
the diftapcjE Pf will be double the
diftance Pe. The ray CPc forms the
image of the top jC at c on the retina,
and the ray DPd forms the image of
the bottom-poir^t D of the objedt ^td
on the retina.— ^Not;^ it is plain, that
as t)>e fpace between f and d is only
equal to hg.][f the fpace between -a and
b, the ii^nage of the object will be but
h^lf as long upoii the retina, when
the diftance Pf of the objedt is twice
as great as its diftance Pe was before.
— And thus, by removing the objedt
further and further from the eye, or
removing the eye further and further
B 4 from

t PERSPECTIVE
from the objedt, it would feem at laf|
to be no bigger than a mere pointy
becaufe the angle under which it wa?
then feen would be next to nothing.
6. An Ang LE is formed by two lines
approaching toward each other till
they meet ; and the point where they
meet is termed the angular poinL. Thus,
in Fig. I. the lines AP and BP tend
ing toward ope another, form an
angle ; and the point where they meet
at P is the angular point : and whe
ther thefe lines be long or ihort, it
makes no alteration in what is termed
the meafure of the angle; as we ihall
ihew in the next fedtion.
In defcribing an angle, three letters
are generally ufed, the middle letter
always meaning the angular point
where

MADE EASY. 9
where the two lines meet.— Thus, .«^PJ5
denotes the angle formed by the two
lines AP and .SP, meeting at P; and
CPJO denotes the angle formed by the
two lines CP and Z)P, meeting at P. —
In this cafe, as the objedt AeB fub-
tends (or is feen under) the angle
APB, and the objecT: CfD is feen
under the angle CPD^ the former is
called the angle of vifion of the objedt
AeBi and the latter the angle of vi
fion of the objedt CfD, But, as the
lines CP and DP fall within the lines
A P and B P, the angle of vifion of
CfD is lefs than the angle of vifion
oi AeB \ and juft as much lefs as the
diftance of the objedt CfD, from the
eye, is greater than the diftance of
the objedt AeB from it. — So that the
apparent height (or breadth) of any
objedt is diredtly as the meafure of
the angle under which it is feen.
• 7.1f

lo P.^ R S P E C T I V E
7. If.a circle, of any, diameter what
ever, be divided into 360 equal parts
or degrees, and the angular point be
at the center, the number of degrees
between the two lines which form
the angle is the meafure thereof.
Thus, in Fig. 2. of Plate I. the lines AC
and BC form the angle AC By of
which, the point C at the center of the
femicircle dABe is the angular point;
and the number of degrees of the fe
micircle contained between the points
A and J5, in the arc AB^ is the mea
fure of the angle ACB.
Let the femicircle be divided into
three equal parts, as d A, AB, and
B e ; then each part will contain 60
degrees (the whole femicircle contain-^
ing 180) and that will be the meafure
of either of the three angles dCAy
ACB, or BCe.
3 Join

MADE EASY; ii
Join the points A and B by the
ftraight line A B, and a triangie will
be formed by the three lines CAy AB^
and BCy all of equal length; and all
the three angles at A, B,. and C, will
be equal, each containing 60 degrees.
— So like wife, in the leffer femicircle
kabl, the lines ab, bC, and Ca are of
equal length ; and each angle, at C, a^
and b, contains 60 degrees.
, 8.' Any triangle whofe fides are all
equal, is called an equilateral triangle '^
and the angle oppofite to either fide
thereof contains 60 degrees.
9. To make an equilaierat triangle upon
a line of any giv^en length, as fuppofe the
line A B (Plate I. Fig. 2.) : take the
length AB between the points of
your compaffes, and, with that ex
tent.

12 PERSPECTIVE
tent, fet one foot on the end of the
line at ^, and with the other foot de-
fcribe the arc/Q-; then, without al
tering the compafies, fet one foot on
the end B, and with the other foot
defcribe the arc hCi: laftly, from the
ends A and B draw the two lines AC
and BC to the interfedtion of thefe
ires at C; and you will have an equi
lateral triangle, formed by the three
lines or fides AB, BC, and CA; and
each fide will fubtend an angle of 60
degrees. — In the fame manner may
an equilateral triangle be made upon
the given line ab, by the lines bC
and Ca.
10. No objedt can be wholly and
diftindtly feen (if the eye be kept
fteady while looking at it) under a
larger angle ths^n that of 60 degrees.^Thus,

MADE EASY. 13
•—Thus, an eye at C may fee the whole
line or objedt AB (or abj without
moving or ftraining, when the dif-*
tance of the eye from each end of the
line is juf^ equal to the length of the
line, or objedt — And as this is gene
rally reckoned to be a good angle of
vifion, we fliall keep generally by it,
in the following pradtical part of this
Work, where the reprefentations of
large objedts are delineated. But it
will not do fo well in reprefenting
fmall objedts, which are better ite.a
under a fmaller angle than that of 60
degrees : for, when a perfon looks ac
a common drinking- glafs, or a die,
he never brings it fo near to his eye
(unlefs he be very near-fighted) as to
view it under fo large an angle as
that of 60 degrees ; becaufe expe
rience teaches him, that he can fee it

14 PERSPECTIVE
it better under 'a fmaller angle ; that
is, when at a greater diftance from
his e^e.— Thus, the fmall objedt ab
will be better feen by an eye at D,
viewing it under an angle of 30 de-.
grees (as aDbJy than if his eye were
only at half that diftance at C, view
ing the fame objedt ab under an angle
(aCb) of 60. And therefore, in de
lineating the perfpedtive figures of
fmall objedts, the artift fhould always
fuppofe the obferver to be>fo far off
from the obje(5tj'as to be viewing it
under a lefs angle than that of 60
degrees : and then the perfpedtive pic
ture will appear more natural, and
confequently fo much the niore pleaf-
ing to the eye.
II. When a perfon ftands right,
againft the middle of one end of a
long

>¦

MADE EASY. t^-
long avenue or walk, which is ftraight;
and equally broad i throughout ; the
fides thereof feem to approach nearer
and nearer to each other as they are
further and further from his eye, as
the angles "under which their differ
ent parts are feen become lefs and
lefs, according as the diftance from
his eye increafes (§ 2. and;5.); and if
the avenue be very long, the fides of
it at the fattheft end will feem no
meet : and there, an" objedt that would
cover the whole breadth'of the ave-
n<i!ie, and be of a height equal to that
breadth, would appear only to be a
mere point.

Thus, in Fig. 3. of Plate L let AB
be part of one fide of a long avenue,
Z) C as much of the other fide thereof,
and thefe fides be parallel to each
other;

i6 PERSPECTIVE
other ; and fuppofe the avenue to h&
divided into equal fquares^ as Ae/D,
eghf, gib ky &c. A perfon ftstndiiig
at 0 will fee thefe two fides as if they
were gradually approaching toward
one another, as in Fig. 4. j and the
fquares will feem to diminifh in fize
as they are further and further from
his eye. So that the firft fquare Ae/D
in Fig. 3. will appear as Ae/D in
Fig. 4. the fecond fquare eghf in Fig. 3.
will appear as eghf in Fig. 4. and fo
on, till the laft fquare of the avenue,
produced to the utmoft bounds of
fight, would vanifh into a point, as S
in Fig. 4. where the fides AS and DS
meet. 12. The point S, where the parallel
fides of the avenue feem to meet, is
called The Paint of Sight ; the point 0,
* where

MADE EASY. 17
where the obferver's eye is placed, is
called The Place of the Obferver: the line
S P, paffing through the point of
fight, is called The Horizon ; and a
point taken therein, either to the right
or left hand from 5, and as far from
/S as (9 is from S, is called The Point of
Diftance.  N. B. In whatever point
the obferver's eye is fuppofed to be
placed, either for a diredt or oblique
view of the fide of the objedt that is
neareft to him. a firaight line drawn
from the point of fight to his eye mufl be
perpendicular to the horizon ; which will
be nearer to the eye, or further froni
it, as the obferver is fuppofed to ftand
upon lower or higher ground.

CHAP.

i8 PERSPECTIVE CHAP. II.
7"^^ Practice 0/ Perspective.
OPERATION L
To put n Square in PerfpeSlivey as n/iewed
by an Obfemjer flanding right agniiift the
Middle of one of its Sides, and'han^iiig 'his
Eye above the Plane of the SqUar'e.
13. TN Fig. 5. of Plate L let ABCD be
-¦- a fquare, viewed by an obferver
at 0, who fees the fide A D (next to
him) under the angle ACD of 60 de
grees (§ 10.).
Make AD in Fig. 6. equal to AD in
Fig. 5. At any convenient diftance, draw

MADE EASY. ig
draw the horizon SP parallel to AD.
Take 0, the place of the obferver, ac
cording to the rule in § 9. ; and from
the point 0^ make OS perpendicular
to SP, meeting it in S, which Ihall be
the point of fight (§ 12.).
Take OS in your compaffes, and
fetting one foot in S, defcribe the qua
drant /0/>P^ of a circle, meeting the
horizon in P, which, in all cafes, ihall
be the true point of diftance (§ 12.).
From A and D (the ends of the fide
of the fquare next the obferver at OJ
draw the ftraight lines AS and DS to
the point of fight S: then, from A,
draw the ftraight line AP to the point
of diftance P in the horizon, cutting
the line DS in the point C: this done,
drasw-BC parallel to -^^ J and ABCP
C 2 will

20 PERSPECTIVE
will be a true perfpedtive reprefenta
tion of the firft fquare ABCD in Fig. 5.
as feen by an obferver at 0.
Remark. If the obferver (Fig. 6.) had
ftood further than 0 from the fide AD
of the fquare, as fuppofe at 0, he
would have feen that fide under a lefs
angle than 60 degrees ; as the angle
AoD is lefs than the angle ADD:
and then, the point of diftance muft
have been at d in the horizon ; be
caufe the point bf diftance in the ho
rizon muft alivays be taken as far from
the point of fight therein, as the place
of the obferver fO or 0) is from the
point of fight, as we fliall prove in
§ 14.; and that, if the point of dif
tance in the horizon be taken either
nearer to or, further from the point of
fight than the diftance of the obferver is

MADE EASY. 21
is fuppofed to be from that point,
there will unavoidably be a falfe per
fpedtive reprefentation of the objedt.
For, fuppofe the placing of the point
of diftance in the horizontal line be
left to the difcretion of the artift, as
is generally done by writers on the
fcience of perfpedtive, and that he
had put it at e (Fig. 6.) in the line
SP ; then, a ftraight line drawn from
A to e would have cut the line DS'xn
the point h ; and g h (parallel to AD)
w^ould have been the top of the fquare
AghD; but it is plain to the eye and
judgment, that AghD would have been
a very bad and unnatural perfpedtive
reprefentation of the fquare ABCD
in Fig. 5. Or, fuppofing the point of
diftance (Fig. 6.) to have been taken
at/, in the horizon SP, the ftraight
C 3 line

22 PERSPECTIVE
line Af would have cut DS in ^ ; and
ik would have been the top of the
fquare. But a child could tell, that
AikD would be a monftrous repre
fentation of a fquare in perfpedtive.
The angle of 60 degrees is only af-
fumed here, as being the largefl; angle
under which the eye can fee an objedt
diftindtly ; and not as a conftant angle,
under which all reprefentations in
perfpedtive. muft be drawn. See § 10.

A Demonftration of the above 'liule (§12.
and 13.) for f tiding the true Point of
Diftance. 14. In Fig. I. of Plate II. let A I and
DA" be part of the two parallel fides of
a ftraight avenue, divided into equal
fquares.

MADE EASY. 23
Iquares, as ABCD, BEFC, EGHF,
&c. and let trees be planted at the
comers of each Iquare, as at A, B, C,
A £, P, G, H, /, and K.
Let 0 be the place of the obferver,
SP his horizon, and 5 the utmoft
point of his viewj called the point of
fight; from which, the Ijne SO is
perpendicular to SP (fee § 12.). To
him, the two fides of the avenue feem
•
to come nearer and nearer to one
adother, as they are farther and far
ther from his* eye, tending toward the
point of fight S, in the direction of the
two flxaight lines AS and DS. § 11.
In the parallel-fided avenue, draw
a ftraight line BO from the tree B to
the qbierver's eye at O ; this line cuts
th^ l^rfpedlive fide <^S of the avenue
C 4 in

84 PERSPECTIVE
in the point b, which is the apparent
place of the tree as feen by the ob
ferver. From the tree C draw the
ftraight line CO to the obferver's eye
at 0, and that line will cut the per
fpedtive fide DSof the avenue in the
point c, which is the apparent place
of the tree as feen from 0: then draw
^(T parallel to AD, and AbcD will be
the true perfpedtive reprefentation of
the fquare ABCD.
In like manner, from the other
trees, E, G, I, and P, H, K, draw
ftraight lines to the obferver's eye at
0 ; and thefe lines will cut the per-^
fpedtive fides AS and DS of the ave
nue in the points e, g, i, and /, h, k ;
which are the apparent places of the
trees, as feen by the obferver. Laftly,
4raw the lines ef, g h, i k, parallel to

MADE EASY. -j
A D, and they will divide the perfpec-
tive view of the avenue fo as to make
it a juft reprefentation thereof, with all
its trees and fquares, as feen from 0.
Thus we find, the apparent places
¦V
of the trees B, E, G, I, muft demon-
ftratively be at b, e, g, i ; and that the
apparent places of the trees C, F, H, K,
muft be at c,f, h, k, as feen from the
point O : — the trees A and D, which
are neareft to the eye, appear in their
true places. — Now we ffiall fee, by
placing the point of diftance in the
horizon SP according to the above-
mentioned rule, whether we Ihall or
ihall not have the apparent places of
the trees in the fame points as before;
without drawing lines from their true
places in the fides of the avenue to
the obferver's eye at 0. Take

a6 PERSPECTIVE
Take SP equal to S(9, and call P
the point of diftance. From A draw
the ftraight line AP, interfedting the
perfpedtive fide DS of the avenue in
the point c, and to that point draw be
parallel to ^ D ; and you have the
firft perfpedtive fquare AbcD of the
avenue, the very fame as was found
before, by the lines BO and CO.
From the point b draw bP, inter
fedting DS in the point/; and to that
point draw £/ parallel to AD, and you
have the fecond perfpedive fquare
be/c, the fame as before.
From the point e draw eP, inter
fedting D S in the point h, and draw
gh parallel to AD; then, eghf will
be the third perfpedtive fquare of the
avenue, as before. From

MADE EASY. 27
From the point g draw g P, inter-
fe(9:ing DS in the point k, and draw
ik parallel to AD, which finiihes the
fourth and laft perfpedtive fquare
gikh of the avenue.
In the fame manner you may go
On, drawing as many more perfpec-
tive fquares up toward S as you
plcafe. Now, as the ftraight lines AP, bP,
eP, and g P, (all drawn to the point
of diftance P) give the fame points
bi e,gy i, and c,f, h, k, for the appa
rent places of the trees as viewed from
O, .that the lines BO, EO, GO, 10,
and CO, FO, HO, and KO, gave be
fore, when drawn from the places of
the trees themfelves ; it is plain that
we have put the point of diftance P
in

28 PERSPECTIVE
in the very point where it ought to
be ; that is, juft as far from the point
of fight S as the obferver's eye. at 0 is
fr6m it.
And hence it is evident, that, fup
pofing the eye to be at 0, if the point
of diitance had been taken any where
between P and S in the horizon SP,
all the lines drawn from it into the
perfpedtive avenue AikD would have
gone above their true places, and
would have given the points for the
apparent places of the trees beyond
thofe in which the eye at 0 could fee
them ; and would alfo have made all
the perfpedtive fquares in the avenue
too broad.  On the contrary, if the
point of diftance had been taken any
where beyond P from S, all the lines
drawn from that point of diftance would

MADE EASY. 29
would have gone below their true
places in the perfpedtive avenue ; and
confequently have brought the ap
parent places of the trees too near
the obferver's eye, and have made all
the perfpedtive fquares of the avenue
narrower than they could really ap
pear to the obferver at 0.
15. Hence it is manifeft, that, when
large objedts are to be drawn in per
fpedtive, the point of diftance muft
be taken at leaft as far from the point
of fight, as the obferver could ftand
from the point of fight when he fees
the fide of the objedt next to him un
der an angle of 60 degrees. But in
drawing agreeable perfpedtive views
of fmall objedts, the obferver Ihould
be confidered as viewing them under
an angle not exceeding 30 degrees ac
moft:

so PERSPECTIVE
moft : and fuppofing him to fee them
under that angle, take the diftance of
his place from the point of fight in
your compafies, and fet off that ex
tent from the point of fight in the
horizon, to find the point of diftance
therein.

OPERATION IL
To put a Square in PerfpeSlive, as feen hy
a Perfon mt flanding right againfl' the
Middle of either of its Sides, but rather
nearly even -with one of its Corners,
i6. In Fig. 7. of Plate I. let ABCD
be a true fquare, viewed by an ob
ferver, not ftanding at 0, diredtly
againft the middle of its fide AD,
but at 0 almoft even with its corner

MADE EASY. 31
D, and viewing the iide AD under
the angle AOD ; the angle AoD (un
der which he wonld have feen AD
from oJ being 60 degrees.
Make AD in Fig. 8. equal to -4 D in
Fig. 7. and draw SP and 00 parallel
to AD. Then, in Fig. 8. let 0 be the
place of the obferver's eye, and SO be
perpendicular to SP (as before, § 12,
1 3.) then S ihall be the point of fight
in the horizon SP.
Take SO in your compaffes, and fet
that extent from S to P .- then P ihall
be the true point of diftance, taken
according to the foregoing rules, § 12.
and 13.
From A and D draw the ftraight
lines J^S and DS: draw alfo the
ftraight line APy interfedting DS in C.
2 Laftly,

32 PERSPECTIVE
-Laftly, to the point of interfedtion
C draw PC parallel to AD ; znd ABCD
in Fig. 8. will be a true perfpedtive
reprefentation of the fquare ABCD
in Fig. 7. The point M is the center
of each' fquare, and AMC and BMD
are their diagonals.

OPERATION IIL
To put a reticulated Square in PerfpeSii've,
as feen. by a Perfonflanding oppofite to the
Middle of one of its Sides.
17. A "reticulated fquare is one that
is divided into feveral little fquares,
like net-work, as Fig. 4. of Plate II.
each fide of which is divided into four
equal parts, and the whole furface
into four times, four (or 16) equal
fquares. Having

MADE EASY. 33
iHaving divided this fquare into the
given number of leffer fquares, draw
the two diagonals -4xC and BxD.
Make AD in Fig. 5. equal to AD in
Fig. 4. and divide it into four equa.1
parts, as A e, eg, g iy and iD.
Draw SP for the horizon, parallel
to AD, and, through the middle
pointy of J D, draw OS perpendicu^
lar to AD and SP.— Make S the point
of fight, and 0 the place of the ob
ferver's eye.
Take SP equal to SO, and P ihall
be the true point Of diiiance.— Draw
AS and DS to the point of fight, and
AP to the point of diftance, inter
fedting DS inC: then draw BC pa
rallel to AD, and the outlines of the
D reti-

34 PERSPECTIVE
reticulated fquare ABCD will be
finiihed. From the divifion-points e, g, i, draw
the ftraight lines ef, gh, ih tending
toward the point of fight Sj and draw
BD for one of the diagonals of the
fquare, the other diagonal A C being
already drawn.
Through the points r and s, where
thefe diagonals cut ef and i k, draw
bn parallel to AD. Through the cen
ter-point X, where the diagonals cut
g h, draw n o parallel to y^D.— Laftly,
through the points v and w, where
the diagonals cut cf and i k, draw p q
parallel to AD; and the reticulated
perfpedtive fquare will be finiihed.
This fquare is truly reprefented, as
if feen by an obferver ftanding at O,
and

MADE EASY. 5J
-and having his eye above th^ hori
zontal plane ABCD on which it is
drawn ; as if 0 S was the height of
his eye abore that plane: and the
lines which fearm. the fmall fquares
within it have the fame letters of re
ference with thofe in Fig. 4. which is
drawn as it would appear to an eye
placed perpendicularly above its cen*

OPERATION IV*
To put a Circle in PerfpeBivd
18. If a circle be viewed by an eye
placed diredtly over its center^ it ap
pears perfedtly round, as Fig. 2. but
if it be obliquely viewed, it appears
of an elliptical ihape, as Fig. 3- This
D 2 is

^6 PERSPECTIVE
is plain by 16oking at a common Wine*
glafs fet upright on a table.
If. Make a true reticulated fquare,
as Fig. 4. of Plate II. of the fame dia
meter as you would have the circle ;
and fetting one foot of your compaffes
in the center x, defcribe as large a
circle as the fides of the fquare will
contain. Then, having put this reti
culated fquare into perfpedtive, as in
Fig. 5*. obferve through what points
of the crofs lines and diagonals of
Fig. 4. the circle pailes ; and through
the like points in Fig. 5. draw the el-
lipfis, which will be' as true a perfpec-
tive reprefentation of the circle, as the
fquare in Fig. 5. is of the fquare in
Fig. 4.

OPERA*

MADE EASY. 37
DP ERA TION V.
! To put a reticulated Square in PerfpeSlive,
as feen by a Perfon tiot flanding right
againfl the Middle of either of its Sides,
but rather nearly even ivith one of its
Corners.20. In Fig. 6. of Plate IL let 0 be
the place of an obferver, viewing the
fquare ABCD almoft even with its
corner D. — Draw at pleafure S P for
the horizon, parallel to A D, and
make SO perpendicular to SP: then,
S ihall be the point of fight ; and P
the true point of diftance, if SP be
made equal to SO,
Draw AS and DS to the point of
fight» and AP to the point of diftance,
D $ inter-

^ PERSPECTIVE
interfedting DS in the point C; then
draw .5 C parallel to AD, and the out
lines of the perfpedtive fquare will be
finiihed. This done, draw the lines
which form the lefler fquaresv as
taught in Oper. HI. and the work will
be completed, — —You may put a per
fpedtive circle in this fquare by the
f^mp rule as it wa? done in Fig. 5,
OPER ATION VI.
To put a Cube in PerfpeSlive, as if viewed
by a Perfon flanding ahnofl even ivitk
one of its Edg^s, and feeing thrfe^of its
Bides. 21. In Fig. 7. of Plate IL let AM be
the breadth of either of the fix equal
fquare fides of the cube AG; 0 the
place of the obferver, almofi even with

MADE EASY. 33
with the edge CD of tlie cube, S the
point of, fight, SP the horizon pa
rallel to AD, and P the point of
diftance taken as before.
Make ABCD a^ true fquare ; draw
BS and CS to the point of fight, and
.SP to the point of diftance, interfedt
ing CS in C— Then draw FG parallel
to BCt and the uppermoft perfpedtive
fquare fide BFGC of the cube will
be finiihed. '
Draw D S to the point of fight, and
AP to the point of diftance, interfedt
ing D S in the point /; then draw G I
parallel to CD ; and, if the cube be
an opaque one, as of w^ood or metal,
all the outlines of it will be finiflied ;
and theh it may be iliaded as in the
figure. " D 4 But

,p PERSPECTIVE
But if you want a perfpedtive view
of a tranfparent glafs cube, all the
fides of which will be feen ; draw AH
toward the point of fight, FH parallel
to BAy and H/ parallel to AD : then
A HID will be the fquare bafe of the
cube, perfpedtively parallel to the top
BFGC; ABFH will be the fquare fide
of the cube parallel to CG ID, and
FGIH will be the fquare fide parallel
Xo ABCD,
As to the ihading part of the work,
it is fuch mere childrens' play, in
comparifon of drawing the lines which
form the ihape of any objedt, that no
rules need be given for it. Let a per
fon fit with his left fide toward a win
dow, and he knows full well, that if
any folid body be placed on a table
before him, the light will fall on the
left.

MADE EASY. 41
left-hand fide of the body, and the
right-hand fide will be in the ihade.
OPERATION VIL
To put a Square Pavement in PerfpeSlive,
cpnfifling of any given Square Number *
of equal black and ivhite Square Pieces of
Marble, and vievued by a Perfonflanding
at a Diflance from it, almofi even ivith
one of its Comers.
22. In Fig. I. of Plate IIL let SP be
the horizon, SO perpendicular to SP,
0 the place of the obferver, viewing
the fquare black and white marble
pavement ABCD, nearly even with
the corner D ; S the point of fight, P
* klquare number is the produ£l of any given tiumber
multiplied by itfelf. Thus, 144. is the fquare of n; for
12 times 12 is 144 ; and 256 is the fquare of 16. the

42 PBRSFECTflVE
the point of diftance (§12.),. arndth;^
fidjt AD be parallel to SR. ,
Suppofe the fide AD^ (equal to the
breadth of the pavement) to b^ 16 feet,
and that each fquare piece of marble
in the pavement is a, foot broad; then
the whole pavement will contain 256
of thefe fquare pieces ; for 16 times 16
is 25^ ; that is, 256 is the iquare of 16.
Divide AD into 16- equal parts, as
Ab, be, cd. Sec. and from thefe points
of divifion, b, c, d, &c. draw ftraight
lines to the point of fight S,
From P the point of diftance draw
the ftraight line PDy interfedting AS
ih the point B; then, from B draw
BC parallel to AD,, which will com
plete the outlines of the perfpedtive
fquare pavement j4 5 CD.
, Through

MADE EASY. 45,
Through the points where the dia
gonal BD interfedts the lines drawn
from b, Cyd, i, &c. towaard the point of
fifght S, dmw ftraight lines parallel to
jiD (as in Oper. III. and V.) and you
will have •divided the j^are pave
ment ABCD into 256 leffer fquares j
one half of which m^ay be fha<ied
black, arfd the other half left white,
to reprefent the 256 iquare pieces of
black and white marble which com^^
pofe the pavement.
OPERATION VIIL
To put an oblong Square Pavement in Per--
fpeSl'ive, ivhofe Length is equal to any
given Number of Time's its Breadth.
23. In Fig. I. of Plate III. fuppofe
the given length DF or AE to be 32
feet.

44 PERSPECTIVE
feet, and the given breadth AD to be
1 6. We have already got half the
given length DC, in the perfpedtivei
iquare ABCD; and fuch another
added to it will complete the perfpec-,
tive figure of the pavement.;
To the right hand top-corner C of
the fquare ABCD, draw the ftraight
line PC from the point of diftance P,
interfedting AS at E: from the point
E draw EF parallel to AD, and the
outlines of the fecond fquare BEFC
will be completed ; which, as in the
figure, may be divided into 256 leilcr
fquares, by the fame method that
AB CD was fo divided : and then, in
perfpedtive, the length of the oblong
fquare pavement AEFD will be twice
as great a§ its breadth.; and the whole
will contain 512 leffer fquares. 24. If

MADE EASY. .4;
24. If the given length be equal to
three times the breadth, we muft have
a third pier fpedtive . fquare E G HF
joined to the top of the fecond fquare
BEFC.
From the point of diftance P, draw
the ftraight line PF to the right hand
top-corner F of the fecond fquare, and
interfedting J S at G: then, from the
point G draw G B parallel to A D,
which will complete the third per
fpedtive fquare ECifP.— This fquare
(like the former two) may be fub-
divided into 2^*6 leffer fquares ; and
l^en we ihall have an oblong fquare
pavement AGHD, whofe perfpedtive
length is equal to three times its
breadth, and divided into 768 leffer
fquares. 25. And

4^ PERSPECTIVE
25. And thus (as is jdain by the
figure) you may proceed, and make
as many more perfpedtive fquares
(GIKH, ILMK^ LNOM, &c.) as ybii
pleafe.— -There are ten fuch fquares
in this figure ; and if we fuppofe each
of them to be 1 6 feet broad, and paved
with black and white marble as ABCD
is, the whole pavement, being ten
times as long as it is broad, will con
tain 2560 fquare feet of marble fur
face. OPERATION IX.
To put a. Square Pyramid in PerfpeSlive, as
if flanding upright on its bafe, and viewed
obliqiiely.26. In Fig. 2. of Plate IIL let AD be
the breadth of either of the four fides
8 of

MADE EASY. 47
of the pyramid AT CD at its bafe
ABCD; ^nd MT" its petpendicular
height. Let 0 be the place of the ob
ferver, S his point of fight, SE his.
Iiorizon, parallel to AD and perpen.-
dicular to OS; and let the proper
point of diftance be taken in S£ pro
duced toward the left hand, as far
from S as (? is from S.
Draw AS and DS to the point of
fight, and DZ, to the point of diftance,
interfedting AS in the point B. Then,
from B, draw i?C parallel to ^D ; and
ABCD ihall be the perfpedtive fquare
bafe of the pyramid.
Draw the diagonal AC, interfedting
the other diagonal PD at M, and this
point of interfedtion iliall be the center
of the fquare bafe. Draw

48 PERSPECTIVE
Draw MT perpendicular to AD, and
of a length equal to the intended
height of the pyramid: then dravir
the ftraight lines AT, CT, and DTi
and the outlines of the pyramid (as
viewed from O) will be finiihed j
which being done, the whole may be
fo ihaded as to give it the appearance
of a folid body.
If the obferver had ftood at o, he
could have only feen the fide ATD of
the pyramid ; and two is the greateft
number of fides that he could fee from
any other place of the ground. But
if he were at any height above the
pyramid, and had his eye dire<3:ly
over its top, it would then appear like
Fig. 3. and he would fee all its four
fides E, F, G, H, with its top /juft over
the center of its fquare bafe ABCD; which

MA D^ EASY. 49
which would be a true geometrical,
and not a perfpeiftive, fquare.
OPERATION X.
To put two equal Squares in PerfpeSlive, one
of ivhich fhall be direSily over the other,
at any given Diflance from it, and both
' of them parallel to the Plane of the HO'
rizon. 27. In Fig. 4. of Plate HI. let ABCD
be a perii<edtive fquare on a horizon
tal plane, drawn according to the fore
going rules (§ 16), S being the point
pf fight, SP the horizon (parallel to
AD), and P the point of diftance.
Suppofe AD, the breadth of this
fquare, to be three feet ; and that it
is required to place juft fuch another
E fquare

,5p PERSfEC'riVE
fqu?^e EFGH ^ir^edtlf ^\m^ »«» pa
rallel to it, and t^o feet from it.
Make AE and DH perpendicular
to AD, and two thirds of its length :
<Jraw EH, wjiich will be equal and
parallel to ^Dj theu dra\y j?S and
BS, to the point of fight S, and EP to
the point of diftance P, interif,dling
HS in the point G : this done, draw
FG parallel to EH; and you will
have twp perfpedtive f^u^yes |4.BCI>
andJSFCi?, equal and parallel tponp
apother, the latter dirpdily ^bpvq tJie
former, ^q4 I^WP fept diftant froni it j
^s was requifpd.
By this method, ihelves may be
drawn, parallel to one another, at any
diftance frpm each othey in prpportion
to their length.
S OPERA-

Imade *easy.

OPERATION XL

^1

Topiit « S^Ui^ Tab'k in PerfpeSlive, ftdnd"
ing ok four upri^ SqUare Legs 'tf any
gitm Length mth refpei^ to the BrtitdPh
28. In Fig. 4. of Plate IIL \€t ABOD
be the fijuare patrt of the floor on
whiieh the table is to ftarid, and
lEFGH the fiirfac&.of iht fquare
table, jJlraWel to the flPUr.
-Suppofe the table to be three feet in
breadth, and its height from the floor
to be two feet; then, two thirds of
AD or EH will be the length of the
legs i and k 5 the other two fl and mj
being of the fame length in per
fpedtive. E 2 Having

^2 PERSPECTIVE
Having drawn the two equal and
parallel fquares ABCD and EFGH,
as ihewn in Oper. X. let the legs be
fquare in form, and fixed into the
table at a diftance from its edges
equal to their thicknefs. Take A a
and D J equal to the intended thick
nefs of the legs, and ab and dc alfo
equal thereto. Draw the diagonals
AC and BD, and draw ftraight lines
from the points a, b, c, d, toward the
poirit of fight S, and terminating at
the fide PC. Then, through the points
where thefe lines cut the diagonals,
draw the ftraight lines n and o, p and
q, parallel to AD; and you will have
formed four perfpedtive fquares (like
ABCD in Fig. 2.) for the bafes of the
four legs of the table : and then it is
eafy to draw the four upright legs by
parallel lines, all perpendicular tp
AD;

MADE EASY. 53
AD; and to ftiade them as in the
figure. To reprefent the intended thicknefs
of the table-board, draw eh parallel to
EH, and HG toward the point of fight
S: then ihade the fpaces between
thefe lines, and the perfpedtive figure
o| the table will be finiihed.

OPERATION XU.
To put an oblong Square Table in PerfpeSlive,
of any given Length voith refpeSl tQ its
Breadth.29. Suppofe the given length to be
four feet, and the breadth to be three.
—In Fig. 6. of Plate IL let AD be the
length, and divide it into four equal
parts Ae^ eg, gi, il) : draw AS and
E 3 DS

54. PE,R&P'EG;TlVjE
DS to,the p^oint of ftghti i^j, aud ARto
the point of diftance P.
From the. poiiit ?, whrichfe iS' tfej^ce
fourdis of ^D, dra^w ij toward the
point; of fight, till i$ meets the dia^
gpnal. -<iC in s :¦ tj^eji, tferpugh; that
point of meetini^ ^^nJm p^aliel tQ
AD J and you wilt haive- aa. obkMig'
fquare AlmD, whofe breadth A I or
l)m is perfpedtively equal to three
quarters of its; length AD.
30. tet the breadth of the table be
equal to half its length -r^D.,— From
g, the middle point between A and
D, dxzwgx towar4,the point of fight
S, till it meets the diagonal, .^C in the
poijft «; , then, through the point a-,.
dijaw n,o parallel to AD, and you wilL
have an oblong fquare: 4n.oD, whofe
length

MADfi EA&Y. 53
length ^D is equal to twice its
breadth .^ or Der.
,. 3J-. Suppofe the kfi^feaoi be equal
to four times the: breatMl: — From e, a
fourth part ; of the r diftance' bfefe^ een A
and D, draw ev toward the point of
fight /Si till it vfSftci^ the di^^ial AC
at" V J then, through thatr pcanc of
meeting, draw^^r parallel to AD\ and
y-ou- will have anoblbiig £quare'.^f/ry;D,
whof^ lengtb -<«fD'is-. four times as
great as^ itS' |iier£|«efbive: breadth Ap or
Dq, In this manner' you may make the
breadifei' bear any/ pnoportioa to the
length that you: pleafe:; and may put
legs: ta-^the-table as ihewn in Opr.yA.

]ff*^4 OPERA-

PERSPECTIVE

OPERATION XIIL
To put five Square Pyramids in PerfpeSlive,
flanding Mpright on a Square Patfement
compofed of -the Surfaces of ?ii Cubes.
32. In Fig. I. of Plate IV. let ABCD
be a perfpedtive fquare drawn ac
cording to the foregoing rules ; S the
point of fight, P the point of diffcance
in the horizon PS, and AC and BD
the two diagonals of the fquare.
Divide the fide AD into 9 equal
parts (becaufe 9 times 9 is 81) as .^a,
aby be, &c. and from thefe points of
divifion, a, b, c, d, &c. draw lines to
ward the point of fight S, terminating
at the furthermoft fide B C oi the
fquare. Then, through the points
where

MADE EASY. 57
where thefe lines cut the diagonals,
draw ftraight lines parallel to AD
(as in Oper. IIL), and the perfpedtive
fquare ABCD will be fubdivided into
81 leffer fquares, reprefenting the up
per furfaces of 8 1 cubes, laid clofe to
one another's fides, in a fquare form.
Draw AK and D L, each equal to
A a, and perpendicular to AD; and
draw LN toward the point of fight S:
then draw JTL parallel to ADy and
its diftance from AD will be equal to
A a. — This done, draw a I, bmy en, do,
ep, fq-i gr, and.^j-, all parallel to AK;
and the fpace ADLK will be fub
divided into nine equal fquares, which
are the outer upright furfaces of the
nine cubes in the fide AD oi the
fquare ABCD. Draw

3^ PERSFEGTIVE
. Draw LN toward the poino of fig^
S:-, and from the points where the
linear which are parallel ta AB jsii
tfeaa fquar^ meet the fide CD thereof^
dmw!&c«?t lines^to hN, all parallel ooi
M^L, and tHey will divide that fid©
into the outer upright furfaaces of iJi®
nine cubes which compofe it: and
then the outfides of all the" cubcs!^ that
can. be vifible to an obferverj- placed
ar, a proper diftance fnomc the comer
D oi the'fquare,j will* be finiihed^
As taught in Cfper. IX. place the
pyramid AE upright on its fquare
ih.ic Atva, making it as high asyou
pleafe; and' the pyramid D.^ on its
fquare bafe JhtwD, of equal height
with AE.
Draw EH from the top of one of
thefe pyramids to the top of the
other i

MADE EASY. ^
Qthep i apd) EH will be parallel to
AD. Prawf E.S and MS to the point of
fights, and HP to the point of di&
tance P, interfedting FS in P.
From- the point P, draw PC?- parallel
to EH; then draw EG, and you will
have a perfpedtive fquare EFGH (pa*
raJlel' tO: ABCDf with its two dia-
gpna,ls. EG andl FH, intexfedljing one
another in. the center of the fquare at
/. The four corners of this, fquare,
E,F,G,H, give the perfpedtive heights
ofe the; four pyaanaids AE, BF, CG,
and D H; andtthe interfedtion' /of the
diagonals givesi the height of the py-
raj»id.M/,, the center of whofe bafe is
the; center ofi the perfpedtive fquare
A.BCM.
Laftly,

^o PERSPECTIVE
Laftly, place the three pyramids
BF, CG, MI, upright on their refpec-
tive bafes at B, C, and M; and the
required perfpedtive reprefentation
will be finiihed, as in the figure.

OPERATION XIV.
To put upright Pyramids in PerfpeSlive,
on the Sides of an ohlong Square or Paral
lelogram; fo that their Diflances from
one another JhaU be equal to the Breadth
of the Parallelogram,
In moft of the foregoing operatioiis,
we have confidered the obferver to be
fo placed, as to have an oblique view
of the perfpedtive objedts : in this, we
ihall fuppofe him to have a diredt
view of Fig. 2. Plate IV. that is, ftand ing

MADE EASY. 6i
ing right againft the middle of the
end AD which is neareft to his eye,
and viewing AD under an angle of
60 degrees. § 10.
Having cut AD in the middle, by
the perpendicular line S s, take S
therein at pleafure for the point of
fight, and draw ES for the horizon,
parallel to ^D. — Here Ss muft be
fuppofed to be produced downward,
below the limits of the plate, to the
place of the obferver ; and SE to be
produced towards the left hand be
yond ^y far enough to take a proper
point of diftance therein, according
to the foregoing rules.
Take Ad at pleafure, and Dg equal
tb Ad, for the breadths of the fquare
bafes of the two pyramids AE and DF

162. P£RS]^Et!lrt¥E
DF next the eye: then draw AS JiM
<dS, and likewife DS and gS, to thfe
point "Of fight S ; and DG on to fht
point of diftance, interfiidting AS iti
G: then, from G draw GI parallel to
AD, and you v^ill have die fifft per-
fpeQ:ive fquare AG ID of the paral
lelogram ABCD.
From /draw Iff to (or toward) the
point of diftance, interfedting -A^ in
H: then, from H draw MKt parallel
to ADy and you will have the fecond
perfpe<9:ive fquare GHKioiistke paral
lelogram. —<k> on in this manner
(which is the fame with the method
demonftrated in ^per. I.) till you have
drawn as many perfpedtive fquares
up toward S as you pleafe.
Through the point e, where D^
interfedts^ S, draw ^/parallel to ^D; and

MADE EA«T. %
I ackd yem. will have foriaaed tiie two
ftexfpe&ive fqaiare bafes Abed and
efD.g ©f ith® two pyramids at ^
and D.
From the point/ (the tapper outward
corner of lefDg) dwcfu fh toward the
point of diftance, till it meets ^ S in
h ; then, from this point of meeting,
draw h m parallel to G I, and you
will have formed the two perfpedtive
fquares Ghik and Imin, for the fquare
bafes of the two pyramids at G and /.
Proceed in the fame manner to find
the bafes of all the other pyramids, at
the comers of the reft of the perfpec-
tive fquares in the parallelogram
ABCD, as &ewn by the figure.—^
Then, Having

€4 PERSPECTIVE
Having placed the firft two pyra
mids at A and D upright on their
fquare bafes, as ihewn in Oper. IX.
and made them of any equal heights
at pleafure, draw ES and FS from
the tops of thefe pyramids to the
point of fight S : place all the reft of
the pyramids upright on their refpec-
tive bafes, making their tops touch
the ftraight lines ES and FS; and all
the work, except the ihading part,
will be finiihed.
33. Remark, — It muft be acknow
ledged, that there is fomething in
this figure not quite agreeable to the
eye ; which is, that the two pyramids
at G and / feem to be too far from
thofe at A and D, when compared
with the diftances between the reft. —
But this arifes from their being viewed (in

MADE EASY. 6.5
(in the figure) at a greater diftance
than the obferver is fuppofed to be at
from the point of fight S; which is
but 7 inches and three fourths of an
inch, in viewing AD under an angle
of 60 degrees: whereas, in viewing
the figure, we feldom bring the paper
within lefs than a foot from the eye.
— But, if a perfon who looks at th6
figure will place his eye diredtly over
the point of fight S, fo that an ima
ginary line 74 inches long, from the
point of fight, and perpendicular to
the furface of the paper, ihall, touch
his ¦ eye ; the difagreeable idea will
vanifh, and the reprefentation will
appear natural.
On which it may be proper to ob
ferve, that, when people look at per
fpedtive drawings, they generally keep
F their

66 PERSPECTIVE
their eye at a greater diftance than
what would form an angle of 60 de
grees with the boundaries of the ob
jedt; and therefore they fee it under
an angle confiderably lefs than 60 de
grees. And, for this reafon, it may
be proper to inform the learner, that,
in drawing perfpedtive reprefentations
of objedts, he had better put his fup
pofed obferver's ftation fo far from the
fide A D next his eye, that it may not
fubtend an angle of more than 45
degrees, or 5a at moft : and then the
drawings will have a much more
agreeable appearance.
It is true, that this caution, though
generally neceflary, is attended in
pradtice with a fmall inconvenience :
which is, that as the point of diftance
muft always be placed as far from the
point

MADE EASY. e^y
point of fight as the obferver is fup
pofed to be from it, the fchemes,
though but fmall, muft be drawn on
large paper; otherwife the point of
diftance rpay fall without the limits
of the paper ; as it does even in this
figure (Fig. 2.), on account of the
breadth thereof from A to D, although
it is drawn as if viewed under an angle
1 of 60 degrees. — But this is of very little
moment, as it is eafy to fix a long flip
of paper by two wafers to the edge
of that on which any fcheme is drawn ;
fo that the horizon-line may be ex
tended out on that flip, to find the
point of diftance therein, as far from
the point of fight as you pleafe.

F 2 OPERA-

en PERSPECTIVE

PPERATIQIi} XV.
To pjjt a Rumr^er or Drinking-Glqf} in
Perfpeflive.
34. According to the foregoing me
thod [Oper. X.) draw the two equ^l ^nd
parallel perfpedtive fquares A_BCD
and EFGH in Fig. 3. of Plate IV. the
latter diredtly above the former. Then,
as in pper. IV. put a perfpedtive circle
in the lowermoft fquare for the bot
tom of the cup, and one in the upper
moft for the top or brim thereof, and
draw out the reft of the figure in
whatever ihape you pleafe.

OPERA-

MADE EASY. 6g
OPERATION XVL
To put a Square Pyramid of equal fiztd
Cubes in PerfpeSlive.
35. Fig. 2. of Plate V. repfeTents i.
pyramid of this kind; corififfing (as
it were) of fquaie t^Mes of cubes, one
table above another ; 8 1 in the lowe^,'
49 in the next, 25 in the third, 9 in
the foufth, jtnd t in the fifth 01* up
permoft. Thefe are the fqua're num
bers of 9, T,^, 3, and I.
i I 1^
ff the artift is already mafter of all
the preceding operations, he will find
lefs difficulty in this than in attending
to the following defcription of it : for
it cannot be defcribed in a few ¦#ords,
but may be executed in a very iliort
time. F 3 In

70 PERSPECTIVE
In Fig. I. having drawn PS for the
horizon, and taken S for the point of
fight therein (the obferver being at
OJ draw AD parallel to PS for the
fide (next the eye) of the firft or lower
moft table of cubes. Draw ^S and
D S to the point of fight S, and D P
to the point of diftance P, interfedt
ing ^S in the point B, Then, from
B, draw BC parallel to AD, and you
will have the furface ABCD of the
firft table.
Divide AD into nine equal parts,
as A a, ab, be, cd, &c. then make AK
and DL equal to A a, and perpendi-r
cular to AD. Draw KL parallel to
AD, and from the points of equal
divifion at a, b, c, &c. draw lines to
KL, all parallel to AK. Then draw
h S to the point of fight S, and from the
3

MADE EASY. 71
the divifion-points a, b, c, &c. draw
lines with a black lead pencil, all
tending toward the point of fight, till
they meet the diagonal B D oi the
fquare. From thefe points of meeting draw
black lead lines to D C, all parallel to
A D ; then draw the parts of thefe
lines with black ink which are mark
ed I, 2, 3, 4, &c. between hE and
DC, Having drawn the firft of thefe lines
j6 q with black ink, draw the parts a i,
bk, cl, &c. (of the former lines which
met the diagonal B D) with black
ink alfo ; and rub out the reft of the
black lead lines, which would other-
wife confufe the following part of the
work. Then, draw LF toward the
F 4 point

12 PERSPECTIVE
poii^t of fight S; and, from the points
^here the lines i, 2, 3» 4, &c. meet
the line DC, draw lines down to ZP,
all parallel to DP ; and all the vifible
lines between the cubes in the firft
table will be finiihed.
Make iG equal and perpendicular
to /S i, a^nd, q M equal and parallel to
iG: then draw G:M, which will be
equal and parallel to. i q. From the
points k, I, m, n, &c. draw kn, lo, mp,
&c. all parallel to iG, and the outfides
of the feven cubes in the fide Gq oi
the fecond table wiU be finiih^.
Draw GS and MS to the point of
fight S, and iVf P to the point of dif-,
tance P, interfedting GS in H; then,
from the point of interfedtion H, draw?
MT parallel to AD ; a,nd you will
have

MADE EASY. 73
have the furface GHIM of the fecond
table of cubes.
From <he points n, 0, p, q, &c. draw
black lead Jines toward the point of
fight S, till they meet the diagonal
MH oi the perfpiedtive fquare furface
GHIM; and draw s N, with black
ink^ toward the point of fight.
From thofe points where the lines
drawn from n, 0, p, q, &c. meet the
diagonal MH, draw black lead lines
to MI, all parallel to AD ; only draw
the whole firft line y i with black ink,
and the parts 2, 3, 4, 8cc. and nt, on,
pVy &c.' of the other lines between y N
and MI, and GMand yi, with the
fame ; and rub out all the reft of the
black, lead lines, to avoid further con-
fi^fion>. Then, from the points where the

74 PERSPECTIVE
the ihort lines i, 2, 3, Sec. meet the
line MI, draw lines down to qE, all
parallel to Mq, and the outer furfaces
of the feven cubes in the fid^ ME
will be finiihed ; and all thefe laft
lines will meet the former parallels
2, 3, 4, See. in the line qE.
Make tO equal and perpendicular
to -y t, and y P equal and parallel to
tO; then draw OP, which will be
equal and parallel to ty. — This done,
draw 0 S and P S to the point of fight
S, and PP to the point of diftance P
in the horizon. Laftly, from the point
^, where P P interfedts 0 S, draw
^R parallel to OP; and you will have
the outlines O^RP of the furface of
the third perfpedtive table of cubes.
From the points u, v, w, x, draw up
right lines to OP, all parallel to tO,
and

MADE EASY. 75
and you will have the outer furfaces
of the five cubes in the fide Oy of this
third table.
From the points where thefe up
right lines meet 0 P, draw lines to
ward the point of fight S, till they
meet the diagonal P ^; and from
thefe points of meeting draw lines to
PR, all parallel to OP, making the
parts 2, 3, 4, 5", of thefe lines with
black ink which lie between Z T and
PR. Then, from the points where
thefe lines meet PR, draw lines down
to y l^i which will bound the outer
furfaces of the five cubes in the fide
PNoi the third table. I
Draw the line (J i with black ink;
and, at a fourth part of its length
between i^and Z, draw an upright line to

76 PERSPECTIVE
to S, equal in length to that fourth
parr, and another equal and paralkl
thereto from Z to V : then draw SV.
parallel to ^ Z, and draw the two up
right and equidiftant lines between
IZ and SV, and you will have the
outer furfaces of the three cubes' in
the fide SZ of the fourth fable'.
Draw SS and VS to the point of fight
S in the horizon, and VP to the point
of diftance therein, interfedting. SS in
T; then draw PC7 parallel to SV, and
you have STUV, the furface of the
fourth table ; which being reticulated
or divided into 9 perfpeciive fmall
fquares, and the uppermoft cube W
placed on the middlemoft of the
fquares, all the outlines will be fi
niihed ; and when the whole is pro
perly ihaded, as in Fig. 2. the work-
will be done. OPERA-

MADE EASY.

11

OPERATION XVIL
To reprefent a double Crofs in PerfpeSlive.
36. In Fig. 3. of Plate V. let ABCD
and EFGH be two perfpedtive fquares,
equal and parallel to one another, the
uppermoft directly above the lower
moft, drawn by the rules laid down
in Oper. X. and as far afunder, as is
equal to the given height of the up
right part of the crofs ; S being the
point of fight» and P the point of dif
tance, in the horizon PS taken paral
lel to AD,
Draw AE, DB, and CG; then,
AEHD and DHGC ihall be the two
vifible fides of the upright part' of the
CFPfsj of which, the length ^P is
here

78 P.E R S P E C T I V E
here made equal to three times the
breadth EH.
Divide D H into three equal parts,
HI, IK, and KD. Through thefe
points of divifion, at / and K, draw
MO and PR parallel to AD; and
make the par;ts MN, 10, P^, KR,
each equal to HI: then draw MP and
CP parallel to DH.
From M and 0, draw MS and OS
to the point of fight S; and from the
point of diftance P draw FN cutting
MS in T: from T draw TU parallel to
MO, and meeting OS in IT ; and you
will have the uppermoft: furface MTUO
of one of the crofs pieces of the figure.
— —From R, draw P S to the point of
fight S; and from U^ draw UV pa
rallel to OR; and OUVR ihall be the
perfpedtive

MADEEASY. 7^
perfpedtive fquare end next the eye of
that crofs-part.
Draw PMx (as long as you pleafe)
from the point of diftance P, through
the corner M; lay a ruler to N and S,
and draw JiNTfrom the line Px .—then
lay the ruler to / and S, and draw
rZS.— Draw XT parallel to MO, and
make XW and TB equal and perpen
dicular to XT: then draw M^B paral
lel to Jr, and /r jrP ftiall be the
fquare vifible end of the other crofs-
part of the figure.
Draw BK toward the point of fight
S ; and from U draw U'P to the point
of diftance P, interfedting TS in Z :
then, from the interfedtion Z, draw
Za parallel to MO, and Zb parallel to
HDy and the whole delineation will
be finiihed. . This

Sc PERSPECTIVE
This done, fhade the whole, as in
Fig. 4. and you will have a true per
fpedtive reprefentation of a double
crofs. OPERATION XVIIL
To put three Koivs of upright Square ObjeSls
in PerfpeSlive, equal in Size, and at equal
Diflances from each other, on an ohlong
Square Plain, the Breadth of ivhich fhall
be of any affigned Proportion to the Length
thereof. 37. Fig. 2. of Plate VL is a perfpec-
tive reprefentation of an oblong fquare
plain, three times as long as it is broad,
having a row of nine upright fquare
objedts on each fide, and one of the
fame number in the middle ; all equal
ly high, and at equal diftances from
2 one

MADE EASY. It
i^ne another, both long^wife and crofs*
wife, on the fame plane.
In Fig. I. PS is the horizon, S the
point of fight, P the point of diftance,
and AD (parallel to PS) the breadth
of the plain.
DrsLw AS, NS, and DS^ to the point
of fight S ; the point N being in the
middle of the line A D : and draw
D P to the point of diftance P, inter
fedting -^S in the point B: then,
from B draw B C parallel to A D,
and you have the perfpedtive fquare
ABCD.
Through the point i, where DB
interfedts NSy draw ae parallel to.^D j
and you will have fubdivided the per
fpedtive fquare /^ PCD into four lef-
G fer

§2 PERSPECTIVE
fer fquares, as AaiN, NieD, aBki,
and ikCe.
From the point C (at the top of the
perfpedtive fquare ABCD) draw CP
to the point of diftance P, interfedting
AS in E; then, from the point E
draw E F parallel to AD; and you
will have the fecond perfpedtive fquare
BEFC.
Through the point /, where CE in
terfedts NS, draw bf parallel to AD j
and you will have fubdivided the
fquare BEFC into the four fquares
Bblk, klfC, bEml, and ImFf.
From the point F (at the top of the
perfpedtive fquare BEFG) draw FP
to the point of diftance P, interfedting
AS in /; then, from the point /draw JK

MADE EASY; ^3
IK, parallel to AD j and you will have
the third perfpedtive fquare EIKFt
Through the point n, where FI in
terfedts Us, draw eg parallel to AD;
and you will have fubdivided the
fquare ElKF into four lefler fquares,
Etnm, mngF, cloii, and no Kg.
From the point K (at the top of the
third perfpedtive fquare EIKFJ draw
KP to the point of diftance P, inter
fedting AS in L ; then, from the point
L draw LM parallel to AD, and you
will have the fourth perfpedtive fquare
ILMK.
Through the point p, where KL
interfedts NS, draw dh parallel to AD;
and you will have fubdivided the
fquare ILMK into the four leffer
G 2 fquares

$4 PERSPECTIVE
fquares Idpo, ophK, dLqp, and
pqMh.
Thus, we have formed an oblong
fquare A L M I), whofe perfpedtive
length is equal to four tiines its
breadth, and it contains i6 equal per
fpedtive fquares. — If greater length
was ftill wanted, we might proceed
further on toward S.
Take Ai equal to the' intended
breadth of the fide of the upright
fquare objedt A ^ (all the other fides
being of the fatne breadth) and AO
for the intended height. Draw 0 iB
parallel to AD, and make D 8 and 4 7
equal to A^; then draw ^ S, 4 S, 7 S,
and 8 S to the point of fight S ; and
among them we ihall have the per
fpedtive fquare bafes of all the 27
upright objedts on the plain.
3 Through

MADE EASY. 85
Through the point 9, where DB
interfedts 8 S, draw i 10 parallel to
AD, and you have the three perfpec-
tive fquare bafes -^123, 4567,
89 10 D of the three upright fquare
objedts at A, N, and D.
Through the point 21, where eb
interfefSts 8 S, draw 14 1 1 parallel to
AD ; and you will hfive the three per
fpedtive fquares <3 14 15 16, 17 18 1920,
and 21 11 e 2.2, for the bafes of the fe
cond crofs row of objedts ; namely,
the next beyond the firft three at A,
Ny and D.
Through the point w, where CE
interfedts 8 S, draw a line parallel to
BC; and you will have three perfpec-
tive fquares, at P, k, and C, for the
bafes of the third row of objedts ; one
of which is fet up at B,
Q 3 Through

U PERSPECTIVE
Through the point x, where fc in*
terfedts & S, draw a line parallel to iff
and you will have three perfpedtive
fquares, at b, I, and x, for the bafes
of the fourth crofs row pf objedts.
Go on in this manner, as ypu fee
in the figure, to find thp reft of the
fquare bafes, up to Z.M; and you will
have 27 upon the whole oblong fquare
plane, on whith you are to place the
like number of objedts, as in Fig. 2.
Having afliimed AO for the per?-
fpedtive height of the three objedts
(at A, N, and D) next the obferver's
eye, and drawn O 18 parallel to AD,
in order to make the objedts at iVand
D of the fame height as that at Oi
and having drawn the upright lines
4 15) 7 ^j 8 J, and D 22, for the
heights

MADE EASY. 87
heights AT and D ; draw 0 S and RS,
15 S and WS, XS and 22 S, all to the
point of fight S ; and thefe lines will
determine the perfpedtively equal
heights of all the reft of the upright
objedts, as ihewn by the |:wo placed
at a and B,
To draw the fquare tops of thefe
objedts, equal and parallel to their
bafes, we need only give one exr
ample, which will ferve for all,
Draw 2^ and 2 ^parallel to AQ,
and up to the line RSi then draw
P^ parallel to OR, and QP%R fiball
be the top of the objedt at A, equal
and parallel to its fquare bafe ^133,
T  In the fame e^fy way the tops of
^11 the other objedts ar^ formed.
Q 4 .When

B8 PERSPECTIVE
When all the reft of the objedts are
delineated, fhadfe them properlyv and
the whole pdrfpedtive fcheme will
have the appearance of Fig. 2.

OPERATION XIX.
To put a Square Box in PerfpeSlive, con
taining a given Number of leffer Square
Boxes, of a Depth equal to their Width,
38. Let the given number of little
fquare boxes or cells be 16, then 4 of
them make the length of each fide of
the four outer fides ab, i c^ c d, 4 a, as
in Fig. 3. and the depth ^/ is equal to
the width ae. — Whoever can draw the
reticulated fquare in Oper. V. (Fig. 6.
of Plate II.) will be at no lofs about
putting this perfpedtive fcheme in
pradtice. OPERA-

MADE EASY.- 89

OPERATION XX.
To put Stairs, ivith equal and parallel
Steps, in PerfpeSlive.
39. In Fig. I. of Plate VIL let ^3 be
the given breadth of each ftep, and ai
the height thereof. — Make be, cd, de,
&c. each equal to ab; and draw all
the upright lines a i, hi, en, dp. Sec.
perpendicular to ah (to which the,
horizon jS is parallel) and from the
points i, I, n, p, r. Sec. draw the equi
diftant lines iB, IC, nD, Sec. parallel
to ah; thefe diftances being equal to
that of iB from ah.
Draw xi, touching all the corner-
points /, n, py r, ty v; and draw 2 16
parallel

^ PERSPECTIVE
parallel to x i, as far from it as you
want the length of the fteps to be.
Toward the point of fight S, draw
the lines a i, i 2, ^ 3, /4, &c. and draw
j6 15, 14 13. 12 II, 109, 87, 65, 43,
and 21, all parallel to Ah, and meet
ing the lines w 15, « 13, / 11, &c. in
the points i^, 13, 11, 9, 7, 5, 3, and i :
then, from thefe points draw 15 14,
13 12, 1 1 10, 98, 76, 54, and 3 2, all
parallel to ha; and the outlines of
the fteps will be finiihed. From the
point 16, draw 16 A parallel te ha,
and Ax 16 will be part of the flat at
the top of the uppermoft ftep. — This
done, ihade the work, as in Fig. 2,
and the whole will be finiihed.

OPERA,

MAPE EASY.

OPERATION XXL
To put Stairs with Flats and Openings in
PerfpeSlive, flanding on a horizontal
pavement of Squares.
4d. In Fig. 3. of Plate VIL having
made S the point of fight, and drawh
a reticulated pavement A B, as di-
iredled in Oper. III. and done it only
with black lead lines, becaufe many
of them muft be rubbed out again;
at any diftance from the fide AB oi
the pavement wHich is neareft to the
eye, and at any point where you
chufe JO begin the ftair at that dif
tance, as a, draw Ga parallel to BA,
and take ^ ^ at pleafure for the height
of each' ftep. Take

92 PERSPECTIVE
Take ^^ in your compaffes, and fet
that extent as many times upward
from P to P as is equal to the firft
required number of fteps 0, N, M, L,fi;
and, from thefe points of divifion in
E F, draw xb, zd, 2,f, 4 h, and E k,
all equidiftant from one another, and
parallel to Fa: then draw the equi
diftant upright lines ab, t d, uf, v h,
IV k, and Im,, all perpendicular toF a:
then draw m b, touching the outer
corners of thefe fteps at m, k, hyf, d,
and b; and draw ns parallel to mb,
as far from it as you want the length
of the fteps K, Ly My N, 0 to be.
Toward the point of fight S, draw
mn. Is, ko, i6, hp,f2, d r, and b s.
Then (parallel to the bottom-line BAJ
through the points n, o, p, q, r, j, draw
w 8, 5 14, 6 15, 7 16, I 17, and 2 s;
which

MADE EASY. '93
which done, draw n 5 and 0 6 parallel
to Im, and the outlines of the fteps
K, L, M, N, O will be finiflied.
At equal diftances with that be
tween the lines marked 8 and' 14,
draw the parallel lines abdve, marked
9 10 II 12 and 13; and draw perpen
dicular lines upward from the points
^> o> pi ?> ^i ^> ^s in the figure.
Make Hm equal tb the intended
breadth of the flat above the fquare
opening at the. left hand, and draw
H^ toward the point of fight S, equal
to the intended length of the flat • then
draw IV P parallel to Hm, and the
outlines of the flat will be finifhed.
Take the width of the opening at
pleafure, as from F to C, and draw CD

94 PERSPECTIVE
CD equal and parallel to FJE.— DraW
Gi/ parallel to CDy and the ihort lines
marked 33, 34, &G. juft even with
the parallel lines i, 2, &c. From the
points where thefe ihort lines meet
CDy draw lines toward the point of
fight S till they meet D E. Then,
from the points where the lines 38,
39, 40, &c. of the pavement meet Cy,
draw upright lines parallel to CD;
and the lines which form the opening
will be finiihed.
The fteps P, ^, R, S, T, and the
flat U above the arch r, are done in
the fame manner with thofe in Fig. i.
as tadght in Oper. XX. and the equi
diftant parallel lines marked 18, 19,
&c. are diredtly even with thofe on
the left-hand fide of the arch F, and
the upright lines on the right-hand
I fide

MADE EASY. 95
fide are equidiftant with thofe on the
left. From the points where the lines
18, 19, 20, &c. meet the right-hand
.fide of the arch, draw lines toward
the point of fight S: and from the
points where the pavement-lines 29,
30, 31* 32 meet the line drawn from
A toward the point of fight, draw
upright lines toward the top of the
arch. Having done the top of the arch, as
in the figure, and the few fteps to the
right-hand thereof ; ihade the whole,
as in Fig. 4. and the work will be
finiihed. And it is my opinion, that if the
young artift is mafter of all the pre*
ceding

96 PERSPECTIVE
ceding operations, he will underftand
thefe two figures better by a bare view,
than by any defcription that can be
given of them.
OPERATION XXIL
To put upright conical Obje^s in PerfpeC"
tive, ds if flanding on the Sides of an
ohlong Square, at Diflances from one
another equal to the Breadth of the
I Oblong.41. In Fig. I. of Plate VlII. the bafes
of the upright cones are perfpedtive
circles infcribed in fquares of the
fame diameter, as ihewn in Oper. IV.
and the cones are fet upright on their
bafes by the fame rules as are given
in Oper. IX. and XIV. for pyramids,
which we need not repeat here. In

MADE EASY. ^7
In the foregoing operations, we
have confidered the obferver's eye to
be above the level of the tops of all
the objedts, as if he viewed thofe in
PI. IV. V. VI. and VII. when ftanding
on high ground. In the three figures
on Plate VIII. we fhall fuppofe him to
be ftanding on low ground, and the
tops of the objedts to be above the
level of his eye*
in Fig. 1. \tt Al) be thfe pei-fpec-
tive breadth of the oblong fquare
A BCD ; and let A a and Dd (equal to
^a) be taken for the diameters of the
Circular bafes Of the two cones next
the eye, whofe intended equal heights
Ihall be ^P and DF.
Having made S the point of fight,
;in the horizon parallel to ADy and
H found

§8 PERSPECTIVE
found the proper point of diftance
therein, draw AS and a S, to contain
the bafes of the cones on the left-hand
fide, and DS and dS for thofe on the
right. Having made the two firft cones at
A and D of equal height at pleafure,
draw E S and FS from their tops to
the point of fight, for limiting the
perfpedtive heights of all the reft of
the cones. Then, according to the
diredtions in Oper, XIV. divide the pa
rallelogram ABCD into as many
equal perfpedtive fquares as you
pleafe; find the bafes of the cones
at the corners of thefe fquares, and
make the cones thereon, as in the
figure. If you would reprefent a cieling,
equal and parallel to ABCDy fup-
port'ed

M A i) E EASY. 9^
ported on the tops of thefe cones,
drawPp; then* PFG.^ fliall be the
cieling, and by drawing ^/parallel to
FIF, you will have the thicknefs of
the floor-boards and beams, which
may be what ypu pleafe.
This ihews hpw any nutt^ber of
equidiftant pillars may be dr^wn pf
equ?.l heights, to fupport the cieling
of a Jong rpom ; and hQW the wall?
pf fuch a room may be reprefented ii>
perfp|?dtive at the b^c^s of thefe. pilr
Jars. It aJfo ihews how a ftreet of
houfp? may be ^pawu in perfpedtiye.

H 2 OPERA-

%&o PERSPECTIVE
OPERATION XXIIL
Te put a Square Hollow in PerfpeSUvCy the
Depth of which fhall bear any affigned
Proportion to its Width.
j^i. Fig. 2. bf Plate VIIL is the re
prefentation of a fquare hollow, of
which the depth -^G is equal to three
times its width A D ; and S is the
point of fight,, over which the ob-
ferver*s eye is fuppofed to be placed,
looking perpendicularly down into
it, but not diredtly over the middle.
Draw AS and DS to the point of
fight S; make ST the horizon, paral
lel to A D, and produce it to fuch a
length beyond T that you may find a
point of diftance therein not nearer S
than

MADE EASY. loi
than ii AD was feen under an angle
of 60 degrees.
Draw DU to the point of diftance,
interfedting AS in B : then, from the
point B draw B C parallel to .^^D ; and
you will have the firft perfpedtive
fquare AB CD, equal to a third part
of the intended depth.
Draw CF" to the point of diftance,
interfedting -f^S in P. -then, from the
point E draw EF parallel to AD;
and you will have the fecond perfpec-
tive fquare BEFC; which, added to
the former one, make§ twQ'^thirds of
the intended depth,
Draw FW to the point of diftance,
interfedting AS in G; then, from the
point 0 draw G H parallel to ^ D ;
H 3 ^ni

fb2 PEIlSl»ECTlVE
and you ^ill have the third perf^^ifeb-
tive fi|uare EGHF; whifclh, with the
former two, makes the whole depth
AGBD three times aS gr6at as the
width ADy in a perfpedtive view.
Divide AD into any niiihbet' of
equal parts, as fuppofe 8 ; and fyiyia.
the divifion-points a, b, c, d, i&e. liraW
lines toward the point of fight S, and
ending at G H. Then, through \he
points where the ^fiagoftafe BD, EC,
GF cut thefe lines, draw lines paral
lel to AD; ^nd you will haSj'e the
parallelogram AGHD reticukred or
divided into 192 fmall and equal per
fpedtive fquares.
Make AI and Dlk equal and per
pendicular to AD: then draw fM^
which Viii be equal and j^arklM to
^Dj

MADE EASY. 103
AD; and draw IS and il^S to the
point of fight S.
Divide A I, I My and MD into rhe
fame number of equal pa^ts as AD ia
divided : and from thefe points of
divifion draw lines toward the point
of fight S, ending refpedtively at GK,
KLy and LH,
From thofe points where the lines
parallel to AD meet AG and DB,
draw upright lines parallel to yf /and
DMi and from the points where
thefe lines meet IK and L M, draw
lines parallel to IM,: then fhade the
work, as in the figure.

H4 OPERA-

104 PERSPECTIVE

OPERATION XXIV.
To reprefent a femicirculaf Arch in Per
fpeSlive, as if it ivere flanding. on tvao
upright Walls, equal in Height to the
Height of the Obferver s Eye.
43. After having gone through the
preceding operation, this will be more
eafy by a bare view of Fig. 5. in Plate
VIII. than it could be made by any
defcription ; the method being fo
much like that of drawing and iha
ding the fquare hollow. — We need
only mention, that aTbE A and
DF ct d are the npright walls on
which the femicircular arch is built ;
that S is the point pf fight in the ho
rizon Tt, taken in the center of th^
arch ; that d (in Fig, 2.) is the ppint

MADE EASY. lo^
of diftance; and that the two per-
fpedive fquares ABCD and DEFC
make the parallelogram AEFD of
a length e<jual to twice its breadth
AD,

OPERATION XXV.
To reprefent a Square in PerfpeSlive, as
yienved by an Obferver flanding direSlly
even with one of its Corners.
44. In Fig. I. of Plate IX. let A^BC
be a true fquare, viewed by an ob
ferver ftanding 9.t fome diftance fi:om
the corner C, and juft even with the
.diagonal Cg.
Let joSP be the horizon, parallel
to the diagonal ABi and S the point
ipf fight, even with thp diagonal Cg.
Here

ro6 PERSPECTIVE
Here it will be prbper to have two
points of diftance p and P, equi
diftant from the point of fight S,
Draw the ftraight line i 17 parallel
to A By and draw AS and B 10 pa
rallel to CS. Take the diftance be
tween 8 and g in your compafles, and
fet it off all the way in equal parts
from 8 to i, and from 10 to 17.— The
line I 17 ihould be produced a good
way further both to right and left
hand from 9, and divided all the way
in the fame manner.
From thefe points of equal divifion,
8, g, ID, BcC. draw lines to the point
of fight S, and alfo to the two points
pf diftance p and P, as in the figure.
Now it is plain, that aci^ is the
perl^peftive r^refentation of AgBC,
I viewed

MADE EASY. 1 67
viewed by an obferver even with the
corner C and diagonal Cg, — But if
there are other fuch fquares lying
even with this, and having the famfe
pofition with refp&dt to the line i 17,
it is evident that the obferver, who
ftands dir^ly even with the corner C
of the fii-ft fquare, Will- not be even
with thfe like cornef s G and K of the
others ; but will have an Oblique view
of them, over the fides FG and IK
which are neareft his eye : and tbeit
perfpedtive reprefentations will be
^gf^ and hki$-, drawn among the
lines in the figure : df whicfe, thfe
Ipiac'es taken up by each iide lie be-
tWeein three of the lines drawn to^
ward the point of diftaWfe p, and threfe
dy^Vn to the othet" point of diftance P.

O P E R x^.

io8 PERSPECTIVE

OPERATION XXVI.
To reprefent a common Chair, in an oblique
VieiVy in PerfpeSlive,
45. The original lines to the point
of fight S, and points of diftance p
and P, being drawn as in the pre
ceding operation, chufe any part of
the pl^ne, las Imn 13, on which you
would have the chair L to ft^nd,-r-
There are juft as many lines (namely
two) between / and w or 13 and n,
drawn toward the point of diftance p,
at the left hand, as between / and 1 3,
or m and «, drawn to the point of
diftance P pn the right; fo that /w,
mn, « 13, and 13 /, form a perfpe^ivp
fquare, Fypm

MADE EASY. i6g
From the four corners l,m,n,ii, oi
this fquare raife the four legs of the
chair to the perfpedtive perpendicular
height you would have them: then
make the feat of the chair a fquare
equal and parallel to lmni$, as taught
in Oper. X. which will make the two
fides of the feat in the diredtion of the
lines drawn toward the point of dif
tance p, and the fore and back part of
the feat in diredtion of the lines drawn
to the other point of diftance P. This
done, draw the. back of the chair
leaning a little backward, and the
crofs bars therein tending toward the
point of diftance P. Then ihade the
work as in the figure ; and the per
fpedtive chair will be finifhed.

OPERA.

ISO PERSFECTI-VE

OPERATION XXVIL
To reprefent an oblong Square Table in art
oblique perfpeSlive Vieiv.
46. In Fig. I. of Plate IX. M is an
oblong fquare table, as feen by an
obferver ftanding diredtly even with
C9 (fee Ojjfr. XXV.), the fide next the
eye being perfpedtively parallel to the
fide acoi the fquare acb 9. — The fore-'
mentioned lines drawn from the line
I 17 to the two points of diftance p
and P, form equal perfpedtive fquares
©n the ground plane.
Choofe any part of this plane of
fquares for the feet of the table to
ftand upon ; as at />, q, r, and j, in di
redtion of the lines op and rs for the
two

MADE EASY. m
two long fides, and t s and q r for the
two ends ; and you will have the ob
long fquare or parallelogram qr s t
for the part of the floor or ground-
plane whereon the table is to ftand :
and the breadth of this plane is here
taken in proportion to the length as 6
to loj fo that, if the length of the
table be ten feet, its breadth will be
fix. On the four little perfpedtive fquares
at q, r, s, and /, place the four upright
legs of the table, of what height you
pleafe, fo that the height of the two
next the eye, at o and p, ihall be ter
minated by a ftraight line u v drawn
to the point of diftance P. This done,
make the leaf Moi the table an ob
long fquare, perfpedtively equal and
parallel to the oblong fquare q r s t
on

112 PERSPECTIVE
on which the feet of the tabic
ftands. Then ihade the whole, as in
the figure, and the work will be
finiihed. If the line 1 17 was prolonged to the
right and left hand, and equally di
vided throughout (as it is from i to
17), and if the lines which are drawn
from p and P to the right and left
hand fides of the plate were prolonged
till they came to the extended line
I 17, they would meet it in the equal
points of divifion. In forming large
plans of this fort, the ends of flips of
paper may be pafted to the right and
left edges of the iheet on which the
plan is to be formed.

CHAP.

MADE EASY. tij

CHAP. III.
7%e Defcription tf a Machine^
hy which any Perfon may deli
neate the true PerfpeBive Figures
of OhjeBsy without having learmd
any of the preceding Rules,
47. T?IG. 2. of Plate IX. is a plane
•*- of this machine, and Fig.: 3.
is a reprefentation of it when made
ufe of in drawing diftant objedts in
perfpedtive. A Iketch of it was given
me feveral years ago by the late in-
genfbus Dr. Bevis, who then told me
he had never feen one of the like
conftrudtion : and as all thofe to whom
I have had the opportunity of ihewing
I it,

114 PERSPECTIVE
it, have told me that they never faw
nor heard of fuch a one before^ I have
great reafon to believe that the Doc
tor was the inventor of it, although
Jie never made it public.
In order that it may be the eafier
undcrftood, I have put the letters of
reference to the plane (Fig. s.) in
fmall Italics, and the fame letters to
the like parts of it in the perfpedtive
view (Fig. 3.) in Roman capitals; that
the reader may look at them both, as
he goes on with the following de
fcription. In Fig. 2. abefis an oblong fquare
board, reprefented by AB EF in
Eig. 3. X and y (X and TJ are two
hinges on which the part eld (CLDJ
is moveable. This part confifts of two
arches

MADE EASY. 115
arches or portions of circles cm I
(CMLJ and dnl (DNL) joined toge
ther at the top / (L) and at bottom
to the crofs bar d ^ (D C) to which
one part of each hinge is fixed, and
the other part to a flat board, half the
length of the board abef fABEF)
and glued to its uppermoft fide. The
center of the arch eml is at d, and the
center of the arch dn lis at c.
On the outer fide of the arch dnl is
a Aiding piece n (much like the nut
of the quadrant of altitude belonging
to a common globe) which may be
moved to any part of the arch between
d and /.• and there, is fuch another
Aider 0 on the arch em I, which may
be fet to any part between c and /. —
A thread cpn (CRN) is ftretched tight
from the center c (C) to the Aider n
I 2 fNJ»

ii6 PERSPECTIVE
(NJ, and fuch another thread is
ftretched from the center d (D) to the
Aider o (0) ; the ends of the threads
being f aftened to thefe centers and
Aiders, Now it is plain, that, by moving
thefe Aiders on their refpedlive arches,
the interfedtion p (P) oi the threads
may be brought to any point of the
open fpace within the arches. — ^In the
groove k (K) is a ftraight Aiding bar
i (I) which may be drawn further
out, or puihed further in, at pleafure.
To the outer end of this bar / (Fig,
3.) is fixed the upright piece HZ,
in which is a groove for receiving the
Aiding piece ^ In this ilider is a
fmall hole r for the eye to look
through, in ufing the machine : and
there

MADE EASY. 117
there is a long Ait in HZ, to let the
hole r be feen through when the eye
is pkced behind it, at any height of
the hole above the level of the bar /.
Bow to delineate the PerfpeSlive Figure of
any diflant ObjeSl for ObjeSls) by means
of this Machine,
48. Suppofe you wanted to delineate
a perfpedtive reprefentation of the
houfc qsrp (which we muft imagine
to be a great way off, without the
limits of the plate) place the machine
on a fteady table, with the end EF oi
the horizontal board yfPPF toward
the houfe, fo that, when the Gothic-
like arch D LC is fet upright, the
middle part of the ppen fpace (about
P) within it may be even with the
houfe when you place your eye at Z
I 3 aad

ai8 PERSPECTIVE
and look at the houfe through the
fmall hole r. Then fix the corners
of a fquare piece of paper with four
wafers on the furface of that half of
the horizontal board which is neareft
the houfe ; 9.nd all is ready for draw
ing- Set the arch upright, as in the
figure ; which it will be when it
comes to the pcTpendicular fide t of
the upright piece s t fixed to the ho
rizontal board behind D. Then place
yout- eye at Z, and look through the
hole r at any point of the houfe, as
q, and move the Aiders N and 0 till
you bring the interfedtion of the
threads at P diredly between your
eye and the point ? ; then put down
the arch flat upon the paper on the
board, as at ST, and the interfedtion of

MADE EASY. ng
of the threads will be at W. Mark
the point W on the paper with the
dot of a black lead pencil, and fet the
arch upright again, as before: then
look through the hole r, and move
the fliders iVand 0 till the interfedtion
of the threads comes between your
eye and any other point of the houfe,
as p : then put down the arch again
to the paper, and make a pencil-mark
thereon at the interfedtion of the
threads, and draw a line from that
mark to the former one at W; which
line will be a true perfpedtive repre
fentation of the corner^ ^ of the houfe.
Ptoceed in the fame manner, by
bringing the interfedtion of the threads
fucceflively between your eye and
other points of the outlines of the
houfe, as r, s, Sec. and put down the
3 arch

I90 PERSPECTIVE
arch to mark the like points on the
paper, at the interfedtion of the
threads : then connedt thefe points
by ftraight lines, which will be the
perfpedtive outlines of the houfe. In
like manner find points for the cor
ners of the door and windows, top of
the houfe, chimnies, Sec. and draw
the finifliing lines from point to
point : then fliade the whole, making
the lights and ihades as you fee them
on the houfe itfelf, and you will have
a true perfpedtive figure of it.— Great
care muft be taken, during the whole
time, that the pofition pf the machine
be not fliifted on the table ; and to
prevent fuch an inconvenience, the
table fhould be very ftrong and fteady,
and the machine fixed t0 it, either by
fcrews or clamps.

In

MADE EASY. 121
In the fame way, a landfcape, or
any number of objedts within the
field of view through the arch, may
be delineated, by finding a fufficient
number of perfpedtive points on the
paper, and connedting them by ftraight
or curved lines as they appear to the
eye. And as this makes every thing
in perfpedtive equally eafy, without
taking the trouble to learn any of the
rules for drawing, the operations
muft be very pleafing and agreeable.
Yet, as fcience is ftill more fo, we
would by all means recommend it to
our Readers to learn the rules for
drawing particular objedts ; and to
draw landfcapes by the eye, for which,
I believe, no perfpedtive rules can be
given. And although any thing may
be very truly drawn in perfpedtive by
means of this machine, it cannot be
faid
8

125, PERSPECTIVE
liaid that there is the leaft degree of
fcience in going that way to work.
The arch ought to be at leaft a foot
wide at bottom, that the eye at Z may
have a large field of view through it ;
and the eye ihould then be, at leaft,
104. inches from the interfedtion of
the threads at P when the arch is fet
upright. For, if it be nearer, the
boundaries of view at the fides near
the foot of the arch will fubtend an
angle at Z of more than 60 degrees,
which will not only ftrain the eye
(§ 10.), but will alfo caufe the outer-
moft parts of the drawing to have a
difagreeable appearance, — To avoid
this, it will be proper to draw back
the Aiding bar /, till Z he i^i inches
diftant from P ; and then the whole
field of view, through the foot wide
arch.

MADE EASY. 123
arch, will not fubtend an angle to the
eye at Z of more than 45 degrees;
which will give a more eafy and plea-
fant view, not only of all the objedts
themfelves, but alfo of their repre
fentations on the paper whereon they
are delineated. So that, whatever the
width oiF the arch be, the diftance of
the eye from it ihould be in this pro
portion : As 12 is to the width of the
arch, fo is 147 to the diftance of the
eye (at ZJ from it.
If a pane of glafs, laid over with
gum water, be fixed into the arch,
and fet upright when dry, a perfon
who looks through the hole r may
delineate the objedts upon the glafs
which he fees at a diftance through
and beyond it, and then transfer the
delineation to a paper put upon the
glafs, as mentioned in § i.
FINIS.

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