590 
PERSPECTIVE. 
also, as before mentioned, on one or both 
sides of the point of sight. 
- These requisites being laid down on the 
drawing-board, we may proceed to examples 
of finding the true positions of points and lines 
on the picture, from theiv ichnography, drawn 
out of, and below, the baseline. 
Suppose the pentagon ABDEF (fig. 2.) 
was. to be represented by the rules of per- 
spective on tiie transparent plane VP, pla- 
ced perpendicularly on the horizontal plane j 
UR; dotted lines are imagined to pass from 
the eve C to each point of the pentagon, as 
CA, CB, CD, &(•. which are supposed in their 
passage through the plane PY, to leave their 
traces or vestigia in the points a, !>, d, &c. on ; 
the plane, and thereby to delineate the pen- 
tagon ( ib dtf ; which, as it strikes the eye by j 
the same rays that the original pentagon | 
ABDEF does, will be a true perspective re- j 
presentation of it. 
The business of perspective, therefore, is 
to lav down geometrical rules for finding the 
points abdfj upon the plane; and hence, 
also, we have a mechanical method of de- 
lineating any object very accurately. 
Perspective is either employed in repre- 
senting the ichnographics, or ground-plots of 
objects ; or the scenographics, or represen- 
tations of the objects themselves. 
But before we give any examples of either, 
it will be proper to explain some technical 
terms in regard to perspective in general; 
and, first, the horizontal line is that supposed 
to be drawn parallel to the horizon through 
the eve of the spectator; or rather it is a line 
which separates the heaven from the earth, 
and which limits the sight. Thus, A, B, fig. 
3, are two pillars below the horizontal line 
CD, by reason the eye is elevated above them ; 
in iig. 4, they are said to be equal with it; 
and in fig. 5, raised above it. Thus, accord- 
ing to the different points in view, the objects 
will be either higher or lower than the hori- 
zontal line. The point of sight, A, fig. 6, is 
that which makes the central ray on the ho- 
rizontal line; or, it is the point where all 
the other visual rays, D, I), unite. The 
points of distance, C, C, are points set off in 
the horizontal line at equal distances on each 
side of the point of sight, A; and, in the same 
figure, BB represents the base line, or funda- 
mental line ; EE is the abridgment of the 
square, of which D, D, are the sides u F, F, 
the diagonal lines, which go to the points of 
distance C, C. Accidental points, are those 
where the objects end : these may be cast 
negligently, because neither drawn to the 
point of Sight, nor to those of distance, but 
meeting each other in the horizontal line. For 
example, two pieces of square timber, G and 
H, fig- 7, make the points I, I, I, I, on the 
horizontal line ; but go not to the point of 
sight K, nor to the points of distance C, C : 
these accidental points serve likewise for case- 
ments, doors, windows, tables, chairs. &c. 
'['he point of direct view, or of the front, is 
when we have the object directly before us ; 
in which case, it shews only the foreside ; 
and, if below the horizon, a little of the top, 
but nothing of the sides, unless the object is 
poiygonous. The point of oblique view, is 
when we see an object aside of us, and as it 
were aslant, or with the comer of the eye; 
the eye, however, being all the while opposite 
to the point of sight ; in which case, we see 
Uie object laterally, and it presents to us two 
sides or faces. The practice is the sarrte in 
the side-points, as in the front-points ; a point 
of sight, points of distance, &c. being laid 
down in the one as well as in the other. 
We shall now give some examples, by 
which it will appear that the whole practice 
of perspective is built upon the foundation al- 
ready laid down. Thus, to find the per- 
spective appearance of a triangle, ABC, fig. 
8, between the eye and the triangle draw the 
line DE, which is called the fundamental line; 
from 2 draw 2 V, representing the perpen- 
dicular distance of the eye above the funda- 
mental line, be it what it will ; and through 
V draw, at right angles to 2 V, 1IH parallel 
to DE: then will the plane DIIHE represent 
the transparent plane, on which the perspec- 
tive representation is to be made. Next, to 
find the perspective points of the angles of the 
triangle, let fall perpendiculars At, C 2, 133, 
from the angles to the fundamental DE: set 
off these perpendiculars upon the fundamental 
opposite to the point of distance II, to B, A, 
C ; from 1,2, 3, draw lines to the principal 
point V ; and from the points A, B, and C, 
on the fundamental line, draw the right lines 
AH, BH, CH, to the point of distance H ; 
which is so called, because the spectator ought 
to l^e so far removed from the figure or paint- 
ing, as it is distant from the principal point V. 
The points a, b, and c, where the visual lines 
V 1, V 2, Y3 intersect the lines of distance 
AC, BH, CH, will be the angular points of the 
triangle abc, the true representation of ABC. 
By proceeding in this manner with the an- 
gular points of any right-lined figure, whether 
regular or irregular, it will be very easy to 
represent it in perspective ; however, in prac- 
tice, several compendious methods will oc- 
cur to every artist. Again, if the scenographic 
appearance of any solid was to be represent- 
ed, suppose of a triangular prism, whose base 
is the triangle mao, fig. 9, you need only find 
the upper surface of it, in the, same manner 
as you, found the lower, or base; and then 
joining the corresponding points by right lines, 
you will have the true representation of the 
solid in perspective. So that the work is the 
same as before ; only you take a new funda- 
mental line, as much higher than the former, 
as is the altitude of that solid whose sceno- 
graphic representation you would delineate. 
But there is still a more commodious way, 
which is this: having found, as above, the 
base or ichnographic plane vino, let per- 
pendiculars be erected to the fundamental 
line from the three angular points, which will 
express the altitudes of those points. But 
because these altitudes, though equal in the 
body or solid itself, will appear unequal in the 
scenographic view, the farthest off appearing 
less than those nearer the eye, their true pro- 
portional heights may be thus determined. 
Any where in the fundamental line, let AB 
be erected perpendicularly, and equal to the 
true altitude ; or, if the figure has different 
altitudes, let them be transferred into the 
perpendicular AB; and from the points A 
and B, and from all the points of intermediate 
altitudes, if there are any such, draw right 
lines to the point of sight V : those lines, 
AV, BV, will constitute a triangle with AB, 
within which all the points of altitude will be 
contained. Through the points o, n, m, draw 
parallels to the fundamental line ; and from 
the pqints a, a, &c. erect perpendiculars to 
those parallels ; »nd the points where they 
intersect the lines AV, BV, as in a, a, b, b, 
&c. will determine the apparent height ol the 
solid in that scenographic position to the eye 
in V. 
Parallel perspective is where the picture is 
supposed to be so situated, as to be parallel 
to the side of the principal object in the pic- 
ture, as a building for instance. 1 hen the 
lines on those sides of the building that are 
parallel to each other, continue parallel on 
the picture, and do not vanish into any point ; 
while the lines at right angles to the former, 
vanish into the centre of the picture. I his 
will be exemplified in fig. 10. 
The picture being supposed to stand 
parallel to the side of the house ABCD, the 
lines AB, DC, which in nature are parallel to 
each, must be made parallel in the perspective 
representation. But the lines BE, CF, which 
in nature are at right angles to AB and DC, 
and consequently also to the picture, tend 
towards a point; and this point G, towards 
which they tend, is the centre of the picture. 
Oblique perspective, is when the plane of 
the picture is supposed to stand oblique to the 
sides of the objects represented, in which 
case the representations of the lines upon those 
sides will not be parallel among themselves, 
but will tend towards their vanishing point. 
This kind of perspective is shewn in fig. 1 1 . 
A bird’s-eye view, is a view supposed to be 
taken in the air, looking down upon the ob- 
ject, and differs from the usual way of draw- 
ing perspective views, in supposing the hori- 
zontal line to be raised much higher. 
When an object is to be drawn in per- 
spective, all its parts must be measured, so 
that we may be able to lay them down from 
a scale of equal parts. 
Having determined whether it is (o be 
parallel or oblique perspective, the first thing 
to be draw'll is the horizontal line, which is to 
be put parallel to the bottom of the drawing, 
and as high above it as the height of a man’s 
head, or live feet six incheq as HG, fig. 10, 
which is five feet six inches above the bottom 
of the house. Next, determine on the cen- 
tre of the picture G, which must be placed so 
as to leave convenient room for the repre- 
sentation. Fix on C the nearest corner of the 
object, and draw the perpendicular CB: lay- 
off CD equal to the length of the building, 
and draw DA and AB. From C, the nearest 
corner, draw CG, to the centre of the pic- 
ture. CG now contains the line which repre- 
sents the bottom of the end of the house ; but 
this is an indefinite representation, of which 
we do not yet know the exact length. The 
method of determining this is as follows : Con- 
tinue the line DC to I, and make Cl equal 
to the width of the house. From G, the 
centre of the picture, lay off GK equal to the 
distance of the picture, the choosing of which 
must be regulated by taste. Draw IK, cut- 
ting CG in F ; then is CF the exact width 
of the house in perspective, which was equal 
to CL r Fo find the middle of this end of the 
house, you cannot divide it by your com- 
passes, because the farthest half will appear 
less than the nearer; but if you divide Cl 
into two equal parts in L, and draw LK, it 
will cut CF into two equal parts perspectively. 
Or it may be found more simply- thus: hav- 
ing drawn the lines BE and CF to the centre 
of the picture, draw the diagonals EC, BE, 
crossing each other hi M, and raise the per- 
