.381 
pendicular MN, which is in the middle of the 
gable- end. 
To find the height of the gable, lay its 
actual height above BE, upon the corner line 
BC continued, as BO, and draw OG ; this 
crossing the perpendicular MN, gives N the 
point of the gable. The top of the chimney 
must be drawn in the same manner, by laying 
its real height, taken from a scale, on OP ; - 
and drawing PG, lay off L m and L n, each 1 
equal to half the width, and draw from these ! 
points to the distance-point K; this will cut I 
the bottom of the house CF, in the points o 1 
and p; from these draw perpendiculars, which 
will give the perspective width of the chim- i 
nev. To obtain its thickness, lay off PQ 
equal to its thickness, and draw QG ; then 
drawing from a the line ab, yon obtain the 
exact width of the chimney. From b draw 
be. and from d draw dc. 'Fhe other end of : 
the gable may be drawn by two different 
methods. The first is by supposing the front > 
of the house transparent, and drawing the i 
other end as if seen through it, in the same 
manner as the end we have described, by lay- 
ing its width from D to R, and drawing to 
the distance-point K. By raising the per- 
pendicular in the middle, you will meet the 
ridge-line from the other gable in d. The 
other method is as follows: Through the centre 
of the picture G draw the line ST, upwards 
and downwards, and perpendicular to the 
horizontal line. Then continue the line of 
the roof B d till it meets ST in S. From A 
draw AS, which will give the other gable, and 
S will be the vanishing-point for all lines 
parallel to BcZ and Ad ; if NE is continued 
in like manner, it will give T for its vanish- 
ing-point. The doors and windows on the 
side ABCD are laid down from a scale, be- 
cause that side being parallel to the picture, 
does not vary from its geometrical delineation, 
except shewing the thickness of the reveals, 
or edges of the doors and windows. It there 
had been any windows in the side BEFC, 
they would be drawn in perspective by the 
same method that was used for finding the 
width of the house and the middle of the end, 
viz. by laying off the actual dimensions from 
C upon Cl, and drawing from these points 
to the distance-point K, which would transfer 
these divisions to the bottom of the house 
CF, and then perpendiculars might be drawn 
upwards. 
This practice is farther explained by the 
following rule : 
To divide a line in perspective which is 
parallel to the horizon, and which tends to a 
vanishing-point, into any number of equal 
parts ; or to divide it into any required pro- 
portion. 
Let AB be the line going to its vanishing- 
point C, tig. 12 ; and first let it be required 
to divide that line into six equal parts. Let 
CD be the horizontal line, and AE the ground- 
line, drawn parallel to it. Lay off, at plea- 
sure, CD for tin? distance of the picture, if C 
is the centre of tne picture. Draw a line 
from D, touching the end B of the line to be 
divided: draw DBE, cutting the ground-line 
in E. Then AE represents the actual dimen- 
sions of the line AB, which is seen in per- 
spective. (Here it may be observed, that 
this gives a rule also for finding the real 
length of any line which tends to a vanishing- 
point.) Divide AE into the same number of 
equal parts into which you proposed to., .divide 
'PERSPECTIVE. 
the given line AB ; as Al, 1 2, 2 3, &c. Then 
from these different divisions draw lines to D, 
cutting the line AB in a, b, c, d, & c. which 
will represent the required number of equal 
parts, but diminishing in size as they are 
farther removed from the eye. If it is wished 
to divide the line AB into any number of un- 
equal parts, or to lay off doors, windows, &c. 
upon it, the line AE, found as before, must 
be divided in the required propoition, and 
lines drawn from those to D will give the re- 
quired divisions on AB, from which perpen- 
diculars may be drawn for the .doors, win- 
dows, &c. 
To draw a circle in perspective. 
The perspective representation of every 
circle is a regular ellipsis, when the eye is 
without the circle ; which may be demon- 
strated by considering that the rays from the 
circumference of the circle to the eye, form 
an oblique cone. But it is well known to 
those who are acquainted with conic' sections, 
that every section of a cone, whether right or 
oblique, is a true ellipsis, except in one case 
only, which is, when the section is taken sub- 
contrary to its base, a situation which hap- 
pens so rarely in drawings that it may be dis- 
regarded altogether, and the section of a 
cone, or the perspective of a circle, in all 
cases considered as a perfect ellipsis.. 
The most correct and easy method'of draw- 
ing an ellipsis is, to find the transverse and 
conjugate axes; the curve may then bejeom- 
pleted by a. trammel, or by hand. Buf as it 
is very difficult to find the transverse and 
conjugate axes of the ellipses which are the 
perspective representations of circles, recourse 
is generally had to another method of obtain- 
ing the curve. The circle is circumscribed 
by a square, as KL.YIN, in fig. 13, anti the 
diagonals and the lines across the centre, and 
parallel to the sides, are drawn ; also the lines 
(d, cd, are drawn parallel to the sides, through 
the points where the circle is cut by the dia- 
gonals. This square, with all these lines 
drawn across it, is now put in perspective as 
follows : Draw AB for the horizontal line, and 
fix 13 for the centre of the picture, and AB for 
the distance of the picture. Make DC equal 
to the width of the square, and draw C13, 
DB; draw CA to the distance-point A, cut- 
ting off DG, equal to the depth of the square ; 
then draw GF parallel to DC, which com- 
pletes the perspective of the square; also 
draw the diagonal DF. Take now the dis- 
tances Mr/,. cN ; and transfer them to D.r, 
o C ; from these points- x ando> draw lines to 
the vanishing-point B, cutting the diagonals of 
the square. The points in this reticulated 
square in perspective, which correspond to 
those in the square KLMN, where the circle 
passes through, must now be observed, and a 
curve traced through them with a steady 
hand it will be the perspective required. Even 
in this process, it is of considerable use to 
know that the curve you are tracing is a re- 
gular ellipsis: for though you .cannot easily 
ascertain the axes exactly, yet you may very 
nearly ; and the eye very soon discovers whe- 
ther the curve which has been drawn is that 
of a regular ellipsis or not. 
Upon the same principle exactly, the row 
of arches, fig. 14, is drawn. The width of 
the arches and piers is obtained in the same 
manner as was shewn in fig. 12, viz. by lay- 
ing their dimensions upon the ground-line 
AB, and drawing lines to the distance-point. 
The curves of the arches are then found by 
drawing the lines which correspond to those 
in half the square, fig. 13, in the same man- 
ner as described above for the circle. 
Fig. 15 shews the appearance of circles 
drawn upon a cylinder, when HI is the hori- 
zontal line. The circle drawn on the cylinder 
at that place, is seen exactly edgeways, and 
appears only as a straight line; that next 
above it is seen a little underneath ; the next 
still more ; and so on, as they rise higher, 
appearing like so many ellipses of the same 
transverse diameter, but whose conjugate 
diameters continually increase in length, as 
they rise above the horizontal line. On the 
contrary, you see the under sides of the cir- 
cles drawn below the horizontal lines; but 
they observe the same law, being so many 
ellipses, whose conjugate diameters vary iu 
the same proportion. A little reflection on 
this simple example, will enable those who 
draw to avoid many ridiculous mistakes which 
are sometimes committed ; such as shewing 
the two ends of a cask, or the top and bottom 
of a cylinder, at the same time. 
Fig. 1 1 shews the method of drawing' a 
building, or other object, in oblique per- 
spective.. AB is the horizontal line, and CD 
the ground-line, parallel to it as before. I lere 
neither of the sides of the house is parallel to 
the picture, but each goes to its respective 
vanishing-point. 1 laving fixed on the nearest 
corner E,draw IT 13, at pleasure, for one side, 
and choose any point F for the centre of the 
picture; then, to find the other side, lay off 
FG equal tothe distance of the picture, which, 
as before, depends upon taste only ; draw BG, 
and GA perpendicular to BG, cutting the 
horizontal line in A, the other vanishing- 
point. Draw now EA for the other side. 
To cut off the several widths of the two sides 
of the house, which as yet are only drawn to 
an indefinite extent, two distance-points must 
be laid down, viz. one for eacli vanishing- 
point. To do this, extend the compasses from 
13 to G, anil lay the distance taken in it from 
B to IT, which will give H for the distance- 
point of 13, and which is to cut off all the di- 
visions on the side E13. Also extend the 
compasses from AG, and lay down AI. I is 
the distance-point of A, and is used for trans- 
ferring all divisions upon the side EA from 
the ground-line GE. These points and lines 
being adjusted, tire process is not much dif- 
ferent from parallel perspective; onlv here 
equal divisions on each side of the building, 
as doors, windows, diminish as they recede la- 
the same way as on the side BEFC, fig. it). 
Lay the real length of the side EL, taken from 
the same scale used for laying down the hori- 
zontal line, and lay it down on the ground- 
line, from E to C, and draw Cl, cutting off 
EL for tire perspective length of the building. 
For the other side of the house, lay its width 
down in the same manner, from E to I), and 
draw DII, cutting off EN for the perspective 
width. Raise the perpendiculars EM, LK, 
and NO, for the. three angles of the house. 
Lay the height of the building upon the corner 
that comes to the ground-line, as EM, and 
draw MK and MO ! to their several vanishing- 
points. Also lay all the heights of the doors 
and windows, and other divisions, upon EM, 
and draw them to the vanishing-points A and 
B. To lay down the widths of the doors and 
windows, put their actual widths upon CE 
and draw from them to the distance-point l ? 
