Armengaud, Jacques Eugène; Leblanc, César Nicolas [Hrsg.]; Armengaud, Jacques Eugène [Hrsg.]; Armengaud, Charles [Hrsg.]: The engineer and machinist's drawing-book: a complete course of instruction for the practical engineer: comprising linear drawing - projections - eccentric curves - the various forms of gearing - reciprocating machinery - sketching and drawing from the machine - projection of shadows - tinting and colouring - and perspective. Illustrated by numerous engravings on wood and steel. Including select details, and complete machines. Forming a progressive series of lessons in drawing, and examples of approved construction (Glasgow, 1855)

PERSPECTIVE.

97

lines on it, a representation of the object, as seen by the
spectator, will be obtained. The transparent plane re-
presents the picture, and the problem in perspective, is as
we have said, to make a section of the pyramid or cone
of rays as the case may be, by a plane, curved, or other
surface. The figure illustrates the mode of doing this.

(Fig. 188.)

A horizontal projection of the visual rays is made, that is
to say, from the plane or horizontal projection of the
point required to be found in perspective, a line is drawn
to the position of the spectator, as A a C, and another line
from its vertical projection to the eye of the spectator, as
A a' 0. At the points of intersection of the first set of
lines with the horizontal projection of the picture, a per-
pendicular a a' is drawn, and the intersection of this with
the corresponding line from the vertical projection, gives
the point a' required.

A much better idea of the mode of operation will be
obtained from the following figures, in which the process
described is repeated geometrically.

Let O and o' (Fig. 189) be the projection of the eye,
E F e f those of the picture, and ABG, ab cdg, those of
a pyramid with quadrangular base.

Now, if from the eye a line is drawn to the points A a
of the object, we shall have for the projections of that

line, the lines AO ,a o'. The points a a, where these pro-
jections cut the projections of the picture, are evidently

the projections of the points in which the visual rays meet
the picture, and all that is required is to find the position
of that point on the picture itself. Conceive E' F' to be
the elevation of the face of the picture. To its base E' D
transfer the distances a" b", b' g", g c", c cT, and from the
points draw indefinite lines perpendicular to E' D. On
this line set up at a from the base E' D, the
height E a', in the vertical projection of the
picture, and ar will be the perspective of the
point required. Proceed in the same manner
with all the other points.

As on the problem of finding the perspec-
tive of any point the whole science of perspec-
tive rests, the student should make himself
thoroughly master of it, and although he may
not be able to perceive the direct utility of
what immediately follows, he is recommended
to study it with care and attention, so as to
understand the principles. The application
of these will be developed by and by, and
methods of abridging the labour will be
pointed out; the student will also be enabled
to devise others for himself.

In addition to the vertical and horizontal planes with
which we are familiar in the operations of projection,
several ausiliary planes are employed in perspective, and
particularly the four following :—

1. The horizontal plane A B, (Fig. 190), on which the
spectator and the objects viewed
are supposed to stand; this is
therefore generally termed the
ground ‘plane or geometrical
plane.

2. The plane C R, which has
been considered as a transparent
plane placed in front of the
spectator, on which the objects
are delineated. It is called the
plane of projection or the plane
of the picture. The intersec-
tion C D of the first and second
planes is called the line of pro-
jection, the ground line, or base
of the picture.

3. The plane E F passing horizontally through the eye
of the spectator, and cutting the plane of the picture at