Elements of descriptive geometry, with applications to isometric projection and othe forms of one-plane projection; a text-book for colleges and ingineering schools by O. E. Randall.

208

DESCRIPTIVE GEOMETRY

The cabinet projection of parallel straight lines which are oblique
to the plane of projection will, in length, have a constant ratio to
their original length.
451. Problem 312. To find the
- - -,- f cabinet projection of a cube one
F,-'y^ / — "/ of whose faces lies in the plane
7K ' ^ ". / of projection.
ia I b, In Fig. 189, which is a picto| - — / rial drawing, let a'-b'-d'-e'-F
represent the cube with the
e't — d' Aface a'-b'-d'-e' in V.
The face a'-b'-d'-e' is its own
projection. Through d' draw
FIG. 189 d'-k' in any direction whatever.
Make d'-k' equal to the edge of the cube. The line d'-k' is the
cabinet projection of d'-K, since d'-K is perpendicular to V and
since the projecting lines are inclined 45 degrees to the plane
of projection.
Through b' draw b'-g' paral- Ws
lel to d'-k' and make b'-g' equal b'
to the edge of the cube. The
line b-g1 is the cabinet projec- e l d'
tion of b'-G. F. 190
In the same way a'-f' is the
cabinet projection of a'-F, and a'-f-g'-k'-d'-e' is the cabinet
projection of the cube.
Fig. 190 represents the cabinet projection of a solid whose face
fy a'-b'-d'-e' is in V, and whose remaining faces are
a'/ g' either parallel or perpendicular to V.
The distances a'-f, b-k', a'-l', l'-rz, l'-n', m'-o',
o'-p', etc., are all made equal to the distances
' which they represent.
et _ d / ~452. Pseudo-Perspective. If the projecting lines
FIG. 191 of oblique projection make a greater angle than
45 degrees with the plane of projection, the oblique projection of
a straight line perpendicular to the plane of projection will be
shorter than the line itself.