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.

8

DESCRIPTIVE GEOMETEY

After the revolution of the plane V into coincidence with if
the projections will again be expressed as shown in Fig. 3, where
that portion of the plane of the paper back of G-L, regarding the
plane of the paper as horizontal, represents both that portion of
H behind V and that portion of V above H, and where that portion
of the plane of the paper in front of G-L represents both that portion of H in front of V and that
To~
portion of V below I-.
ir", It will be observed that whether
we revolve f into coincidence with
Gi LV or whether we revolve V into coincidence with H the result will be
"pti the same. When working on the
blackboard, where the surface is
usually vertical, the former method. ' ll will be found convenient. When
Fin. 4
working on the drawing board, where
the surface is usually horizontal, the latter method will be found
more natural.
Again referring to Fig. 1, let us first project the four points
M, N, 0, and P upon H alone. As the plane V is perpendicular
to H it will in this projection appear as a straight line coincident
with G-L, and the four projections will appear as shown in Fig. 4,
where that portion of the plane of m
the paper back of G-L represents If n'
back of V, and where that portion of
the plane of the paper in front of G-L G,! L
represents H in front of V. tot
Now project the four points upon
V alone. The plane H in this projec- p
tion will appear as a straight line FIG. 5
coincident with G-L, and the four projections will appear as shown
in Fig. 5, where that portion of the plane of the paper above G-L
represents V above H, and where that portion of the plane of the
paper below G-L represents V below H.
Now if we place Fig. 5 upon Fig. 4 in such a way that the
ground line of one shall coincide with the ground line of the