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.

12

DESCRIPTIVE GEOMETRY

-It will be noticed that when the horizontal and vertical projections of a straight line are given, the line is in general definitely
determined, for the horizontal and vertical projecting planes determined by the projections of the line intersect in the only line which
can have its horizontal and vertical projections in these lines.
It will be also noticed that the two projections of a line determine the position of the line with reference to H and V. For
example, in Fig. 6 the vertical projection of the line shows that
the line slopes downward to the right, the horizontal projection
shows that the line approaches Vas it extends toward the right,
FIr,. 7 FIG. 8
and the two projections together show that the line slopes downward toward V to the right.
24. Representation of the Straight Line upon H and V in their
Position of Coincidence. In Fig. 7 the projections m,,-n,, and
m"-n1" are those previously found in Fig. 6, and represent a
straight line in the third quadrant.
If the plane V remains stationary and the plane HI be revolved
as previously directed, the points m" and n" will remain stationary,
while the points n,, and n,, will revolve and fall at the points m,
and n, respectively. The line in-n,, then, will represent the
horizontal projection of the line I-NV after H has been revolved,
and the result may be expressed as shown in Fig. 8.