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.

THE POINT, LINE, AND PLANE

13

It will be easily seen that we shall obtain the same result if we
allow the horizontal plane of projection to remain stationary and
revolve V as directed in Section 14.
It will be observed that the two projections of the line in Fig. 8
bear the same relation to G-L as they did in Fig. 6, and therefore
reveal just as much in regard to the position of the line itself.
25. Projections of Straight Lines occupying Various Positions with
Reference to H and v. In Fig. 9, ll1-N represents a straight line
in the third quadrant perpendicular to H. The horizontal projection is a point m,, n,. The vertical projection is a straight line
mn'-n perpendicular to G-L and parallel to M-N. That portion
v. n, of
0,
O L
-----------
FIG. 9 FIG. 10
of the vertical projection included between m' and n' is equal to
the distance between 11 and N.
In the same figure O-P represents a straight line in the third
quadrant perpendicular to V. The vertical projection is a point
o', p'. The horizontal projection is a straight line o,-p, perpendicular to G-L and parallel to O-P. That portion of the horizontal
projection included between o, and p, is equal to the distance
between O and P.
Fig. 10 shows how the projections of Fig. 9 will appear after
H and V take their position of coincidence.
In Fig. 11, l1-N represents a straight line in the third quadrant,
parallel to H but oblique to V. The vertical projection m'-n' is
parallel to G-L and at the same distance below G-L that M-N is