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.

10

DESCRIPTIVE GEOMETRY

known that the point N must be above H, that is, either in the
first quadrant or in the second quadrant, and therefore it will be
known that the point N must be in the second quadrant.
If a horizontal projection, as o,, is situated back of G-L, it will
be known that the point 0 must be back of V, that is, either in
the second quadrant or in the third quadrant; and if the corresponding vertical projection, as o', is situated below G-L, it will be
known that the point O must be below H, that is, either in the
third quadrant or in the fourth quadrant, and therefore it will be
known that the point 0 must be in the third quadrant.
If a horizontal projection, as p,, is situated in front of G-L, it
will be known that the point P must be in front of V, that is,
either in the first quadrant or in the fourth quadrant; and if the
corresponding vertical projection, as p', is situated below G-L, it
will be known that the point P must be below H, that is, either in
the third quadrant or in the fourth quadrant, and therefore it will
be known that the point P must be in the fourth quadrant.
It will be observed, from a comparison of Figs. 1, 2, and 3, that
the horizontal and vertical projections of a point, in the transformed position shown in Fig. 3, must lie in the same straight line
perpendicular to G-L.
It will be also observed that in the transformed position the
distance of the horizontal projection of a point from G-L still
indicates the distance of the point itself from V, and that the
distance of the vertical projection of a point from G-L still
indicates the distance of the point itself from H.
15. To assume a Point at Random. To assume a point at random,
assume its projections at random, provided they fall in the same
straight line perpendicular to G-L.
16. Problem 1. Determine the projections of a point situated in
the first quadrant, 2 units from H and 4 units from V.
17. Problem 2. Determine the projections of a point in the third
quadrant, 1 unit from H and 4 units from V.
18. Problem 3. Determine the projections of a point situated in H
and 3 units back of V.
19. Problem 4. Determine the projections of a point situated in
V and 5 units below If.