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.

22

DESCRIPTIVE GEOMETRY

Construction. In Fig. 33 let S-s, represent the horizontal trace
and let S-s' represent the vertical trace of a plane oblique to G-L.
Assume any point, as 3, on the horizontal trace. The point n,
is the horizontal projection of this point, and the vertical projection
must be in G-L at m'.
Assume another point, as N, anywhere in the vertical trace. The
point n' is the vertical projection of this point, and the horizontal
projection must be in G-L at n,.
Since M is a point in the horizontal trace of the plane S, it must
be a point'in the plane; and since V is a point in the vertical trace of
the plane S, it must be a point
s, in the plane. The line M-N is
therefore a line of the plane.
Principle. If through any
Gt L L point in a plane a straight line
is drawn parallel to another
straight line already in the
plane, the line so drawn is also
FIG. 33 in the plane.
Principle. If a straight line is in a plane and is parallel to H,
it will be parallel to the horizontal trace of the plane, and its
horizontal projection will be parallel to the horizontal trace of
the plane.
Principle. If a straight line is in a plane and is parallel to V, it
will be parallel to the vertical trace of the plane, and its vertical
projection will be parallel to the vertical trace of the plane.
43. To assume a Point in a Plane. First, by Section 42, assume
a straight line in the plane; then by Section 28 assume a point
upon this line.
44. Proposition 1. If a straight line is perpendicular to a plane,
its horizontal projection will be perpendicular to the horizontal trace
of the plane, and its vertical projection will be perpendicular to the
vertical trace of the plane.
Proof. Since the line is perpendicular to the given plane, the
horizontal projecting plane of the line must be perpendicular to
the given plane. The horizontal projecting plane of the line is
also perpendicular to H, and therefore since it is perpendicular