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.

SURFACES OF SINGLE CURVATURE

135

given point must be a line of the required plane. The remainder
of the analysis differs little from that given in connection with
Problem 183, Section 307.
CASE 1. When the base of the cone is a circle on H.
Construction. In Fig. 130 let A-B represent the axis of the
cone, and let O represent the point without the surface.
Connect O and B by a straight line and produce it to pierce H
at d, and to pierce V at e'. Through d, draw d,-S-f,-s, tangent to
the circular base at f,.
According to analysis this is a line of the required plane, and
since it is in H, it is the required horizontal trace. Through S and
e' draw the required vertical trace S-s'.
Se\d
G a L
FIG. 130
The element B-F is the element of tangency and a line of the
required plane.
Since from the point d, another straight line may be drawn tangent to the base, another plane answering the conditions of the
problem may be constructed.
Check. Note whether the element of tangency pierces V in the
vertical trace now located.
CASE 2. When the plane of the base of the cone is perpendicular
to H but oblique to V.
Construction. In Fig. 131 let A-B represent the axis of the
cone and let 0 represent the point without the surface.