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

137

required to assume a point without the surface and to draw a plane
through this point and tangent to the cone.
325. Problem 201. To draw a plane tangent to a cone and parallel
to a given straight line.
Analysis. Since the required plane must contain the vertex of
the cone, a straight line through the vertex of the cone and parallel to the given line will be a line of the required plane. A plane
containing this auxiliary line and tangent to the cone will be the
required plane.
CASE 1. When the base of the cone is a circle on H.
Construction. In Fig. 132 let A-B represent the axis of the cone
and let ll-N represent the given line.
Through the vertex of the cone draw B-D parallel to Ml-N,
piercing H at d, and piercing V at e'. Through d, and tangent to
mls ~ ~ N~,
FIG. 132
the circular base draw the required horizontal trace d,-S-s,.
Through S and e' draw the required vertical trace S-e'-s'.
The element of tangency is the straight line drawn through the
vertex of the cone and the point of tangency F on the base.
Since another straight line may be drawn through d, and tangent to the circular 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 already located.