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.

CHAPTER XIII

DETERMINATION OF PLANES TANGENT TO SURFACES
OF SINGLE CURVATURE
301. General Instructions. Note carefully the conditions imposed
by the problem; then by an application of the principles already
established with reference to tangency, determine at least two
straight lines of the required
/s, // plane. The points in which
/ J / these lines intersect H and,/,?fb / 7 V will be points in the horizontal and vertical traces of
the required plane.
302. Problem 178. To
\> a;/' aL_ draw a plane tangent to a
Se, ^\XR\ \ ^cylinder at a point on the
surface.
Analysis. Since the surface is of single curvature,
the rectilinear element of the
surface through the assumed
FI'. 119
Fiu. 119 ~point is the element of tangency and must be a line of the required plane (see Section 226).
Since the required plane will be tangent to the surface all along
this element of tangency, a straight line tangent to the surface at
any point on this element will be a line of the required plane (see
Section 226).
CASE 1. When the base of the cylinder is a circle on H.
Construction. In Fig. 119 let A-B represent the axis of the
cylinder, and let 0, assumed as in Section 234, represent the point
on the surface.
According to analysis the element 0-D through O is a line of
the required plane. This element pierces H at d1 and pierces V at
122