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 XIV

DETERMINATION OF PLANES TANGENT TO SURFACES
OF DOUBLE CURVATURE
332. General Instructions. By Section 226 straight lines which
are tangent to a surface of double curvature at a point on the surface, lie in a plane tangent to the surface at this point. Therefore through the point of tangency draw two planes cutting from
the surface two simple curved lines intersecting at the point
of tangency. Tangent to these curved lines at the point of tangency draw two straight lines which shall determine the required
plane.
When the given surface is one of revolution, it will be found
convenient to use as the cutting planes the meridian plane and a
plane perpendicular to the axis.
Sometimes an auxiliary surface may be passed tangent to the
given surface at the point of tangency; then of course a plane tangent to the auxiliary surface at the point of tangency will also be
tangent to the given surface at the point of tangency.
333. Problem 208. To draw a plane tangent to a sphere at a point
on the surface.
Analysis 1. See Section 332.
Analysis 2. Draw a plane perpendicular to the radius of the
sphere at the point of tangency.
Construction. See Fig. 137. Let C represent the sphere and let
0, assumed as in Section 287, represent the point on the surface.
By Analysis 1 draw through O a vertical meridian plane T, cutting the sphere in a great circle. Revolve T about its horizontal
trace into H. The center of the great circle will fall at,e and the
point of tangency will fall at o,. Through o, draw oH-a, tangent
to the circle c. This last line is the revolved position of a tangent
to the sphere at the point O. This tangent in true position pierces
H at a,, a point in the required horizontal trace.
144