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.

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DESCRIPTIVE GEOMETRY

will fall at q-rpt, where p, represents the point in which this line
of intersection in true position pierces H and where Q represents
any point assumed on the line.
The points rl and u, are then the revolved positions of the two
points of tangency sought.
Through rH and tangent to the circle o, draw rH-w,. This is
the revolved position of a line of the required plane, since it is the
revolved position of a straight line tangent to the sphere at the
point at which the required plane is to be tangent. The line
R-W in true position pierces H at w, and pierces V at x', where
x,-x' is equal to x,-xH measured on a straight line, xt-xH, perpendicular to w,-x,.
Through a, and w, draw the required horizontal trace S-s,.
Through b' and x' draw the required vertical trace S-s'.
Check. The two traces should cross G-L at the same point. Or,
the two traces, S-s, and S-s', should be perpendicular respectively
to the two projections of the radius R-C.
Since the line Q-P intersects the surface of the sphere in another
point U, another plane answering the conditions of the problem
may be constructed.
343. Problem 218. Given a sphere whose center is in G-L, and
given a straight line parallel to G-L and in the third quadrant;
required to draw a plane containing the line and tangent to the sphere.
344. Problem 219. Given a sphere whose center is in G-L, and
given a straight line situated in a profile plane and in the third
quadrant; required to pass a plane through the line and tangent to
the sphere.
345. Problem 220. Given a sphere in the second quadrant equidistant from H and V, also given a straight line in the first quadrant;
required to pass a plane through the line and tangent to the sphere.