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

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309. Problem 185. Given a cylinder whose axis is oblique to H and
V, the plane of whose base is perpendicular to V but oblique to H,
and the horizontal projection of whose base is a circle; required to
assume a point without the surface and to draw a plane through this
point tangent to the cylinder.
310. Problem 186. Given a cylinder whose axis is oblique to H
and V and whose base is a circle in a plane parallel to V and in
front of it; required to assume a point without the surface and to
draw through this point a plane tangent to the cylinder.
311. Problem 187. Given a cylinder whose axis is [A = - 4, 0,
- 4; B = - 4, 6, 4] and whose base on V is a circle of 3-unit radius;
also given the point 0 = 2, 4, 2; required to draw through the point
a plane tangent to the cylinder.
312. Problem 188. To draw a plane tangent to a cylinder and
parallel to a given straight line.
Analysis. Since the required plane must contain an element of
the cylinder and must be parallel to the given line, the required
plane will be parallel to
any plane which is paral- \
lel both to the axis of the
cylinder and to the given.
line. Therefore, through
the given line pass a plane
parallel to the axis of the d \
cylinder and draw the re- i a ' ' L
quired plane tangent to// G q
the cylinder and parallel /i / /
to this plane.
CASE 1. When the base
of the cylinder is a circle
on H.
Construction. In Fig. F.
FIG. 125
125 let A-B represent
the axis of the cylinder and let M-N represent the given line.
Through any point D of M-N draw D-E parallel to A-B.
D-E pierces H at e, and pierces V at f'; M-N pierces H at g, and
pierces Vat k'. The plane U whose traces are located by the