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.

132

DESCRIPTIVE GEOMETRY

plane must be parallel to F-G and be tangent to the circle C, since
the required plane is both parallel to the auxiliary plane and tangent to the surface of the cylinder (see Section 226).
Revolve the profile plane about its horizontal trace into H. The
circle C falls at the circle whose center is c, and the line F-G
falls atf,-g.
The line k,-lH drawn parallel to f~-gH and tangent to the circle
CH is the revolved position of the intersection of the required plane
with the profile plane. In true position K-L pierces H at k, and
pierces V at 1', points respectively in the horizontal and vertical
traces of the required plane. The two traces S-s, and S-s' may
now be drawn.
The element of tangency may be determined by drawing through
R, the point of tangency on the circle C, a straight line parallel
to the axis A-B.
Since another straight line tangent to the circle cH and parallel
to f,-gH may be drawn, another plane answering the conditions
of the problem may be constructed.
Check. Through some point on the element of tangency draw
a straight line parallel to the given line M-N, and note whether
this line pierces H and V in the traces now located.
313. Problem 189. Given a cylinder whose axis is oblique to H
and V and whose base is a circle on V; required to assume a straight
line and to draw a plane tangent to the cylinder and parallel to
the line.
314. Problem 190. Given a cylinder whose axis is oblique to H
and V, the plane of whose base is perpendicular to H but oblique to
V, and the vertical projection of whose base is a circle; required to
assume a straight line and to draw a plane tangent to the cylinder
and parallel to the line.
315. Problem 191. Given a cylinder whose axis is parallel to G-L;
required to assume a straight line in a profile plane and to draw
a plane tangent to the cylinder and parallel to the line.
316. Problem 192. Given a cylinder whose axis is oblique to H
and V and whose base is a circle in a plane parallel to H and above
it; required to assume a straight line parallel to G-L and to draw
a plane tangent to the cylinder and parallel to the line.