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.

130

DESCRIPTIVE GEOMETRY

points just found will, by analysis, be parallel to the required plane.
The horizontal trace of the required plane, then, must be parallel
to U-u, and must also be tangent to the circular base on H whose
center is a,. Therefore draw the horizontal trace S-s, under these
conditions, and through S draw the vertical trace S-s' parallel to
U-u'.
The element of tangency may be located by drawing through L,
the point of tangency on the base, a straight line parallel to the
axis.
Since another straight line can be drawn parallel to U-u, and
tangent to the circle whose center is a,, another plane answering
the conditions of the probs / lem may be constructed.
i\ / // Check. Through some
/ \\/ // point on the element of, \. \/ / / // / tangency draw a straight
\x\ >daf / line parallel to Ai-N and
':~^',,. _ ': Hnote whether it pierces H
[ - \ /1 K,s and V in the traces
G_{k' i; r s, \ already located.
-X\:: / / CASE 2. When the
o', \i f \9 ~/^ plane of the base of the
/ '"'// / jV/ cylinder is perpendicular;bk /.' \f,' to V bt oblique to H.
7-m',,a': /j. Am'x '_, Construction. In Fig.
126 let A-B represent the
axis of the cylinder and
~s "^-.71' e -let M-N represent the
FIG. 126 given line.
Through any point D
of the given line M-N draw D-E parallel to the axis A-B. The
plane of the two lines M-N and D-E is parallel to the required
plane, D-E pierces the plane of the base of the cylinder at E,
and M-N pierces the same plane at F. The line E-F is the intersection of the auxiliary plane with the plane of the base of the
cylinder, and must be parallel to the intersection of the required
plane with the plane of the base.