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

131
aEL

The intersection of the required plane with the plane of the
base must also be tangent to the curve of the base. Therefore
k-g,-l,, drawn parallel to e,-f, and tangent to the circle whose
center is a,, is the horizontal projection, and k'-g'-l' is the vertical
projection of the intersection of the required plane with the plane
of the base. K-G-L, which is a line of the required plane, intersects H at k, and intersects V at 1', points respectively in the horizontal and vertical traces of the required plane.
Through G draw the element of tangency G-0, another line of
the required plane, and produce it to pierce H at o, and to pierce
Vatp'. The two required pI
traces S-o,-k,-s, and S-l'- S kr- s,
p'-s' may now be drawn. U — d _\ _..
Since another straight \\
line can be drawn parallel - -
to e,-f, and tangent to the a,: -CH
circle whose center is a,,
another plane answering ' ' L
the conditions of the prob- i'a / n;_
lem may be constructed. __
Check. Through some _
point of the element of g "' - u
tangency draw a straight
line parallel to the given
line M-N, and note FIG. 127
whether it intersects H and V in the traces now located.
CASE 3. When the cylinder is one of revolution with its axis parallel to G-L.
Construction. In Fig. 127 let A-B represent the axis of the
cylinder and let M-iN represent the given line.
Since the axis of the cylinder is parallel to G-L, the traces of
the required plane will also be parallel to G-L.
Through M-N draw the plane U parallel to the axis A-B. This
auxiliary plane must be parallel to the required plane.
Draw a profile plane P cutting the cylinder in the circle
whose center is C, and cutting the auxiliary plane U in the line
F-G. The intersection of the required plane by the profile