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 SINNLE CURVATURE

123

e', the former a point in the horizontal trace and the latter a point
in the vertical trace of the required plane.
Through d, draw S-d,-s, tangent to the circular base at d,.
This is a line of the required plane, since it is tangent to a curve
of the surface at a point on 0-D. As this tangent is also in H it
is the required horizontal trace. To draw the required vertical
trace, connect S with e' and produce.
Check. Through F, any point on the element 0-D, draw F-G
parallel to s,-S. This must be a line of the required plane, since
it is drawn through a point F in the plane parallel to a line s,-S
also in the plane, and
therefore should pierce /
V in the vertical trace /
already found. \ / /
CASE 2. When the /
plane of the base of the
cylinder is oblique to H:
but perpendicular to V. g' e
Construction. In Fig. \ r /// br
120 let A-B represent
the axis of the cylinder, \ /
let the circle with center
at at represent the horizontal projection of the
base, let the straight line s
d'-a'-ce represent the FIG. 120
vertical projection of the base, and let O represent the point on
the surface.
The element of tangency O-D through O pierces H at et and
pierces V at ft, points in the required traces.
Through d, draw d,-g, tangent to the horizontal projection of
the base. The line d,-g, is the horizontal projection, and the line
d'-a'-c' is the vertical projection of a line tangent to the base of
the cylinder at the point D on the element 0-D, and therefore a
line of the required plane. D-G pierces H at g, and pierces V at k',
two more points in the required traces. The two traces S-s, and
S-s' are now located.