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.

134 DESCRIPTIVE GEOMETRY
CASE 2. When the plane f the base of the cone is perpenldicular
to V but oblique to H.
Construction. In Fig. 129 let A-B represent the axis of the cone,
let the circle whose center is a, represent the horizontal projection
of the base, let the straight line g'-k'-a'-d' represent the vertical
projection of the plane of the base, and let O represent the point
on the surface.
The element B-O-D through O pierces H at e, and pierces V at
f', 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 d'-g' is
the vertical projection of a line tangent to the base of the cone at
a point D on the element B-O-D, and therefore a line of the required
plane. D-G pierces H at g, and
b, s, pierces V at k', two more points
bf" y~, ein the required traces.
(I C(4//9. Check. Same as in Case 1.
\ic \ i b, 318. Problem 194. Given a
G o S b2 -/ '.cone whose axis is oblique to H, i: ~> -'//,L and V and whose base is a circle
on V; required to draw a plane
7\\ // / tangent to the cone at a point on
\ i:/ / /the surface.
~\ /^/~ 319. Problem 195. Given a
\\ / cone whose axis is oblique to H
fJ~\ ~ and V and whose base is in a
FIG. 129 plane perpendicular to H but
FIG 129
oblique to VI; required to draw
a plane tangent to the cone at a point on the surface.
320. Problem 196. Given a cone 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 draw a plane tangent to the cone at a point on the
surface.
321. Problem 197. To draw a plane tangent to a cone and through
a point without the surface.
Analysis. Since the required plane must contain the vertex of
the cone, a straight line through the vertex of the cone and the