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 DOUBLE CURVATURE

151

and that E is at the same distance back of V as the center of
the sphere.
The axis of the cone D is D-C and by construction is parallel
to H. The axis of the cone E is E-C and by construction is
parallel to V.
To represent the horizontal projection of the cone D, draw
through d,, and tangent to the horizontal projection of the sphere,
the two lines d,-f, and
d,-g,.
To represent the vertical projection of the cone q
E, draw through e', and
tangent to the vertical pro- - / /
jection of the sphere, the
two lines e'-k' and e'-l'. )
The base of the coneD / \ /0 / /\
is a circle whose plane
is perpendicular to H and G --- — L
whose horizontal projection is f,-g,. The base of, li
the cone E is a circle
whose plane is perpendic-
ular to V and whose ver- /
tical projection is k'-l'.
The planes of these
bases will intersect in a
FIG. 141
straight line whose hori- FIG. 141
zontal projection will fall on f,-g, and whose vertical projection
will fall on k'-1'.
This line of intersection will pierce the surface of the sphere in
the two points in which the circumferences of the two bases intersect, and which by analysis are the points of tangency sought.
To find these points of tangency revolve the plane of the base
of the cone whose vertex is D about its horizontal trace f-g, into
H. The circular base whose center is 0 will take the position of
the circle whose center is oH, where o,-O0 is equal to the distance
of c' from G-L. The intersection of the planes of the two bases