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.

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DESCRIPTIVE GEOMETRY

CASE 1. To find the intersection.
Analysis. Draw the auxiliary planes through the two vertices.
Construction. See Fig. 161. Let A-B represent the axis of the
first cone, which is right circular with base parallel to H; and let
C-D represent the axis of the second cone, whose base is a circle
with its plane perpendicular to T. The vertical trace of the plane
of the base of the second cone is S-s', and the intersection of this
plane with the plane of the base of the first cone is the line U-G- W.

FIG. 161

A straight line through the two vertices will be common to all
the auxiliary planes. Therefore through the two vertices draw
B-D and produce it to meet the plane of the base of the first cone
at E, a point common to all the lines cut from this plane by the
auxiliary planes. This line B-D pierces S, the plane of the base
of the second cone, in F, a point common to all the lines cut from
S by the auxiliary planes.
Through e, draw e,-g, to represent the horizontal projection of
the intersection of one of the auxiliary planes with the plane of