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.

INTERSECTI)N OF SURFACES BY PLANES

169

385. Problem 257. To find the intersection of a right circular cone
by an oblique plane, to draw a rectilinear tangent to the curve of
intersection, to find the true size of the intersection, and to develop
the surface of the cone.
CASE 1. To find the intersection.
Analysis 1. Pass the auxiliary planes through the axis of
the cone.
Analysis 2. Pass the auxiliary planes perpendicular to the axis.
B
FIG. 156:i,
\ \TK f TZ L Construction. Let
the cone be represented as
in Fig. 155, and let S rep'\///\ \/ resent the cutting plane.
/7 j\\\ in Following Analysis 1, let
LL4n. ^^ ^T represent one of the auxl' a p' iliary planes. This plane
w|I \\ intersects the surface of, the cone in two elements,
FIG. 155 t'x' B-A and B-D, and intersects S in the line E-F.
E-F crosses B-A and B-D at G and K respectively, two points in
the required curve of intersection.
Another auxiliary plane U parallel to V will intersect the surface in the two extreme elements B-L and B-iM and will locate
the two points N and 0.
Another auxiliary plane TV, parallel to S-s,, will intersect the
surface of the cone in the two elements B-P and B-Q and will
locate the two points R and X.