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.

INTERSECTION OF SURFACES BY PLANES

171

etc., equal respectively to the distances of the points R, K, O, X, etc.,
on the surface of the cone, from the vertex, and trace the curve
R-K-O-X-G-N-R' through these points.
In Fig. 155 the true distance from B to N is expressed by the
distance b'-n', since the element B-L is parallel to V. The distance B-O is expressed by '-o' for the same reason.
The distance from B to any other point on the surface may be
found by revolving the cone about its axis until the element on
which the point stands is parallel to V. The vertical projection of the
required distance in this position will be equal to the distance itself.
For example, suppose it is required to find the distance B-X on
the element B-Q. After revolution the element B-Q will take the
position B-Mi, vertically projected at b'-m'. The point x' will take
the position x" and b'-x" will be the measure of -the distance B-X.
The tangent R-I of Fig. 155 will in development take the position R-I, Fig. 156, where P-I is drawn tangent to P-D-M-A-P'
at P, and where P-I is made equal to p,-i,, Fig. 155.
386. Problem 258. Given a right circular cone with axis perpendicular to H, and given an intersecting plane oblique to H and V;
required to find the intersection by passing auxiliary planes parallel
to H.
387. Problem 259. Given a right circular cone with axis perpendicular to H, and given an intersecting plane parallel to H; required
to determine the character of the intersection.
388. Problem 260. Given a right circular cone with axis perpendicular to H, and given an intersecting plane passing through the
axis; required to determine the character of the intersection.
389. Problem 261. Given a right circular cone with axis perpendicular to H, and given an intersecting plane making a smaller angle
with IH than the elements of the cone; required to determine the
character of the intersection.
390. Problem 262. Solve Problem 261 when the intersecting plane
makes the same angle with -H as the elements of the cone.
391. Problem 263. Solve Problem 261 when the intersecting plane
makes a greater angle with H than the elements of the cone.
392. Conic Sections. By an examination of the results obtained
in Problems 259 and 260 it will be observed that when the surface