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.

174

DESCRIPTIVE GEOMETRY

The true size of the curve of intersection is represented by,l-PFH —oH —k~.
The tangent Q-L will when revolved take the position q,-l,,
the point q, remaining stationary.
The development of an oblique cone requires knowledge of a problem not yet explained, and will be taken up later (see Section 421).
394. Problem 265. Given an oblique cone with base on V, and given
a cutting plane oblique to G-L; required to find the intersection, to
draw a rectilinear tangent to the curve of intersection, and to find
the true size of the intersection.
395. Problem 266. Given an oblique cone with axis in a profile
plane, and given an intersecting plane parallel to G-L but oblique to
H and V; required to find the intersection, to draw a rectilinear
tangent to the curve of intersection, and to find the true size of the
intersection.
396. Problem 267. Given a right circular cone with axis parallel
to G-L, and given a cutting plane oblique to G-L; required to find
the intersection, to draw a rectilinear tangent to the curve of intersection, and to find the true size of the intersection.
397. Problem 268. To find the intersection of any surface of revolution by a plane, to draw a rectilinear tangent to the curve of intersection, and to find the true size of the intersection.
CASE 1. To find the intersection.
Analysis. Pass the auxiliary planes perpendicular to the axis
(see Section 284).
Construction. Let the surface of revolution be represented as in
Fig. 158, where A-B is the axis and where S is the cutting plane.
Let T represent one of the auxiliary planes perpendicular to
A-B. This plane cuts the given surface in the circumference of
a circle whose vertical projection is d'-e' and whose horizontal
projection is d,-g,-e,-k,. This same plane intersects S in the
straight line G-K-F parallel to S-s,. G-K-F crosses the circumference D-G-EC-K at G and K, two points of the required curve
of intersection.
Pass a meridian plane U perpendicular to S-s,, cutting from
the surface a meridian curve and cutting S in a straight line
1-L which intersects the axis at M.