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.

CHAPTER XVI

INTERSECTION OF SURFACES BY PLANES
367. General Instructions. Pass a series of auxiliary planes
intersecting both the given plane and the given surface in lines.
The points in which these two sets of lines intersect will be
common to both the plane and the surface, and will therefore
be points in their line of intersection.
Pass the auxiliary planes in such a way as not only to cut from
the given surface the simplest lines, but also in such a way as to
simplify the work of construction.
If the given surface is that of a prism or of a pyramid, it will be
found convenient to pass the auxiliary planes through the edges.
If the given surface is one of revolution, it will be found convenient to pass the auxiliary planes perpendicular to the axis of
revolution, since such planes will cut circumferences of circles from
the surface.
368. Problem 240. To find the line in which one plane intersects
another (see Section 146).
369. Problem 241. To find the intersection of a triangular prism
by a plane, to find the true size of the intersection, and to develop
the surface of the prism.
CASE 1. To find the intersection.
Analysis. Pass the auxiliary planes through the edges of the
prism.
Construction. In Fig. 147 let A-B-D ---E-F-G represent a prism
with edges perpendicular to i, and let S represent the cutting
plane.
The plane of the face A-D-G-E, which is the plane U, contains
the two edges A-E and D-G. This plane, which may be used as
an auxiliary plane, cuts S in the line K-L, crossing A-E and D-G
at X and Z respectively. X-Z is the line of intersection between
the plane S and the face A-D-G-E.
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