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.

160

DESCRIPTIVE GEOMETRY

Since the plane of the base of the prism is perpendicular to the
edges of the prism, the straight line A-B-D-A', where A-B, B-D,
and D-A' are made equal respectively to a,-b,, b,-d,, and d,-a, of
Fig. 147, may represent the development of the base of the surface.
The edges of the prism will, in development, take the positions
A-E, B-F, D-G, and A'-E', all perpendicular to A-A' and all
equal to the altitude of the prism.
The rectangle A-A'-E'-E (Fig. 148) represents the developed
prism.
The vertices of the triangle of intersection, X-Y-Z of Fig. 147,
will in development take the positions X, Y, Z, and X' (Fig. 148)
where A-X, B- Y D-Z, and A'-X' are made equal respectively to
a'-x', b'-y', d'-z', and a'-x' of Fig. 147. The line X-Y-Z-X' of
Fig. 148 represents the line of intersection in development.
The plane surface E-X-Y-Z-X'-E'-E (Fig. 148) is the templet or pattern of that portion of the surface of the prism below
the plane S, and might be used in the construction of a duplicate
prism to take the place of that portion of the prism now there.
370. Problem 242. Given a triangular prism whose edges are
oblique to H and V, and given a cutting plane perpendicular to the
edges of the prism; required to find the intersection, the true size of
this intersection, and the development of the surface of the prism.
NOTE. In developing this surface use the cutting plane as a basal plane.
371. Problem 243. Given a square prism whose edges are parallel
to G-L, and given a cutting plane oblique to H and V; required to
find the intersection, the true size of this intersection, and the development of the surface of the prism.
NOTE. In developing this surface use an auxiliary profile plane as a basal
plane.
372. Problem 244. Given an hexagonal prism whose edges are
oblique to H and V, and given a cutting plane parallel to H; required
to find the intersection, the true size of this intersection, and the development of the surface of the prism.
NOTE. In developing this surface use an auxiliary cutting plane perpendicular to the edges of the prism, as a basal plane.