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.

154

DESCRIPTIVE GEOMETRY

Construction. Let the prism be assumed with its edges perpendicular to H, as shown in Fig. 142, and let JM-N represent the
given line.
The auxiliary plane is taken perpendicular to H and intersects
the surface in two lines, A-B and D-E, each parallel to the edges.
These lines are crossed by M-nr at X
and Y, the two points required.
/, B ~ 350. Problem 223. Find the points in:G/:::face of a prism whose edges are oblique
//m0b wc to H and V.
351. Problem 224. Find the points in
which a straight line intersects the surm1, I I l face of an hexagonal prism.
eb eL 352. Problem 225. Given a hollow
square prism; required to find the points
FIG. 142 in which a given straight line intersects
the outer and the inner surface of the prism.
353. Problem 226. To find the points in which a given straight line
intersects the surface of a square
pyramid.
Analysis. Pass the auxiliary
plane through the line and the
vertex of the pyramid.
Construction. Let the pyramid
G L
be represented as in Fig. 143, i a
and let il-NV represent the given i
line. Produce M-N to meet the /\
plane of the base of the pyramid ^
at B. Through the vertex A and
any point D of the line M-N f i \
draw a straight line and produce. 1
FIG. 143
it to meet the plane of the base
at E. The straight line through B and E is the intersection of
the auxiliary plane and the plane of the base of the pyramid.
This auxiliary plane intersects the pyramid in two lines, A-F and
A-G. M-N crosses these lines at X and Y, the points required.