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 LINES

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354. Problem 227. Find the points in which a given straight line
intersects the surface of an oblique hexagonal pyramid.
355. Problem 228. Find the points in which a given straight line
intersects the surface of the frustum of a square pyramid.
356. Problem 229. Given a hollow square pyramid; required to
find the points in which a given straight line intersects the outer and
the inner surface of the pyramid.
357. Problem 230. To find the points in which a given straight
line intersects the surface of a cylinder.
Analysis. Pass the auxiliary plane through the line and parallel
to the elements of the cylinder, or, what is the same thing, parallel
to the axis of the cylinder.
Construction. Let the cylinder
be represented as in Fig. 144,
and let M-N represent the given e,
line. Produce M-N to pierce H ' X
at d,. Through N, any point on:
M-N, draw N-E parallel to the G ' ' er
axis of the cylinder and produce i /
it to pierce H at e,. The straight u
line U-d,-e,-u,, determined by b A
the points d, and e,, is the hori-
zontal trace of the auxiliary
plane. FIG. 144
plane.
This plane U cuts the cylinder in two elements, F-X and
G-Y, which are intersected by M-N at X and Y, the two points
required.
358. Problem 231. Given a right circular cylinder in the third
quadrant with axis parallel to G-L; required to find the points in
which a given straight line intersects the surface of the cylinder.
359. Problem 232. Given a right circular cylinder in the third
quadrant with axis perpendicular to H; required to find the
points in which a given straight line intersects the surface of the
cylinder.
360. Problem 233. Given a hollow cylinder; required to find the
points in which a given straight line intersects the inner and the
outer surface of the cylinder.