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.

168

DESCRIPTIVE GEOMETRY

perpendicular to K-L and equal in length to the rectification of
the true size of the right section of the surface made by the plane
S, represents the development of this section.
The points L, B, X, E, etc., of Fig. 153 will, in Fig. 154, take the
positions L, B, X, E, etc., where the distances L-B, L-X, L-E, etc.,
are made equal to the rectified arcs 1H-bH, 1H-bI-xH, tH-bH-xH-eH,
etc., of Fig. 153.
The elements through the points L, B, E, N, etc., Fig. 153, will
in development, since they are perpendicular to the plane of the
section, take the positions L-K, B-A, E-D, etc., Fig. 154.
The points K, A, D, etc., Fig. 153, which are situated upon the
elements just named and also situated in the base of the surface,
will in development take the positions K, A, D, etc., Fig. 154,
where the distances L-K, B-A, E-D, etc., are made equal to the
actual distances of the same name in Fig. 153.
The development of the curve of the base of the surface is then
K-A-D-J~I-K', Fig. 154.
The development of that portion of the surface of the cylinder
between H and the plane S is the surface K-A-D-K'-L'-L,
Fig. 154.
The tangent r,-k,, tangent to the base of the cylinder at the
point k,, Fig. 153, will in development take the position R-K,
Fig. 154, where L-R is made equal to 1,-r, of Fig. 153.
382. Problem 254. Given an oblique cylinder with its axis in a
profile plane, and given a cutting 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, to find the true size of the
intersection, and to develop the surface of the cylinder.
383. Problem 255. Given a right circular cylinder with its axis
parallel to G-L, and given a cutting plane oblique to I and V;
required to find the intersection, to find the true size of the intersection, and to develop the surface of the cylinder.
384. Problem 256. Given an oblique cylinder and a cutting plane
oblique to the elements of the cylinder; required to find the intersection, to draw a rectilinear tangent to the curve of intersection, to find
the true size of the intersection, and to develop the surface of the
cylinder.