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.

166

DESCRIPTIVE GEOMETRY

381. Problem 253. To find the intersection of an oblique cylinder
by any plane, to draw a rectilinear tangent to the curve of intersection, to show the true size of the intersection, and to develop the
surface of the cylinder.
CASE 1. To find the intersection.
Analysis. Pass the auxiliary cutting planes parallel to the axis
of the cylinder and perpendicular to H.
Construction. Let the cylinder be represented as in Fig. 153,
and let X, in this case assumed perpendicular to the elements of
the cylinder, represent the given cutting plane.
Pass an auxiliary plane T through the axis and perpendicular
to H. This plane cuts the cylinder in two elements, A-B and
D-E, and intersects the plane S in F-G. F-G crosses A-B and
D-E at B and E respectively, two points in the required curve
of intersection.
Owing to the position of the plane T with reference to S-s,,
the points B and E will be respectively the lowest and the highest
points of the curve of intersection.
Pass another auxiliary plane U parallel to T. This plane cuts
the cylinder in two elements, K-L and M-N, and intersects the
plane S in O-P, where O-P is necessarily parallel to F-G. O-P
crosses K-L and M-N at L and N respectively, two more points
in the required curve.
By passing other auxiliary planes parallel to T we may obtain
a sufficient number of points to locate the required curve.
This method of construction applies equally well when the
given plane S is oblique to the elements of the cylinder.
CASE 2. To draw a rectilinear tangent to the curve of intersection.
Analysis. See Problem 249, Case 2.
Construction. See Fig. 153. Let it be required to draw a rectilinear tangent to the curve of intersection at the point L. Draw
the plane W tangent to the cylinder along the element K-L (see
Section 302). The intersection of the planes W and S is Q-L-R,
the required tangent.
CASE 3. To find the true size of the intersection.
Analysis and Construction. See Fig. 153. Revolve the plane S,
which is the plane of the curve, about S-s, into H. Any point, as B,