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.

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DESCRIPTIVE GEOMETRY

An auxiliary sphere with center at D and with radius equal to
d'-f will cut the surface of the cone in the circumference of a
circle whose vertical projection is f-g' and whose horizontal projection isf,-m,-g,-n,. The same sphere will cut the surface of the
cylinder in the circumference of another circle whose vertical projection is k'-'. The circumferences of these two circles intersect in
two points vertically projected at (m', n') and horizontally projected at m, and n, respectively. M and N are two points of the
required curve of intersection, and others may be found in the
same way.
The meridian plane of the axes will cut the cone and the cylinder in those elements which, when projecting upon V, appear as
extreme elements. These elements intersect at O and P respectively, the lowest and the highest points of the curve of intersection.
When projecting on H, if we regard the inverted cone as hollow,
that portion of the curve of intersection lying on the upper surface
of the cylinder will be visible.
When projecting on V, that portion of the curve of intersection
lying on the front surface of the cylinder and on the front surface
of the cone will be visible.
CASE 2. To draw a rectilinear tangent to the curve of intersection.
The rectilinear tangent to the curve of intersection at any point
will be the intersection of two planes, one tangent to the cone
at the given point and the other tangent to the cylinder at the
same point.
By use of methods already explained we may develop both of
the given surfaces and show the character of the curve of intersection when rolled out into a plane surface.
426. Problem 295. By the process just explained find the intersection of two cylinders of revolution whose axes intersect.
427. Problem 296. By the above process find the intersection of a
cone of revolution and a sphere.
428. Problem 297. By the above process find the intersection of
two cylinders of revolution, axes intersecting, the larger horizontal
and the smaller vertical.