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

Through et draw any horizontal trace, as S-s,, cutting the base
of the cylinder. Through S and ft draw the vertical trace S-s'.
S is one of the auxiliary planes and cuts the cylinder in two
elements, G-K-L and M-~N-O; and cuts the cone in two elements,
P-D and Q-D.
The element G-K-L of the cylinder crosses the two elements
of the cone at K and L, two points of the required curve of
intersection. The element JM-l-O of the cylinder crosses the
two elements of the cone at N and 0, two more points of the
curve.
In this way we may pass any number of auxiliary planes and
obtain any number of points on the required curve of intersection.
If it is desired to obtain a point of the curve upon any particular
element of the cylinder or of the cone, we have but to draw the
traces of the auxiliary plane through the points in which this
element pierces the corresponding planes of projection.
It will be noticed that since the horizontal and vertical projections of the curve of intersection are found independently, the
accuracy of the work may be tested by noting whether the horizontal and vertical projections of the several points of the curve
lie in straight lines perpendicular to G-L.
When projecting on H, that portion of the curve which lies upon
the upper surface of the cylinder and also upon the upper surface
of the cone, and between extreme elements, will be visible and
should be so represented.
When projecting on V, that portion of the curve which lies
upon the front surface of the cylinder and also upon the front surface of the cone, and between extreme elements, will be visible
and should be so represented.
CASE 2. To draw a rectilinear tangent to the curve of intersection
at a given point.
Analysis. Since the curve of intersection lies upon both surfaces, the required tangent must lie both in a plane tangent to the
cone at the given point, and in a plane tangent to the cylinder at
the same point. Therefore draw two planes, one tangent to the
cylinder and the other tangent to the cone at the given point. The
intersection of these two planes is the required tangent.