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

whose vertical projection coincides with the vertical projection of
the hemisphere. This plane will locate the points of the curve
whose vertical projections fall on the vertical projection of the
hemisphere.
In the same way other planes may be passed and a sufficient
number of points may be determined to locate the curve of
intersection.
When projecting on H, if we regard the hemisphere as hollow,
the whole curve will be visible.
When projecting on V, that portion of the curve which lies on
the front portions of both surfaces and between extreme elements
will be visible.
CASE 2. To draw a rectilinear tangent to the curve of intersection.
A rectilinear tangent to the curve of intersection at any point
will be the intersection of two planes, one of which is tangent to
the hemisphere at the given point and the other tangent to the
cone at the same point.
421. Problem 290. To develop an oblique cone.
Analysis. The intersection of the surface of any cone by the
surface of a sphere whose center is at the vertex of the cone is a
curve whose points are all equidistant from the vertex of the cone,
because the curve lies on the surface of the sphere as well as on
the surface of the cone.
For this reason, in the development of the cone, this particular
curve of intersection will roll out into the arc of a circle whose
center is the vertex of the cone and whose radius is equal to the
radius of the sphere.
If upon this arc, starting from any point, we lay off successively
the actual arc distances between the points in which the elements
of the cone cut the curve of intersection before development, and
if we connect these points of division and the center of the arc by
straight lines, these straight lines will represent the elements of
the cone in development.
We may now use these elements to determine points in the
development of other curves on the surface of the cone.
Construction. Let it be required to develop the oblique cone
given in Fig. 163. The intersection of the surface of the cone by