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

291. Problem 172. Given a sphere whose center is in the third
quadrant; required to represent the sphere and to assume a point
upon the surface.
292. Problem 173. Given a sphere whose center is in G-L;
required to represent the sphere and to assume a point upon the
surface.
293. Problem 174. Given a sphere whose center is in the second
quadrant and equidistant from H and V; required to represent the
sphere and to assume a point upon the surface.
294. Problem 175. Represent an ellipsoid of revolution and assume
a point upon the surface.
295. Problem 176. Represent a paraboloid of revolution and assume a point upon the surface.
296. Problem 177. Represent a hyperboloid of revolution and assume a point upon the surface.
297. The Hyperboloid of Revolution of One Nappe. The hyperboloid of revolution of one nappe is a warped surface of revolution
generated by the revolution of a straight line about a rectilinear
axis not in the plane of the generatrix.
To represent the hyperboloid of revolution of one nappe we must
know the relation of the generatrix to the axis. This may be
expressed by giving the distance of the generatrix from the axis
and the inclination of the generatrix to a plane perpendicular to
the axis. The distance of the generatrix from the axis will, of
course, be measured on a straight line perpendicular to the two
(see Section 199).
In Fig. 118 let A-B, assumed perpendicular to H, represent the
rectilinear axis.
When the generatrix occupies a position parallel to V, the angle
which its vertical projection makes with G-L must equal the angle
which the generatrix makes with H; and the perpendicular distance from the point in which the axis pierces H to the horizontal
projection of the generatrix must equal the distance of the generatrix from the axis (see Problem 137, Analysis 2).
Therefore through any point, as e', on the vertical projection of
the axis draw d'-e'-f', making with G-L the angle which the generatrix is to make with H. Draw d,-e,-g, parallel to G-L and at