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.

SURFACES OF DOUBLE CURVATURE

145

Through O pass another plane U parallel to H. This plane cuts
the sphere in a small circle whose horizontal projection is 0,-o0-b,
and whose vertical projection is o"-b'. Through 0 draw O-D tangent to the small circle at O. 0-D is another line of the required
plane, and pierces V at d',
a point in the required
vertical trace.
Since O-D is a line of a, /
the required plane and par-
allel to H, its horizontal / /
projection o,-d, must be
parallel to the required hor- G S/ / -T.
izontal trace (see Section
42). Therefore through a,
and parallel to o,-d, draw u'
the required horizontal U d\ '
trace S-s,. Through Sand
d' draw the required ver-
tical trace S-s'. 137
Check. The traces of the required plane should be perpendicular
to the projections of the radius C-O.
334. Problem 209. Solve the above problem by Analysis 2.
335. Problem 210. Given a sphere with center in G-L; required
to assume a point upon the surface and to pass a plane tangent to the
surface at this point.
336. Problem 211. Given a sphere in the second quadrant with its
center equidistant from H and V; required to assume a point upon
the surface and to pass a plane tangent to the surface at this point.
337. Problem 212. To draw a plane tangent to an ellipsoid of
revolution at a point on the surface.
Analysis 1. See Section 332.
Analysis 2. Determine the meridian curve of the surface which
contains the given point, and draw a rectilinear tangent to the
curve at this point. If this tangent is revolved about the axis of
the ellipsoid as an axis, it will generate a conical surface which
will be tangent to the surface of the ellipsoid in the circumference
of a circle containing the point of tangency (see Section 284).