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.

146

DESCRIPTIVE GEOMETRY

A plane tangent to this cone along the element passing through
the given point of tangency will also be tangent to the ellipsoid
at the same point.
Construction. Let the ellipsoid be represented as in Fig. 138,
where A-B represents the long axis and where O represents the
point assumed on the surface.
Following Analysis 1, pass a meridian plane T, containing the
point O and cutting the surface in a meridian ellipse. Revolve T
about A-B as an axis until it is parallel to Y. The point O will then
be vertically projected
K? /' at o" and the meridian
e,~\ /~ ellipse will be vertically
projected in the vertical
f___-b / b'' s\ ~projection of the ellipsoid.
iV ' \ ' \. Tangent to the ellipse
G T/' ' e' \e a'-o"-lb-fi at the point o"
i,\/ /i / draw d'-o"-e" This line
1 |h/ /,~ / is the vertical projection. |,//./ of the revolved position
of a straight line D-E,
which in true position is
\di~/ / ~tangent to the surface at
d' / sOy~ 0, and therefore in the
required plane. In reFIG. 138
volved position D-E
pierces H at e,,, but in true position, since D is in the axis, it will

pierce H at e,.
Through 0 pass another auxiliary plane U perpendicular to the
axis A-B. This plane cuts the ellipsoid in a circle whose horizontal
projection is f,-o,-o,, and whose vertical projection is f'-o".
The remainder of the construction corresponds with that given
in connection with the sphere (see Section 333).
Check. Construct according to Analysis 2.
338. Problem 213. Solve the above problem by Analysis 2.
339. Problem 214. Given an ellipsoid of revolution with the long
axis perpendicular to V; required to assume a point upon the surface
and to draw a plane tangent to the surface at this point.