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

If the generatrix is the curve of a hyperbola and the axis is one
of the axes of the hyperbola, the surface generated is that of the
hyperboloid of revolution.
225. Representation of Surfaces. Surfaces which exist within
definite limitations are usually represented by projecting upon
H and V the limiting lines as seen from the two principal standpoints of projection. Other surfaces are too irregular in their
formation to be represented in this way, and all that is attempted
is to represent by projection a sufficient number of the elements of
the surface to reveal the character of some small portion of the
surface under consideration.
226. Tangents to Surfaces. A straight line is tangent to a surface at a given point when it is tangent to a line of the surface at
that point.
A plane is tangent to a surface at a given point when it contains all the rectilinear tangents to the surface at that point. In
other words, if a plane is tangent to a surface, and any cutting
plane be passed through the point of tangency, the cutting plane
will cut from the surface a line, and from the tangent plane a
straight line, tangent to the first line at the point of tangency.
Therefore, to draw a plane tangent to a surface at a given point,
draw two rectilinear tangents to the surface at this point and
determine their plane.
If the surface has rectilinear elements, the tangent plane must
contain the rectilinear element passing through the point of tangency, since the rectilinear tangent to a rectilinear element is the
element itself. This element is the element of tangency.
If the surface is of single curvature, we may say that a plane is
tangent to the surface at a given point when it represents the
plane in which the generatrix is moving at the instant in which it
passes through the point of tangency.
For this reason we may say that a plane is tangent to a single
curved surface at a given point when it contains both the element
through the point of tangency and its consecutive one. If through
the element containing the point of tangency we pass a secant
plane, it will cut the surface in two distinct lines, one of which is
the element through the point of tangency and the other another