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.

CHAPTER XII

REPRESENTATION OF SURFACES OF REVOLUTION
284. General Properties of Surfaces of Revolution. The intersection of a surface of revolution by a plane perpendicular to the
axis is the circumference of a circle, since from the nature of
the generation of such surfaces (see Section 223) each point of
the generatrix generates the circumference of a circle whose plane
is perpendicular to the axis.
If two surfaces of revolution have a colnmon axis, and the surfaces either intersect or are tangent to each other, their line of
intersection or of tangency will be the circumference of a circle
whose center is in the common axis and whose plane is perpendicular to the axis. For if through the axis and any point
of the line of intersection or of tangency we pass a plane, it will
cut from the two surfaces two lines which will either intersect or
be tangent at the assumed point. If now these two lines with
their point of intersection or of tangency be revolved about the
common axis, the lines will generate their respective surfaces,
and the point of intersection or of tangency, which will remain
common to the two surfaces, and therefore generate their line of
intersection or of tangency, will generate the circumference of a
circle whose center is in the axis and whose plane is perpendicular
to the axis.
Two surfaces of revolution are tangent to each other when they
are tangent to the same surface at a common point, or when planes
passed through their point of contact cut from the two surfaces
lines which are tangent to each other at the point of contact.
A plane tangent to a single curved surface of revolution at a
given point will be tangent to the surface all along the rectilinear
element passing through this point (see Section 226).
285. The Meridian Plane and the Meridian Line. Any plane containing the axis of a surface of revolution is called a meridian plane
and its intersection with the surface is called a meridian line.
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