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.

CLASSIFICATION OF SURFACES

85

of its consecutive positions lie in the same plane, the surface is a
cylindrical surface.
When the rectilinear generatrix moves in such a way that all its
positions pass through a common point and no three of its consecutive positions lie in the same plane, the surface is a conical
surface.
When the rectilinear generatrix moves in such a way that consecutive positions intersect two and two and at the same time in
such a way that no three consecutive positions lie in the same
plane, the surface is a convolute.
223. Surfaces of Revolution. Surfaces of revolution are those
which may be generated by the revolution of a line about a
straight line as an axis.
If the generatrix is a straight line and is parallel to the axis,
the surface is a cylindrical surface of revolution,- a single curved
surface.
If the generatrix is a straight line and intersects the axis
obliquely, the surface is a conical surface of revolution, - a single
curved surface.
If the generatrix is a straight line and does not lie in the same
plane with the axis, the surface is a warped surface of revolution,
since from the nature of the generation consecutive elements of
the surface cannot lie in the same plane.
If the generatrix is a curved line, as it will be in all cases save
those mentioned above, the surface will be one of double curvature, or a double curved surface of revolution.
224. Double Curved Surfaces of Revolution. If the generatrix of
a double curved surface of revolution is the circumference of a
circle and the axis is a diameter of the circle, the surface generated
is that of a sphere.
If the generatrix is the curve of an ellipse and the axis is one of
the axes of the ellipse, the surface generated is that of the ellipsoid
of revolution. The ellipsoid of revolution is called a prolate or an
oblate spheroid according as the long or the short axis is used.
If the generatrix is the curve of a parabola and the axis is the
axis of the parabola, the surface generated is that of the paraboloid
of revolution.