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.

SINGLE CURVED SURFACES

97

The generating line is called the generatrix, the curved line is
called the directrix, the fixed point is called the vertex, and the
various positions occupied by the generatrix are called rectilinear
elements of the surface.
It is evident from the nature of the generation of the conical
surface that there will be generated simultaneously, on opposite
sides of the vertex, two equivalent portions of the surface. These
portions of the surface are called nappes of the surface.
It is also evident that if the vertex be removed to an infinite
distance from the directrix, the conical surface will become cylindrical.
The intersection of a conical surface by any plane not containing the vertex is called a section, or base, of the surface. When
this plane is taken perpendicular to the axis* the section is called
a right section, and conical surfaces are classified according to
the nature of this section as circular, elliptical, parabolic, hyperbolic, etc.
The section of a conical surface made by the plane H will often
serve as a convenient base.
A plane containing the vertex of a conical surface and intersecting the surface will cut the surface in elements, since all the
elements of such surfaces pass through the
vertex.
If the base of a conical surface is a closed f Gb g,
curve, like a circle or an ellipse, the space
inclosed by the conical surface is called a G ' L
cone, and the straight line connecting the! '
center of the base with the vertex is called
the axis of the cone.
240. To represent the Cone. A cone is usu- /
ally represented by projecting the vertex, a / \\
base, and the extreme or limiting elements. g'
CASE 1. To represent a circular cone whose FIG. 104
axis is perpendicular to H and whose base is a right section. See
Fig. 104, in which A-B represents the axis of the cone and in which
F-D-G-E represents the circular base.
* For definition of axis, see few lines below.