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 VII

GENERATION AND CLASSIFICATION OF LINES
203. Generation of Lines. We may regard a line as the generation resulting from the movement of a point which in the course
of the generation occupies an infinite number of consecutive positions at infinitely small distances apart.
The portion of the line generated by the point while moving
from one position to its consecutive position is called an elementary
line, and while in theory it may be regarded as having length,
practically speaking it has none.
204. Classification of Lines. If the generating point moves continuously in one direction, the line so generated is called a straight
or a right line.
If the generating point is constantly changing its direction
of movement, the line so generated is called a curved line, or a
curve.
When the generating point of a curved line confines its movement to a plane the line is called a curve of single curvature.
When the generating point of a curved line does not confine its
movement to a plane, the line is called a curve of double curvature.
205. Curves of Single and of Double Curvature. The character of
a curve, whether of single or of double curvature, will depend
upon the law which governs the motion of the generating point,
and there may be as many distinct curves as there are distinct
laws governing the motion of a point.
If the generating point moves in a plane and retains a constant
distance from a fixed point in the plane, it will generate a curve
of single curvature called the circle.
If the generating point moves in a plane and in such a way that
the sum of its distances from two fixed points in the plane is a
constant quantity, it will generate a curve of single curvature
called the ellipse.
74