An introduction to mathematics, by A. N. Whitehead.

120 INTRODUCTION TO MATHEMATICS
The straight line, considered as a whole,
is accordingly the root idea from which
modern geometry starts. But then other
sorts of lines occur to us, and we arrive at the
conception of the complete curve which at
every point of it exhibits some uniform characteristic, just as the straight line exhibits
at all points the characteristic of straightness. For example, there is the circle which
at all points exhibits the characteristic of
being at a given distance from its centre, and
again there is the ellipse, which is an oval
curve, such that the sum of the two distances
of any point on it from two fixed points, called
its foci, is constant for all points on the curve.
It is evident that a circle is merely a particular case of an ellipse when the two foci are
superposed in the same point; for then the
sum of the two distances is merely twice
the radius of the circle. The ancients knew
the properties of the ellipse and the circle and,
of course, considered them as wholes. For
example, Euclid never starts with mere segments (i.e., bits) of circles, which are then prolonged. He always considers the whole circle
as described. It is unfortunate that the
circle is not the true fundamental line in
geometry, so that his defective consideration
of the straight line might have been of less
consequence.
This general idea of a curve which at any