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

134 INTRODUCTION TO MATHEMATICS
a plane-which yields three cases, so in any
"plane" definition there also should be one
uniform method of procedure which falls into
three cases. Their shapes when drawn on
their planes are those of the curved lines in
the three figures 16, 17, and 18. The points
A and A' in the figures are called the verPN r,' H,
Fig. 18.'
tices and the line AA' the major axis. It
will be noted that a parabola (cf. fig. 17) has
only one vertex. Apollonius proved * that
the ratio of PM to AM.MA' (i.e. PM-1
AMMA
remains constant both for the ellipse and the
hyperbola (figs. 16 and 18), and that the ratio
* Cf. Ball, loc. cit., for this account of Apollonius and
Pappus.