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

140 INTRODUCTION TO MATHEMATICS
the consideration of sets (or pencils, as they
are called) of lines passing through a common
point (the vertex of the "pencil"). Now
(cf. fig. 19) if A, B, C, D, be any four fixed
points on a conic section and P be a variable
point on the curve, the pencil of lines PA,
A_ P
Fig. 19.
PB, PC, and PD, has a special property,
known as the constancy of its cross ratio. It
will suffice here to say that cross ratio is a
fundamental idea in projective geometry.
For projective geometry this is really the
definition of the curves, or some analogous
property which is really equivalent to it. It