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

122 INTRODUCTION TO MATHEMATICS
sented by the corresponding correlation
between x and y. Finally to correlations
expressible in some general algebraic form,
such as ax+by=c, there correspond loci of
some general type, whose geometrical conditions are all of the same form. We have
thus arrived at a position where we can
effect a complete interchange in ideas and
results between the two sciences. Each
science throws light on the other, and itself
gains immeasurably in power. It is impossible not to feel stirred at the thought
of the emotions of men at certain historic
moments of adventure and discoveryColumbus when he first saw the Western
shore, Pizarro when he stared at the Pacific
Ocean, Franklin when the electric spark
came from the string of his kite, Galileo
when he first turned his telescope to the
heavens. Such moments are also granted to
students in the abstract regions of thought,
and high among them must be placed the
morning when Descartes lay in bed and invented the method of coordinate geometry.
When one has once grasped the idea of
coordinate geometry, the immediate question which starts to the mind is, What sort of
loci correspond to the well-known algebraic
forms? For example, the simplest among
the general types of algebraic forms is ax+
by =c. The sort of locus which corresponds