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

116 INTRODUCTION TO MATHEMATICS
Again, coordinate geometry illustrates
another feature of mathematics which has
already been pointed out, namely, that mathematical sciences as they develop dovetail into
each other, and share the same ideas in common. It is not too much to say that the
various branches of mathematics undergo a
perpetual process of generalization, and that
as they become generalized, they coalesce.
Here again the reason springs from the very
nature of the science, its generality, that is
to say, from the fact that the science deals
with the general truths which apply to all
things in virtue of their very existence as
things. In this connection the interest of coordinate geometry lies in the fact that it
relates together geometry, which started as
the science of space, and algebra, which has
its origin in the science of number.
Let us now recall the main ideas of the two
sciences, and then see how they are related
by Descartes' method of coordinates. Take
algebra in the first place. We will not trouble
ourselves about the imaginaries and will
think merely of the real numbers with positive or negative signs. The fundamental idea
is that of any number, the variable number,
which is denoted by a letter and not by any
definite numeral. We then proceed to the
consideration of correlations between variables. For example, if x and y are two vari