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

CHAPTER IX
COORDINATE GEOMETRY
THE methods and ideas of coordinate geometry have already been employed in the
previous chapters. It is now time for us to
consider them more closely for their own
sake; and in doing so we shall strengthen our
hold on other ideas to which we have attained.
In the present and succeeding chapters we
will go back to the idea of the positive and
negative real numbers and will ignore the
imaginaries which were introduced in the last
two chapters.
We have been perpetually using the idea
that, by taking two axes, XOX' and YOY',
in a plane, any point P in that plane can be
determined in position by a pair of positive
or negative numbers x and y, where (cf.
fig. 13) x is the length OM and y is the length
PM. This conception, simple as it looks, is
the main idea of the great subject of coordinate geometry. Its discovery marks a
momentous epoch in the history of mathematical thought. It is due (as has been
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