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

COORDINATE GEOMETRY 121
point of it exhibits some uniform property is
expressed in geometry by the term "locus."
A locus is the curve (or surface, if we do not
confine ourselves to a plane) formed by points,
all of which possess some given property.
To every property in relation to each other
which points can have, there corresponds
some locus, which consists of all the points
possessing the property. In investigating
the properties of a locus considered as a
whole, we consider any point or points on
the locus. Thus in geometry we again meet
with the fundamental idea of the variable.
Furthermore, in classifying loci under such
headings as straight lines, circles, ellipses,
etc., we again find the idea of form.
Accordingly, as in algebra we are concerned with variable numbers, correlations
between variable numbers, and the classification of correlations into types by the idea of
algebraic form; so in geometry we are concerned with variable points, variable points
satisfying some condition so as to form a
locus, and the classification of loci into types
by the idea of conditions of the same form.
Now, the essence of coordinate geometry
is the identification of the algebraic correlation with the geometrical locus. The point
on a plane is represented in algebra by its
two coordinates, x and y, and the condition
satisfied by any point on the locus is repre