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

COORDINATE GEOMETRY 125
The group of loci which we next come
upon are sufficiently important to deserve a
chapter to themselves. But before going on
to them we will dwell a little longer on the
main ideas of the subject.
The position of any point P is determined
by arbitrarily choosing an origin, 0, two
axes, OX and OY, at right-angles, and then
by noting its coordinates x and y, i.e. OM
and PM. Also, as we have seen in the last
chapter, P can be determined by the "vector" OP, where the idea of the vector includes a determinate direction as well as a
determinate length. From an abstract
mathematical point of view the idea of an
arbitrary origin may appear artificial and
clumsy, and similarly for the arbitrarily
drawn axes, OX and OY. But in relation to
the application of mathematics to the events
of the Universe we are here symbolizing with
direct simplicity the most fundamental fact
respecting the outlook on the world afforded
to us by our senses. We each of us refer
our sensible perceptions of things to an origin
which we call "here": our location in a
particular part of space round which we
group the whole Universe is the essential fact
of our bodily existence. We can imagine
beings who observe all phenomena in all space
with an equal eye, unbiassed in favour of any
part. With us it is otherwise, a cat at our