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

DYNAMICS 57
Hence for the fundamental vectors of
science, namely transportations, velocities,
and forces, the addition of any two of the same
kind is the production of a "resultant"
vector according to the rule of the parallelogram law.
By far the simplest type of parallelogram
is a rectangle, and in pure mathematics it is
the relation of the single vector AC to the
two component vectors, AB and AD, at right
angles (cf. fig. 7), which is continually recurring. Let x, y, and r units represent the
lengths of AB, AD, and AC, and let m units
of angle represent the magnitude of the angle
BAC. Then the relations between x, y, r,
and m, in all their many aspects are the continually recurring topic of pure mathematics;
and the results are of the type required for
application to the fundamental vectors of
mathematical physics. This diagram is the
chief bridge over which the results of pure
mathematics pass in order to obtain application to the facts of nature.