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

CIAPTER III
METHODS OF APPLICATION
THE way in which the idea of variables
satisfying a relation occurs in the applications of mathematics is worth thought, and
by devoting some time to it we shall clear
up our thoughts on the whole subject.
Let us start with the simplest of examples:
-Suppose that building costs Is. per cubic
foot and that 20s. make ~1. Then in all
the complex circumstances which attend the
building of a new house, amid all the various
sensations and emotions of the owner, the
architect, the builder, the workmen, and the
onlookers as the house has grown to completion, this fixed correlation is by the law
assumed to hold between the cubic content
and the cost to the owner, namely that if x
be the number of cubic feet, and ~y the cost,
then 20y =x. This correlation of x and y is
assumed to be true for the building of any
house by any owner. Also, the volume of
the house and the cost are not supposed to
have been perceived or apprehended by any
particular sensation or faculty, or by any
25