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

CHAPTER VI
GENERALIZATIONS OF NUMBERS
ONE great peculiarity of mathematics is the
set of allied ideas which have been invented
in connection with the integral numbers from
which we started. These ideas may be called
extensions or generalizations of number. In
the first place there is the idea of fractions.
The earliest treatise on arithmetic which we
possess was written by an Egyptian priest,
named Ahmes, between 1700 B.C. and 1100
B.C., and it is probably a copy of a much older
work. It deals largely with the properties of
fractions. It appears, therefore, that this
concept was developed very early in the history of mathematics. Indeed the subject is
a very obvious one. To divide a field into
three equal parts, and to take two of the
parts, must be a type of operation which had
often occurred. Accordingly, we need not
be surprised that the men of remote civilizations were familiar with the idea of two71