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

20 INTRODUCTION TO MATHEMATICS
y2=x, satisfied by pairs of such numbers.
Then whatever integral value is given to y,
x can assume one corresponding integral
value. So the "field" for y is unrestricted
among these positive or negative integers.
But the "field" for x is restricted in two
ways. In the first place x must be positive,
and in the second place, since y is to be integral, x must be a perfect square. Accordingly, the "field" of x is restricted to the set
of integers 12, 22, 32, 42, and so on, i.e., to 1,
4, 9, 16, and so on.
The study of the general properties of a
relation between pairs of numbers is much
facilitated by the use of a diagram constructed
as follows:
B
y Y
Ox J M / A K
Fig. 1.
Draw two lines OX and OY at right angles;
let any number x be represented by x units