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

IMAGINARY NUMBERS 95
couple (x, y), where x and y are any positive
or negative numbers, and the corresponding
point reciprocally determine each other. It
is convenient to introduce some names at this
juncture. In the ordered couple (x, y) the
first number x is called the "abscissa" of the
corresponding point, and the second number
y is called the "ordinate" of the point, and
the two numbers together are called the
"coordinates" of the point. The idea of determining the position of a point by its "coordinates" was by no means new when the
theory of "imaginaries" was being formed.
It was due to Descartes, the great French
mathematician and philosopher, and appears
in his Discours published at Leyden in 1637
A.D. The idea of the ordered couple as a
thing on its own account is of later growth
and is the outcome of the efforts to interpret
imaginaries in the most abstract way possible.
It may be noticed as a further illustration
of this idea of the ordered couple, that the
point M in fig. 9 is the couple (+3, 0), the
point N is the couple (0, +1), the point M'
the couple (-3, 0), the point N' the couple
(0, -1), the point O the couple (0, 0).
Another way of representing the ordered
couple (x, y) is to think of it as representing
the dotted line OP (cf. fig. 8), rather than the
point P. Thus the ordered couple represents
a line drawn from an "origin," O, of a certain