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

94 INTRODUCTION TO MATHEMATICS
to (+3, +1), the lengths OM' and ON together correspond to (-3, +1), OM' and
ON' together to (-3, -1), and OM and
ON' together to (+3, -1). But by completing the various rectangles, it is easy to
see that the point P completely determines
and is determined by the ordered couple
P' N P
-3 +3
Ea. 3, o.
Y'
Fig. 9.
(+3, +1), the point P' by (-3, +1), the
point P" by (-3, -1), and the point P"'
by (+3, -1). More generally in the previous figure (8), the point P corresponds to
the ordered couple (x, y), where x and y in
the figure are both assumed to be positive, the
point P' corresponds to (x', y), where x' in
the figure is assumed to be negative, P" to
(x', y'), and P"' to (x, y'). Thus an ordered