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

IMAGINARY NUMBERS 93
is a first number (+3 in the above example),
and a second number (+1 in the above example), represents measurements from O
along XOX' for the first number, and along
YOY' for the second number. Thus (cf.
fig. 9) in (+3, +1) a length of 3 units is to
be measured along XOX' in the positive
direction, that is from O towards X, and a
length +1 measured along YOY' in the positive direction, that is from O towards Y.
Similarly in (-3, +1) the length of 3 units
is to be measured from O towards X', and of
1 unit from O towards Y'. Also in (- 3, -1)
the two lengths are to be measured along
OX' and OY' respectively, and in (+3, -1)
along OX and OY' respectively. Let us for
the moment call such a pair of numbers an
"ordered couple." Then, from the two
numbers 1 and 3, eight ordered couples can
be generated, namely
(+1, +3), (-1, +3), (-1, -3), (+1, -3),
(+3, +1), (-3, +1), (-3, -1), (+3, -1).
Each of these eight "ordered couples" directs
a process of measurement along XOX' and
YOY' which is different from that directed
by any of the others.
The processes of measurement represented
by the last four ordered couples, mentioned
above, are given pictorially in the figure.
The lengths OM and ON together correspond