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

IMAGINARY NUMBERS 97
All these requisites are satisfied by taking
(x, y)+(x', y') to mean the ordered couple
(x+x', y+y'). Accordingly by definition we
put
(x, y) + (x', y') = (x +x', y +y').
Notice that here we have adopted the mathematical habit of using the same symbol + in
different senses. The + on the left-hand side
of the equation has the new meaning of +
which we are just defining; while the two
+'s on the right-hand side have the meaning
of the addition of positive and negative numbers (operations) which was defined in the
last chapter. No practical confusion arises
from this double use.
As examples of addition we have
(+3, +1)+(+2, +6)=(+5, +7),
(+3, -1)+(-2, -6)=(+1, -7),
(+3, +1)+(-3, -1)=(0, 0).
The meaning of subtraction is now settled
for us. We find that
(x, y)- (u, v) = (x-u, y-v).
Thus
(+3, +2)-(+1, +1)=(+2, +1),
and
(+1, -2)-(+2, -4)=(-1, +2),
and
(-1, -2)-(+2, +3)=(-3, -5).