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

SYMBOLISM OF MATHEMATICS 67
last equation, x2 -4 = 0, and the preceding two
equations, due to the fact that x (as distinct
from x2) does not appear in the last and
does in the other two. This distinction is
very unimportant in comparison with the
great fact that they are all three quadratic
equations.
Then further there are the forms of equation
stating correlations between two variables;
for example, x +y - 1 =, 2x +3y -8 =0, and
so on. These are examples of what is called
the linear form of equation. The reason for
this name of "linear" is that the graphic
method of representation, which is explained
at the end of Chapter II, always represents
such equations by a straight line. Then there
are other forms for two variables-for example, the quadratic form, the cubic form,
and so on. But the point which we here insist upon is that this study of form is facilitated, and, indeed, made possible, by the
standard method of writing equations with
the symbol O on the right-hand side.
There is yet another function performed by
O in relation to the study of form. Whatever
number x may be, OXx=O, and x+O=x.
By means of these properties minor differences of form can be assimilated. Thus the
difference mentioned above between the quadratic equations x2 = 3x +2 = O, and x2 -4 = 0,
can be obliterated by writing the latter