Page:IntroductionToMathematicsWhitehead.pdf/71

last equation, ${\displaystyle x^{2}-4=0}$, and the preceding two equations, due to the fact that ${\displaystyle x}$ (as distinct from ${\displaystyle x^{2}}$) 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, ${\displaystyle x+y-1-0}$, ${\displaystyle 2x+3y-8=0}$, 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 ${\displaystyle 0}$ on the right-hand side.

There is yet another function performed by ${\displaystyle 0}$ in relation to the study of form. Whatever number ${\displaystyle x}$ may be, ${\displaystyle 0\times x=0}$, and ${\displaystyle x+0=x}$. By means of these properties minor differences of form can be assimilated. Thus the difference mentioned above between the quadratic equations ${\displaystyle 2-3x+2=0}$, and ${\displaystyle 2-4=0}$, can be obliterated by writing the latter