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representing some definite number other than zero, such as ${\displaystyle 1}$ or ${\displaystyle 2}$ in the examples above, are written on the left-hand side, so that the whole left-hand side is equated to the number zero. The first man to do this is said to have been Thomas Harriot, born at Oxford in 1560 and died in 1621. But what is the importance of this simple symbolic procedure? It made possible the growth of the modern conception of algebraic form.

This is an idea to which we shall have continually to recur; it is not going too far to say that no part of modern mathematics can be properly understood without constant recurrence to it. The conception of form is so general that it is difficult to characterize it in abstract terms. At this stage we shall do better merely to consider examples. Thus the equations ${\displaystyle 2x-3=0}$, ${\displaystyle x-1=0}$, ${\displaystyle 5x-6=0}$, are all equations of the same form, namely, equations involving one unknown ${\displaystyle x}$, which is not multiplied by itself, so that ${\displaystyle x^{2}x^{3}}$, etc., do not appear. Again ${\displaystyle 3x^{2}-2x+1=0}$, ${\displaystyle x^{2}=3x+2=0}$, ${\displaystyle x^{2}-4=0}$, are all equations of the same form, namely, equations involving one unknown ${\displaystyle x}$ in which ${\displaystyle x\times x}$, that is ${\displaystyle x^{2}}$, appears. These equations are called quadratic equations. Similarly cubic equations, in which ${\displaystyle x^{3}}$appears, yield another form, and so on. Among the three quadratic equations given above there is a minor difference between the