The following is an illustration of this type: a square and 21 units equal 10 roots [X^2+21=10x. This equation and other examples from Al-Khowarizmi repeatedly occur in mathematical literature]. ... You ought to understand also that when you take the half of the roots in this form of equation and then multiply the half by itself, if that which proceeds or results from the multiplication is less than the units above mentioned as accompanying the square, you have no equation [i.e., b^2-4ac<0]. If equal to the units, it follows that a root of the square will be the same as the half of the roots which accompany the square, without either addition or diminuation [i.e., equal roots when b^2-4ac=0]
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Published before 1923