Page:The Algebra of Mohammed Ben Musa (1831).djvu/51

 OF THE SIX PROBLEMS. the chapters on computation and the several species thereof, I shall now introduce six problems, as instances of the six cases treated of in the beginning of this work. I have shown that three among these cases, in order to be solved, do not require that the roots be halved, and I have also mentioned that the calculating by completion and reduction must always necessarily lead you to one of these cases. I now subjoin these problems, which will serve to bring the subject nearer to the understanding, to render its comprehension easier, and to make the arguments more perspicuous.

First Problem.

I have divided ten into two portions; I have multiplied the one of the two portions by the other; after this. I have multiplied the one of the two by itself, and the product of the multiplication by itself is four times as much as that of one of the portions by the other.

Computation: Suppose one of the portions to be thing, and the other ten minus thing: you multiply