Page:The Algebra of Mohammed Ben Musa (1831).djvu/37

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We have observed that every question which requires equation or reduction for its solution, will refer you to one of the six cases which I have proposed in this book. I have now also explained their arguments. Bear them, therefore, in mind.

 

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ON MULTIPLICATION.

I shall now teach you how to multiply the unknown numbers, that is to say, the roots, one by the other, if they stand alone, or if numbers are added to them, or if numbers are subtracted from them, or if they are subtracted from numbers; also how to add them one to the other, or how to subtract one from the other.

Whenever one number is to be multiplied by another, the one must be repeated as many times as the other contains units.^[1]

If there are greater numbers combined with units to be added to or subtracted from them, then four multiplications are necessary;^[2] namely, the greater numbers by the greater numbers, the greater numbers by the

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1. If $x$ is to be multiplied by $y,x$ is to be repeated as many times as there are units in $y$.
2. If $x\pm a$ is to be multiplied by $y\pm b$, $x$ is to be multiplied by $y$, $x$ is to be multiplied by $b$, $a$ is to be multiplied by $y$, and $a$ is to be multiplied by $b$.