Page:The Algebra of Mohammed Ben Musa (1831).djvu/39

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negative one by ten is ten negative; the other negative one by ten is likewise ten negative, so that it becomes eighty: but the negative one by the negative one is one positive, and this makes the result eighty-one.

Or if the instance be “ten and two, to be multipled by ten less one,”^[1] then ten times ten is a hundred, and the negative one by ten is ten negative; the positive two by ten is twenty positive; this together is a hundred and ten; the positive two by the negative one gives two negative. This makes the product a hundred and eight.

I have explained this, that it might serve as an introduction to the multiplication of unknown sums, when numbers are added to them, or when numbers are subtracted from them, or when they are subtracted from numbers.

For instance: “Ten less thing (the signification of thing being root) to be multipled by ten.”^[2] You begin by taking ten times ten, which is a hundred; less thing by ten is ten roots negative; the product is therefore a hundred less ten things.

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1. ${\begin{aligned}(10+2)&\times (10-1)=\\10\times 10&\ldots 100\\-1\times 10&\ldots -10\\+10\times 2&\ldots +20\\-1\times 2&\ldots -2\\&108\end{aligned}}$
2. $(10-x)\times 10=10\times 10-10x=100-10x.$