Page:The Algebra of Mohammed Ben Musa (1831).djvu/43

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a multiplication, such as thing positive and minus thing, the last multiplication gives always the negative product. Keep this in memory.

 

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ON ADDITION and SUBTRACTION.

Know that the root of two hundred minus ten, added to twenty minus the root of two hundred, is just ten.^[1]

The root of two hundred, minus ten, subtracted from twenty minus the root of two hundred, is thirty minus twice the root of two hundred; twice the root of two hundred is equal to the root of eight hundred.^[2]

A hundred and a square minus twenty roots, added to fifty and ten roots minus two squares,^[3] is a hundred and fifty, minus a square and minus ten roots.

A hundred and a square, minus twenty roots, diminished by fifty and ten roots minus two squares, is fifty dirhems and three squares minus thirty roots.^[4]

I shall hereafter explain to you the reason of this by a figure, which will be annexed to this chapter.

If you require to double the root of any known or unknown square, (the meaning of its duplication being

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1. $20-{\sqrt {200}}+({\sqrt {200}}-10)=10$
2. $20-{\sqrt {200}}-({\sqrt {200}}-10)=30-2{\sqrt {200}}=30-{\sqrt {800}}$
3. $50+10x-2x^{2}+(100+x^{2}-20x)=150-10x-x^{2}$
4. $100+x^{2}-20x-[50-2x^{2}+10x]=50+3x^{2}-30x$