Page:The Algebra of Mohammed Ben Musa (1831).djvu/45

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In the same manner, if you require to triple the root of nine,^[1] you multiply three by three, and then by nine: the product is eighty-one; take its root, it is nine, which becomes equal to thrice the root of nine.

If you require to have the moiety of the root of nine^[2]. you multiply a half by a half, which gives a quarter, and then this by nine; the result is two and a quarter: take its root; it is one and a half, which is the moiety of the root of nine.

You proceed in this manner with every root, whether positive or negative, and whether known or unknown.

 

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ON DIVISION.

If you will divide the root of nine by the root of four,^[3] you begin with dividing nine by four, which gives two and a quarter: the root of this is the number which you require—it is one and a half.

If you will divide the root of four by the root of nine,^[4] you divide four by nine; it is four-ninths of the unit: the root of this is two divided by three; namely, two-thirds of the unit.

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1. $3{\sqrt {9}}={\sqrt {9\times 9}}={\sqrt {81}}=9$
2. ${\tfrac {1}{2}}{\sqrt {9}}={\sqrt {\tfrac {9}{4}}}={\sqrt {2{\tfrac {1}{4}}}}=1{\tfrac {1}{2}}$
3. ${\tfrac {\sqrt {9}}{\sqrt {4}}}={\sqrt {\tfrac {9}{4}}}={\sqrt {2{\tfrac {1}{4}}}}=1{\tfrac {1}{2}}$
4. ${\tfrac {\sqrt {9}}{\sqrt {4}}}={\sqrt {\tfrac {9}{4}}}={\tfrac {2}{3}}$