Page:The Algebra of Mohammed Ben Musa (1831).djvu/70

This page has been proofread, but needs to be validated.

( 54 )

amounts to twenty?^[1]” the answer is this: If you multiply it by itself it will be five: it is therefore the root of five.

If somebody ask you for the amount of a square-root,^[2] which when multiplied by its third amounts to ten,^[3] the solution is, that when multiplied by itself it will amount to thirty; and it is consequently the root of thirty.

(39) If the question be: “To find a quantity^[2], which when multiplied by four times itself, gives one-third of the first quantity as product,”^[4] the solution is, that if you multiply it by twelve times itself, the quantity itself must re-appear: it is the moiety of one moiety of one-third.

If the question be: “A square, which when multiplied by its root gives three times the original square as product,”^[5] then the solution is that if you multiply the root by one-third of the square, the original square is

↑ ${\begin{aligned}4x^{2}=20\\x={\sqrt {5}}\end{aligned}}$
↑ ^2.0 ^2.1 “Square” in the original.
↑ ${\begin{aligned}&x\times {\tfrac {x}{3}}=10\\&x^{2}=30\\&x={\sqrt {30}}\end{aligned}}$
↑ ${\begin{aligned}&x\times 4x={\tfrac {x}{3}}\\&x={\tfrac {1}{12}}\end{aligned}}$
↑ ${\begin{aligned}&x^{2}\times x=3x^{2}\\&x=3\end{aligned}}$

[1] ${\begin{aligned}4x^{2}=20\\x={\sqrt {5}}\end{aligned}}$

[p70_r1-2] 2.0 ^2.1 “Square” in the original.

[3] ${\begin{aligned}&x\times {\tfrac {x}{3}}=10\\&x^{2}=30\\&x={\sqrt {30}}\end{aligned}}$

[4] ${\begin{aligned}&x\times 4x={\tfrac {x}{3}}\\&x={\tfrac {1}{12}}\end{aligned}}$

[5] ${\begin{aligned}&x^{2}\times x=3x^{2}\\&x=3\end{aligned}}$

[1]

[2]

[3]

[4]

[5]