Proposition IX.5 — If a cube number by multiplying any number make a cube numbe…

Proof

a^{3} \cdot n = m^{3}

then

n = m^{3} / a^{3}

; by VIII.25 the quotient of two cubes (when integer) is a cube.

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Depends on (2)

VIII.25Proposition VIII.25If two numbers have to one another the ratio which a cube number has to a cube number, and the first be cube, the…
IX.4Proposition IX.4If a cube number by multiplying a cube number make some number, the product will be cube.

Required by (dependents) (1)

IX.6Proposition IX.6If a number by multiplying itself make a cube number, it itself will also be cube.

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