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Source — Euclid's Elements, encoded as an rrxiv paper — rrxiv

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Source — Euclid's Elements, encoded as an rrxiv paper

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IX.5 Proposition IX.5

If a cube number by multiplying any number make a cube number, the multiplied number will also be cube.

Proof

If

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.

lines 74–74 in main.tex