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

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VIII.12 Proposition VIII.12

Between two cube numbers there are two mean proportional numbers, and the cube has to the cube the ratio triplicate of that which the side has to the side.

Proof

For cubes

a^{3}

,

b^{3}

: the two means are

a^{2} b

and

a b^{2}

, and

a^{3} : b^{3}

is the triplicate of

a : b

.

lines 74–74 in main.tex