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

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VIII.13 Proposition VIII.13

If there be as many numbers as we please in continued proportion, and each by multiplying itself make some number, the products will be proportional; and if the original numbers by multiplying the products make certain numbers, the latter will also be proportional.

Proof

Squares (and cubes) of terms in continued proportion are themselves in continued proportion, by VII.27 and VIII.2.

lines 74–74 in main.tex