Proposition VIII.13 — If there be as many numbers as we please in continued propor…

Proof

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

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Depends on (2)

VII.27Proposition VII.27If two numbers be prime to one another, and each by multiplying itself make a certain number, the products will be…
VIII.2Proposition VIII.2To find numbers in continued proportion, as many as may be prescribed, and the least that are in a given ratio.

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