Proposition VIII.8 — If between two numbers there fall numbers in continued propo…

Proof

The number of geometric means between two numbers depends only on their ratio; scaling by a common factor changes the magnitudes but not the ratio, so the same number of means fall between the scaled pair.

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Depends on (2)

VII.13Proposition VII.13If four numbers be proportional, they will also be proportional alternately.
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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