Proposition VIII.4 — Given as many ratios as we please in least numbers, to find …

Proof

Reduce each ratio to lowest terms by VII.33. Compound them by multiplying numerators and denominators across; the resulting sequence is in continued proportion with the prescribed ratios.

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Depends on (2)

VII.33Proposition VII.33Given as many numbers as we please, to find the least of those which have the same ratio with them.
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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