Proposition VIII.9 — If two numbers be prime to one another, and numbers fall bet…

Proof

Coprime extremes correspond to a least continued proportion (VIII.1); the unit extends the proportion at both ends, and VIII.2 gives the matching extension on each side.

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Depends on (2)

VIII.1Proposition VIII.1If there be as many numbers as we please in continued proportion, and the extremes of them be prime to one another, the…
VIII.2Proposition VIII.2To find numbers in continued proportion, as many as may be prescribed, and the least that are in a given ratio.

Required by (dependents) (1)

VIII.10Proposition VIII.10If numbers fall between each of two numbers and a unit in continued proportion, however many numbers fall between each…

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