Proposition VIII.6 — If there be as many numbers as we please in continued propor…

Proof

Contrapositive of VIII.7: divisibility propagates through the sequence, so failure at the first step prevents any later divisibility relation.

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Depends on (2)

VII.20Proposition VII.20The least numbers of those which have the same ratio with them measure those which have the same ratio the same number…
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…

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