Proposition IX.17 — If as many numbers as we please be in continued proportion, …

Proof

Generalisation of IX.16: a coprime-extremes proportion cannot be extended further while remaining a proportion of integers in the same ratio.

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Depends on (2)

VIII.3Proposition VIII.3If as many numbers as we please in continued proportion be the least of those which have the same ratio with them, the…
IX.16Proposition IX.16If two numbers be prime to one another, the second will not be to any other number as the first is to the second.

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