Proposition VIII.10 — If numbers fall between each of two numbers and a unit in co…

Proof

Concatenate two unit-anchored continued proportions; VII.14 (ex aequali) confirms the joined sequence remains in continued proportion.

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Depends on (2)

VII.14Proposition VII.14If there be as many numbers as we please, and others equal to them in multitude, which taken two and two are in the…
VIII.9Proposition VIII.9If two numbers be prime to one another, and numbers fall between them in continued proportion, then, however many…

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