Proposition IX.12 — If as many numbers as we please beginning from a unit be in …

Proof

A prime dividing

r^{n}

must divide

r

(Euclid's lemma, VII.30), which is the second term after the unit.

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Depends on (2)

VII.30Proposition VII.30If two numbers by multiplying one another make some number, and any prime number measure the product, it will also…
IX.11Proposition IX.11If as many numbers as we please beginning from a unit be in continued proportion, the less measures the greater…

Required by (dependents) (1)

IX.13Proposition IX.13If as many numbers as we please beginning from a unit be in continued proportion, and the number after the unit be…

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