Proposition IX.13 — If as many numbers as we please beginning from a unit be in …

Proof

r

is prime, the divisors of

r^{n}

are exactly

1, r, r^{2}, \dots, r^{n}

(Euclid's lemma). These are exactly the prefix of the sequence.

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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.12Proposition IX.12If as many numbers as we please beginning from a unit be in continued proportion, by whatever prime numbers the last is…

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