Commentary on Proposition IX.16

Back to Proposition IX.16.

[Folio 0412 | p. 406]

If a, b are prime to one another, they can have no integral third proportional.

If possible, let

$$a : b = b : x.$$

Therefore [VII. 20, 21] a measures b ; and a, b have the common measure a, which is contrary to the hypothesis.