Commentary on Proposition VII.31

Back to Proposition VII.31.

[Folio 0339 | p. 333]

Heiberg relegates to the Appendix an alternative proof of this proposition, to the following effect. Since A is composite, some number will measure it. Let B be the least such number. I say that B is prime. For, if not, B is composite, and some number will measure it, say C; so that C is less than B. But, since C measures B, and B measures A, C must measure A. And C is less than B: which is contrary to the hypothesis.