Similarly we can prove that B, C added together are prime to A. I say next that A, C added together are also prime to B. For, since DF is prime to each of the numbers DE, EF, the square on DF is also prime to the product of DE, EF. [VII. 24, 25] But the squares on DE, EF together with twice the product of DE, EF are equal to the square on DF; [II. 4] therefore the squares on DE, EF together with twice the product of DE, EF are prime to the product of DE, EF. Separando, the squares on DE, EF together with once the product of DE, EF are prime to the product of DE, EF. Therefore, separando again, the squares on DE, EF are prime to the product of DE, EF. And the square on DE is A, the product of DE, EF is B, and the square on EF is C. Therefore A, C added together are prime to B. Q. E. D.
Euclid. Euclid's Elements. Sir Thomas Little Heath. New York. Dover. 1956.
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