Commentary on Proposition VII.25

Back to Proposition VII.25.

[Folio 0333 | p. 327]

If $a$, $b$ are prime to one another,

$$a^2\text{ is prime to }b.$$

Euclid takes $d$ equal to $a$, so that $d$, $a$ are both prime to $b$. Hence, by VII. 24, $da$, i.e. $a^2$, is prime to $b$. The proposition is a particular case of the preceding proposition ; and the method of proof is by substitution of different numbers in the result of that proposition.