| If an odd number is multiplied by an odd number, then the product is odd. | ||
| Let the odd number A multiplied by the odd number B make C.
I say that C is odd. | ||
| Since A multiplied by B makes C, therefore C is made up of as many numbers equal to B as there are units in A. And each of the numbers A and B is odd, therefore C is made up of odd numbers the multitude of which is odd. Thus C is odd. | VII.Def.15
IX.23 | |
| Therefore, if an odd number is multiplied by an odd number, then the product is odd. | ||
| Q.E.D. | ||
Book IX Introduction - Proposition IX.28 - Proposition IX.30.