| If an odd number is multiplied by an even number, then the product is even. | ||
| Let the odd number A multiplied by the even number B make C.
I say that C is even. | ||
| 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 B is even, therefore C is made up of even numbers. | VII.Def.15 | |
| But, if as many even numbers as we please be added together, the whole is even. Therefore C is even. | IX.21 | |
| Therefore, if an odd number is multiplied by an even number, then the product is even. | ||
| Q.E.D. | ||
Book IX Introduction - Proposition IX.27 - Proposition IX.29.