| If an even number is subtracted from an odd number, then the remainder is odd. | ||
| Let the even number BC be subtracted from the odd number AB.
I say that the remainder CA is odd. |
||
| Subtract the unit AD, therefore DB is even. | VII.Def.7 | |
| But BC is also even, therefore the remainder CD is even. Therefore CA is odd. | IX.24
VII.Def.7 | |
| Therefore, if an even number is subtracted from an odd number, then the remainder is odd. | ||
| Q.E.D. | ||
Book IX Introduction - Proposition IX.26 - Proposition IX.28.