| If an odd number is subtracted from an odd number, then the remainder is even. | ||
| Let the odd number BC be subtracted from the odd number AB.
I say that the remainder CA is even. |
||
| Since AB is odd, subtract the unit BD, therefore the remainder AD is even. For the same reason CD is also even, so that the remainder CA is also even. | VII.Def.7
IX.24 | |
| Therefore, if an odd number is subtracted from an odd number, then the remainder is even. | ||
| Q.E.D. | ||
Book IX Introduction - Proposition IX.25 - Proposition IX.27.