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