|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
|Therefore, if an even number is subtracted from an odd number, then the remainder is odd.|
Next proposition: IX.28