|If an even number is subtracted from an even number, then the remainder is even.|
|Let the even number BC be subtracted from the even number AB.
I say that the remainder CA is even.
|Since AB is even, therefore it has a half part. For the same reason BC also has a half part, so that the remainder CA also has a half part, and CA is therefore even.||VII.Def.6|
|Therefore, if an even number is subtracted from an even number, then the remainder is even.|
Next proposition: IX.25