## Proposition 24

 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. Q.E.D.
This proposition is used in four of the next five propositions.

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