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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.

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

Book IX Introduction - Proposition IX.23 - Proposition IX.25.

© 1996
D.E.Joyce
Clark University