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Proposition 27

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 VII.Def.7
Therefore, if an even number is subtracted from an odd number, then the remainder is odd.
Q.E.D.

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(Forthcoming)

Book IX Introduction - Proposition IX.26 - Proposition IX.28.

© 1996
D.E.Joyce
Clark University