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Proposition 26

If an odd number is subtracted from an odd number, then the remainder is even.
Let the odd number BC be subtracted from the odd number AB. I say that the remainder CA is even. |
Since AB is odd, subtract the unit BD, therefore the remainder AD is even. For the same reason CD is also even, so that the remainder CA is also even. | VII.Def.7 IX.24
Therefore, if an odd number is subtracted from an odd number, then the remainder is even.
Q.E.D.

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This proposition is used in IX.29.

Book IX Introduction - Proposition IX.25 - Proposition IX.27.

© 1996
D.E.Joyce
Clark University