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Proposition 25

If an odd number is subtracted from an even number, then the remainder is odd.
Let the odd number BC be subtracted from the even number. I say that the remainder CA is odd. |
Subtract the unit CD from BC, therefore DB is even. | VII.Def.7
But AB is also even, therefore the remainder AD is also even. And CD is a unit, therefore CA is odd. | IX.24 VII.Def.7
Therefore, if an odd number is subtracted from an even number, then the remainder is odd.
Q.E.D.

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(Forthcoming)

Book IX Introduction - Proposition IX.24 - Proposition IX.26.

© 1996
D.E.Joyce
Clark University