PROPOSITION 26.

If from an odd number an odd number be subtracted, the remainder will be even.

For from the odd number AB let the odd number BC be subtracted ;

I say that the remainder CA is even.

A C D B
For, since AB is odd, let the unit BD be subtracted ;
[VII. Def. 7]therefore the remainder AD is even.
[VII. Def. 7]For the same reason CD is also even ;
[IX. 24]so that the remainder CA is also even.
Q. E. D.

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