PROPOSITION 27.

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

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

I say that the remainder CA is odd.

A D C B

Let the unit AD be subtracted ;

[VII. Def. 7]therefore DB is even.
But BC is also even ;
[IX. 24]therefore the remainder CD is even.
[VII. Def. 7]Therefore CA is odd.
Q. E. D.

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