G.358 odd number even — Heath

IX.27

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

For from the odd number / A B / let the even number / B C / be subtracted ;

I say that the remainder / A C / is odd.

Let the unit / A D / be subtracted ;

[G.352]therefore / B D / is even.

But / B C / is also even ;

[G.355]therefore the remainder / C D / is even.

[G.352]Therefore / A C / is odd.

Q. E. D.

Dependency Graph