G.354 many odd numbers — Heath

IX.23

If as many odd numbers as we please be added together, and their multitude be odd, the whole will also be odd.

For let as many odd numbers as we please, / A B /, / B C /, / C D /, the multitude of which is odd, be added together ;

I say that the whole / A D / is also odd.

Let the unit / D E / be subtracted from / C D / ;

[G.352]therefore the remainder / C E / is even.

[G.353]But / A C / is also even ;

[G.351]therefore the whole / A E / is also even.

And / D E / is an unit.

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

Q. E. D.

Dependency Graph

Required for

G.360, G.361, G.362