[Folio 0422 | p. 416]

PROPOSITION 29.

If an odd number by multiplying an odd number make some number, the product will be odd.

For let the odd number A by multiplying the odd number B make C ;

I say that C is odd.

For, since A by multiplying B has made C,

[Folio 0423 | p. 417]

therefore C is made up of as many numbers equal to B as there are units in A. [VII. Def. 15]

And each of the numbers A, B is odd;

therefore C is made up of odd numbers the multitude of which is odd.

[IX. 23]Thus C is odd.

Q. E. D.

Dependency Graph