If an odd number is multiplied by an even number, then the product is even.

Let the odd number *A* multiplied by the even number *B* make *C.*

I say that *C* is even.

Since *A* multiplied by *B* makes *C,* therefore *C* is made up of as many numbers equal to *B* as there are units in *A.* And *B* is even, therefore *C* is made up of even numbers.

But, if as many even numbers as we please be added together, the whole is even. Therefore *C* is even.

Therefore, *if an odd number is multiplied by an even number, then the product is even.*

Q.E.D.

Note that the proof for this theorem makes no use of the assumption that *A* is an odd number. The statement of this theorem might just as well be “if any number is multiplied by an even number, then the product is even.”