---
book: 9
number: 28
id: "IX.28"
kind: "theorem"
uses: ["[[book-9/proposition-21]]"]
source: "https://scaife.perseus.org/reader/urn:cts:greekLit:tlg1799.tlg001.perseus-eng2:9.prop.28"
license: "CC-BY-SA-4.0"
---

# IX.28

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

## Proof

For let the odd number *A* by multiplying the even number *B* make *C*; I say that *C* is even.

For, since *A* by multiplying *B* has made *C*, therefore *C* is made up of as many numbers equal to *B* as there are units in *A*. [[book-7/definitions#Definition 15|VII. Def. 15]]

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. [[book-9/proposition-21|IX. 21]]

Therefore *C* is even. Q. E. D.