---
book: 9
number: 29
id: "IX.29"
kind: "theorem"
uses: ["[[book-9/proposition-23]]"]
source: "https://scaife.perseus.org/reader/urn:cts:greekLit:tlg1799.tlg001.perseus-eng2:9.prop.29"
license: "CC-BY-SA-4.0"
---

# IX.29

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

## Proof

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*, 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 each of the numbers *A*, *B* is odd; therefore *C* is made up of odd numbers the multitude of which is odd.

Thus *C* is odd. [[book-9/proposition-23|IX. 23]] Q. E. D.