---
book: 9
number: 26
id: "IX.26"
kind: "theorem"
uses: ["[[book-9/proposition-24]]"]
source: "https://scaife.perseus.org/reader/urn:cts:greekLit:tlg1799.tlg001.perseus-eng2:9.prop.26"
license: "CC-BY-SA-4.0"
---

# IX.26

*If from an odd number an odd number be subtracted, the remainder will be even.*

## Proof

For from the odd number *AB* let the odd number *BC* be subtracted; I say that the remainder *CA* is even.

For, since *AB* is odd, let the unit *BD* be subtracted; therefore the remainder *AD* is even. [[book-7/definitions#Definition 7|VII. Def. 7]]

For the same reason *CD* is also even; [[book-7/definitions#Definition 7|VII. Def. 7]] so that the remainder *CA* is also even. [[book-9/proposition-24|IX. 24]] Q. E. D.