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

# IX.24

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

## Proof

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

For, since *AB* is even, it has a half part. [[book-7/definitions#Definition 6|VII. Def. 6]]

For the same reason *BC* also has a half part; so that the remainder [*CA* also has a half part, and] *AC* is therefore even. Q. E. D.