---
book: 10
number: 7
id: "X.7"
kind: "theorem"
uses: ["[[book-10/proposition-6]]"]
source: "https://scaife.perseus.org/reader/urn:cts:greekLit:tlg1799.tlg001.perseus-eng2:10.prop_1.7"
license: "CC-BY-SA-4.0"
---

# X.7

*Incommensurable magnitudes have not to one another the ratio which a number has to a number*.

## Proof

Let *A*, *B* be incommensurable magnitudes; I say that *A* has not to *B* the ratio which a number has to a number.

For, if *A* has to *B* the ratio which a number has to a number, *A* will be commensurable with *B*. [[book-10/proposition-6|X. 6]]

But it is not; therefore *A* has not to *B* the ratio which a number has to a number.

Therefore etc.