---
book: 8
number: 17
id: "VIII.17"
kind: "theorem"
uses: ["[[book-8/proposition-15]]"]
source: "https://scaife.perseus.org/reader/urn:cts:greekLit:tlg1799.tlg001.perseus-eng2:8.prop.17"
license: "CC-BY-SA-4.0"
---

# VIII.17

*If a cube number do not measure a cube number, neither will the side measure the side; and, if the side do not measure the side, neither will the cube measure the cube.*

## Proof

For let the cube number *A* not measure the cube number *B*, and let *C* be the side of *A*, and *D* of *B*; I say that *C* will not measure *D*.

For if *C* measures *D*, *A* will also measure *B*. [[book-8/proposition-15|VIII. 15]]

But *A* does not measure *B*; therefore neither does *C* measure *D*.

Again, let *C* not measure *D*; I say that neither will *A* measure *B*.

For, if *A* measures *B*, *C* will also measure *D*. [[book-8/proposition-15|VIII. 15]]

But *C* does not measure *D*; therefore neither will *A* measure *B*. Q. E. D.