---
book: 8
number: 7
id: "VIII.7"
kind: "theorem"
uses: ["[[book-8/proposition-6]]"]
source: "https://scaife.perseus.org/reader/urn:cts:greekLit:tlg1799.tlg001.perseus-eng2:8.prop.7"
license: "CC-BY-SA-4.0"
---

# VIII.7

*If there be as many numbers as we please in continued proportion, and the first measure the last, it will measure the second also.*

## Proof

Let there be as many numbers as we please, *A*, *B*, *C*, *D*, in continued proportion; and let *A* measure *D*; I say that *A* also measures *B*.

For, if *A* does not measure *B*, neither will any other of the numbers measure any other. [[book-8/proposition-6|VIII. 6]]

But *A* measures *D*.

Therefore *A* also measures *B*. Q. E. D.