---
book: 8
number: 23
id: "VIII.23"
kind: "theorem"
uses: ["[[book-8/proposition-21]]"]
source: "https://scaife.perseus.org/reader/urn:cts:greekLit:tlg1799.tlg001.perseus-eng2:8.prop.23"
license: "CC-BY-SA-4.0"
---

# VIII.23

*If four numbers be in continued proportion, and the first be cube, the fourth will also be cube.*

## Proof

Let *A*, *B*, *C*, *D* be four numbers in continued proportion, and let *A* be cube; I say that *D* is also cube.

For, since between *A*, *D* there are two mean proportional numbers *B*, *C*, therefore *A*, *D* are similar solid numbers. [[book-8/proposition-21|VIII. 21]]

But *A* is cube; therefore *D* is also cube. Q. E. D.