---
book: 7
number: 38
id: "VII.38"
kind: "theorem"
uses: ["[[book-7/proposition-15]]"]
source: "https://scaife.perseus.org/reader/urn:cts:greekLit:tlg1799.tlg001.perseus-eng2:7.prop.38"
license: "CC-BY-SA-4.0"
---

# VII.38

*If a number have any part whatever, it will be measured by a number called by the same name as the part.*

## Proof

For let the number *A* have any part whatever, *B*, and let *C* be a number called by the same name as the part *B*; I say that *C* measures *A*.

For, since *B* is a part of *A* called by the same name as *C*, and the unit *D* is also a part of *C* called by the same name as it, therefore, whatever part the unit *D* is of the number *C*, the same part is *B* of *A* also; therefore the unit *D* measures the number *C* the same number of times that *B* measures *A*.

Therefore, alternately, the unit *D* measures the number *B* the same number of times that *C* measures *A*. [[book-7/proposition-15|VII. 15]]

Therefore *C* measures *A*. Q. E. D.