---
book: 11
number: 3
id: "XI.3"
kind: "theorem"
uses: []
source: "https://scaife.perseus.org/reader/urn:cts:greekLit:tlg1799.tlg001.perseus-eng2:11.prop.3"
license: "CC-BY-SA-4.0"
---

# XI.3

*If two planes cut one another*, *their common section is a straight line.*

## Proof

For let the two planes *AB*, *BC* cut one another, and let the line *DB* be their common section; I say that the line *DB* is a straight line.

For, if not, from *D* to *B* let the straight line *DEB* be joined in the plane *AB*, and in the plane *BC* the straight line *DFB*.

Then the two straight lines *DEB*, *DFB* will have the same extremities, and will clearly enclose an area: which is absurd.

Therefore *DEB*, *DFB* are not straight lines.

Similarly we can prove that neither will there be any other straight line joined from *D* to *B* except *DB* the common section of the planes *AB*, *BC*.

Therefore etc. Q. E. D.