---
book: 11
number: 1
id: "XI.1"
kind: "theorem"
uses: []
source: "https://scaife.perseus.org/reader/urn:cts:greekLit:tlg1799.tlg001.perseus-eng2:11.prop.1"
license: "CC-BY-SA-4.0"
---

# XI.1

*A part of a straight line cannot be in the plane of reference and a part in a plane more elevated.*

## Proof

For, if possible, let a part *AB* of the straight line *ABC* be in the plane of reference, and a part *BC* in a plane more elevated.

There will then be in the plane of reference some straight line continuous with *AB* in a straight line.

Let it be *BD*; therefore *AB* is a common segment of the two straight lines *ABC*, *ABD*: which is impossible, inasmuch as, if we describe a circle with centre *B* and distance *AB*, the diameters will cut off unequal circumferences of the circle.

Therefore a part of a straight line cannot be in the plane of reference, and a part in a plane more elevated. Q. E. D.