# Proposition: Prop. 11.20: Sum of Two Angles of Three containing Solid Angle is Greater than Other Angle

### (Proposition 20 from Book 11 of Euclid's “Elements”)

If a solid angle is contained by three rectilinear angles then (the sum of) any two (angles) is greater than the remaining (one), (the angles) being taken up in any (possible way).

• For let the solid angle $A$ have been contained by the three rectilinear angles $BAC$, $CAD$, and $DAB$.
• I say that (the sum of) any two of the angles $BAC$, $CAD$, and $DAB$ is greater than the remaining (one), (the angles) being taken up in any (possible way).

### Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1

Thank you to the contributors under CC BY-SA 4.0!

Github:

non-Github:
@Fitzpatrick

### References

#### Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

#### Adapted from CC BY-SA 3.0 Sources:

1. Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016