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Proposition: Prop. 11.21: Solid Angle contained by Plane Angles is Less than Four Right Angles

(Proposition 21 from Book 11 of Euclid's “Elements”)

Any solid angle is contained by rectilinear angles (whose sum is) less [than] four right angles.

• Let the solid angle $A$ be contained by the rectilinear angles $BAC$, $CAD$, and $DAB$.¹
• I say that (the sum of) $BAC$, $CAD$, and $DAB$ is less than four right angles.

Modern Formulation

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Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1
Propositions: 2

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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

Footnotes