Proposition: Prop. 11.23: Sum of Plane Angles Used to Construct a Solid Angle is Less Than Four Right Angles

(Proposition 23 from Book 11 of Euclid's “Elements”)

To construct a solid angle from three (given) rectilinear angles, (the sum of) two of which is greater than the remaining (one, the angles) being taken up in any (possible way). So, it is necessary for the (sum of the) three (angles) to be less than four right angles [Prop. 11.21].


Modern Formulation

(not yet contributed)

Proofs: 1

  1. Lemma: Lem. 11.23: Making a Square Area Equal to the Difference Of Areas of Two Other Incongruent Squares

Proofs: 1

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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",, 2016