Proposition: Prop. 13.07: Equilateral Pentagon is Equiangular if Three Angles are Equal

(Proposition 7 from Book 13 of Euclid's “Elements”)

If three angles, either consecutive or not consecutive, of an equilateral pentagon are equal then the pentagon will be equiangular. * For let three angles of the equilateral pentagon $ABCDE$ - first of all, the consecutive (angles) at $A$, $B$, and $C$ - -be equal to one another. * I say that pentagon $ABCDE$ is equiangular.


Modern Formulation

(not yet contributed)

Proofs: 1

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