Proposition: 4.03: Circumscribing about Circle Triangle Equiangular with Given Angles

(Proposition 3 from Book 4 of Euclid's “Elements”)

To circumscribe a triangle, equiangular with a given triangle, about a given circle. * Let $ABC$ be the given circle, and $DEF$ the given triangle. * So it is required to circumscribe a triangle, equiangular with triangle $DEF$, about circle $ABC$.


Modern Formulation

It is possible to circumscribe a triangle with a given angles, about a given circle.

Proofs: 1

Sections: 1

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



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