Proposition: 3.25: Construction of Circle from Segment

(Proposition 25 from Book 3 of Euclid's “Elements”)

For a given segment of a circle, to complete the circle, the very one of which it is a segment.

Modern Formulation

It is possible to extend a given segment of a circle to the original circle, circle of which it is.

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