Proposition: 3.23: Segment on Given Base Unique

(Proposition 23 from Book 3 of Euclid's “Elements”)

Two similar and unequal segments of circles cannot be constructed on the same side of the same straight line.

Modern Formulation

The arc on a given base is unique.

Proofs: 1

Proofs: 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