Proposition: 3.24: Similar Segments on Equal Bases are Equal

(Proposition 24 from Book 3 of Euclid's “Elements”)

Similar segments of circles on equal straight lines are equal to one another. * For let $AEB$ and $CFD$ be similar segments of circles on the equal straight lines $AB$ and $CD$ (respectively). * I say that segment $AEB$ is equal to segment $CFD$.


Modern Formulation

Similar segments are congruent if their bases are equal in length.

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