Proposition: 3.05: Intersecting Circles have Different Centers

(Proposition 5 from Book 3 of Euclid's “Elements”)

If two circles cut one another then they will not have the same center. * For let the two circles $ABC$ and $CDG$ cut one another at points $B$ and $C$. * I say that they will not have the same center. fig05e

Modern Formulation

If two circles intersect, then their centers are different.

Proofs: 1

Proofs: 1
Sections: 2

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