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.

Modern Formulation

If two circles intersect, then their centers are different.

Proofs: 1

Proofs: 1
Sections: 2


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References

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", https://proofwiki.org/wiki/Main_Page, 2016