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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.

Modern Formulation

If two circles intersect, then their centers are different.

Table of Contents

Proofs: 1

Mentioned in:

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