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Proposition: 3.10: Two Circles have at most Two Points of Intersection

(Proposition 10 from Book 3 of Euclid's “Elements”)

A circle does not cut a(nother) circle at more than two points.

Modern Formulation

Two circles cut or touch one another in at most two points.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1

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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