Proposition: 3.28: Straight Lines Cut Off Equal Arcs in Equal Circles
(Proposition 28 from Book 3 of Euclid's “Elements”)
In equal circles, equal straight lines cut off equal circumferences, the greater (circumference being equal) to the greater, and the lesser to the lesser.
![fig28e](https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/euclid/Book03/fig28e.png?raw=true)
Modern Formulation
The arcs are congruent (the longer ones ${ACB}\cong {DFE}$ and the shorter ones ${AGB}\cong {DHE}$) if segments with equal lengths ($|\overline{AB} | = | \overline{DE} |$) connect their endpoints in congruent circles.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2
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References
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016