Proposition: 3.29: Equal Arcs of Circles Subtended by Equal Straight Lines
(Proposition 29 from Book 3 of Euclid's “Elements”)
In equal circles, equal straight lines subtend equal circumferences.
- Let $ABC$ and $DEF$ be equal circles, and within them let the equal circumferences $BGC$ and $EHF$ have been cut off.
- And let the straight lines $BC$ and $EF$ have been joined.
- I say that $BC$ is equal to $EF$.
Modern Formulation
The segments ($\overline{BC}$, $\overline{EF}$) have equal lengths, if they connect the endpoints of two arcs being congruent in congruent circles.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3
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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
