Proposition 29
Theorem
In equal circles, equal arcs (ABC , DEF ) are subtended by equal chords (AC , DF ).
Commentary
1. Let circle ABC and circle DEF be equal and let arc ABC and arc DEF be two equal arcs of the circles.
2. The chordAC subtends the arc ABC and the chord DF subtends the arc DEF .
3. ThenAC and DF are equal.
4. This proposition is a partial converse of the previous proposition, Euclid Book 3 Proposition 28.
2. The chord
3. Then
4. This proposition is a partial converse of the previous proposition, Euclid Book 3 Proposition 28.
Original statement
ἐν τοῖς ἴσοις κύκλοις τὰς ἴσας πϵριϕϵρϵίας ἴσαι ϵὐθϵῖαι ὑποτϵίνουσιν.
English translation
In equal circles equal circumferences are subtended by equal straight lines.
