◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--3-circles / Definition: 3.06: Segment of a Circle, Arc

Definition: 3.06: Segment of a Circle, Arc

A segment of a circle is the figure contained by a straight line and a circumference of a circle.

Modern Formulation

A segment of a circle is a figure bounded by a chord and an arc of a circle, whose endpoints are the endpoints of the chord.

Please note that each chord generates two segments, because there are two arcs whose endpoints are the endpoints of the chord. Which segment is meant, shall be made clear from the context.

Mentioned in:

Definitions: 1 2 3
Proofs: 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Propositions: 25 26 27 28 29 30 31 32 33 34 35 36 37 38

Thank you to the contributors under CC BY-SA 4.0!

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References

Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"