Proposition: 3.34: Construction of Segment on Given Circle Admitting Given Angle

(Proposition 34 from Book 3 of Euclid's “Elements”)

To cut off a segment, accepting an angle equal to a given rectilinear angle, from a given circle.


Modern Formulation

It is possible to construct segment of a circle, such that its inscribed angle ($\angle{CAB}$) is equal to a given rectilinear angle ($\angle D$) and its vertex ($A$) is located on this segment.

Proofs: 1

Sections: 1

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



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",, 2016