Proposition: 1.09: Bisecting an Angle

(Proposition 9 from Book 1 of Euclid's “Elements”)

To cut a given rectilinear angle in half. * Let $BAC$ be the given rectilinear angle. * So it is required to cut it in half.


Modern Formulation

It is possible to bisect a given angle \(\angle{BAC}\).

Proofs: 1

Corollaries: 1
Proofs: 2 3 4 5 6
Propositions: 7 8
Sections: 9

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



Adapted from CC BY-SA 3.0 Sources:

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

Adapted from (Public Domain)

  1. Casey, John: "The First Six Books of the Elements of Euclid"

Adapted from (subject to copyright, with kind permission)

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