Proposition: 3.04: Chords do not Bisect Each Other

(Proposition 4 from Book 3 of Euclid's “Elements”)

In a circle, if two straight lines, which are not through the center, cut one another then they do not cut one another in half.


Modern Formulation

Let $AC$ und $BD$ be chords, which do not go through the center of a given circle. If $AC$ and $BD$ cut one another, then they do not bisect each other.

Proofs: 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