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.
 Let $ABCD$ be a circle, and within it, let two straight lines, $AC$ and $BD$, which are not through the center, cut one another at (point) $E$.
 I say that 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.
Table of Contents
Proofs: 1
Thank you to the contributors under CC BYSA 4.0!
 Github:

 nonGithub:
 @Fitzpatrick
References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016