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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

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References

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", https://proofwiki.org/wiki/Main_Page, 2016