Proposition: 4.01: Fitting Chord Into Circle

Euclid's Formulation

To insert a straight line equal to a given straight line into a circle, (the latter straight line) not being greater than the diameter of the circle.


Modern Formulation

It is possible to construct a chord of a circle with a length less or equal to the diameter.

Proofs: 1

Proofs: 1 2 3 4 5
Sections: 6

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