◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--4-inscription-and-circumscription / Proposition: 4.01: Fitting Chord Into Circle

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.

• Let $ABC$ be the given circle, and $D$ the given straight line (which is) not greater than the diameter of the circle.
• So it is required to insert a straight line, equal to the straight line $D$, into the circle $ABC$.

Modern Formulation

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

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3 4 5
Sections: 6

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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