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Proposition: 1.01: Constructing an Equilateral Triangle

(Proposition 1 from Book 1 of Euclid's “Elements”)

To construct an equilateral triangle on a given finite straight line.

• Let $A$ be the given point, and $BC$ the given straight line.
• So it is required to place a straight line at point $A$ equal to the given straight line $BC$.

Modern Formulation

Given an arbitrary segment, it is possible to construct an equilateral triangle on that segment.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3 4
Sections: 5

Thank you to the contributors under CC BY-SA 4.0!

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non-Github:

@Calahan

@Casey

@Fitzpatrick

References

Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

1. Casey, John: "The First Six Books of the Elements of Euclid"

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"