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.


Proofs: 1

Proofs: 1 2 3 4
Sections: 5

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



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"