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 $BC$.
Given an arbitrary segment, it is possible to construct an equilateral triangle on that segment.
Table of Contents
Proofs: 1 2 3 4
Thank you to the contributors under CC BY-SA 4.0!
Adapted from CC BY-SA 3.0 Sources:
- Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014
Adapted from (Public Domain)
- Casey, John: "The First Six Books of the Elements of Euclid"
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"