Proposition: 1.02: Constructing a Segment Equal to an Arbitrary Segment

(Proposition 2 from Book 1 of Euclid's “Elements”)

To place a straight line equal to a given straight line at a given point (as an extremity).


Modern Formulation

Given an arbitrary point \(A\) and an arbitrary segment \(\overline{BC}\), it is possible to construct a segment \(\overline{AF}\) such that its length is equal to the length of \(\overline{BC}\).

Proofs: 1

Proofs: 1
Sections: 2

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"