Axiom: 1.1: Straight Line Determined by Two Distinct Points
(Postulate 1 from Book 1 of Euclid's “Elements”)
Let it have been postulated to draw a straight line from any point to any point.
Modern Formulation
Two distinct points \(A\) and \(B\) always completely determine a straight line \(a\).
Instead of saying "is determined", we also say that
- \(a\) "goes through" \(A\) and \(B\),
- \(A\) and \(B\) "lie" on \(a\).
Table of Contents
Explanations: 1
Mentioned in:
Axioms: 1
Definitions: 2 3 4
Motivations: 5
Parts: 6
Proofs: 7 8 9 10 11 12
Theorems: 13
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:
- 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"
