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

Explanations: 1

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!



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"