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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 \(a\).

| | | | | created: 2014-06-14 20:33:50 | modified: 2019-03-23 08:20:05 | by: bookofproofs | references: [626], [628], [6419]

1.Explanation: Why did Euclid postulate the axiom of straight line determined by two points?


This work was contributed under CC BY-SA 3.0 by:

This work is a derivative of:

CC BY-SA 4.0

[626] Callahan, Daniel: “Euclid’s ‘Elements’ Redux”, http://starrhorse.com/euclid/, 2014

Freely downloadable

[6419] Fitzpatrick, Richard: “Euclid’s Elements of Geometry”, http://farside.ph.utexas.edu/Books/Euclid/Euclid.html, 2007

Public domain

[628] Casey, John: “The First Six Books of the Elements of Euclid”, http://www.gutenberg.org/ebooks/21076, 2007

Bibliography (further reading)

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