**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?

### 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

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