**Axiom**: 1.2: Circle Determined by its Center and its Radius

### (Postulate 3 from Book 1 of Euclid’s “Elements”)

### Modern Formulation

A point \(A\) and a given segment \(\overline{AB}\) always completely determine a circle \(c\). Instead of saying “determine”, we also say that \(c\) “is the circle with the center” \(A\) “of the radius” \(\overline{AB}\).

| | | | | created: 2014-06-14 21:01:23 | modified: 2019-03-23 08:20:23 | by: *bookofproofs* | references: [626], [628], [6419]

### 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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