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

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

And to draw a circle with any center and radius.

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]


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[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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