Definition: Def. 11.17: Diameter of a Sphere
(Definition 17 from Book 11 of Euclid's “Elements”)
And the diameter of the sphere is any straight line which is drawn through the center (of the sphere) and terminated in both directions by the surface of the sphere.
Modern Formulation
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Mentioned in:
Corollaries: 1
Proofs: 2 3 4 5 6 7 8
Propositions: 9 10 11 12
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016