Definition: Def. 11.16: Center of a Sphere
(Definition 16 from Book 11 of Euclid's “Elements”)
And the center of the sphere is the same as that of the semicircle (constructing the sphere).
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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