Definition: Def. 11.19: Axis of a Cone
(Definition 19 from Book 11 of Euclid's “Elements”)
And the axis of the cone is the fixed straight line about which the (rightangled) triangle (constructing the cone) is turned.
Modern Formulation
(not yet contributed)
Mentioned in:
Definitions: 1 2
Thank you to the contributors under CC BYSA 4.0!
 Github:

 nonGithub:
 @Fitzpatrick
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