Definition: Def. 11.22: Axis of a Cylinder
(Definition 22 from Book 11 of Euclid's “Elements”)
And the axis of the cylinder is the stationary straight line about which the rectangle (constructing the cylinder) is turned.
Modern Formulation
(not yet contributed)
Mentioned in:
Definitions: 1
Proofs: 2
Propositions: 3
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