Definition: 4.4: Circumscribing Rectilinear Figures about Circles
(Definitions 4 from Book 4 of Euclid's “Elements”)
And a rectilinear figure is said to be circumscribed about a circle when each side of the circumscribed (figure) touches the circumference of the circle.
Modern Formulation
A rectilinear figure (\(n\)sided figure, \(n \ge 3\)) is said to be circumscribed about a circle when each side of the figure is tangent to the circumference of the circle.
Example
The pentagon is circumscribed about a circle:
Mentioned in:
Corollaries: 1
Definitions: 2
Proofs: 3 4 5 6 7
Propositions: 8 9 10
Thank you to the contributors under CC BYSA 4.0!
 Github:

 nonGithub:
 @Fitzpatrick
References
Bibliography
 Byrne, O.: "The First Six Books of the Elements of Euclid, in Which Coloured Diagrams and Symbols are used Instead of Letters", London William Pickering, 1847
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