Explanation: 1.1: Equality is an Equivalence Relation
(related to Subsection: Common Notions (all Books))
(Common Notion 1 from Book 1 of Euclid's “Elements”)
Things equal to the same thing are also equal to one another.
Modern Formulation
see any equality is an equivalence relation.
Mentioned in:
Axioms: 1
Proofs: 2 3 4 5 6 7
Propositions: 8
Sections: 9
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"