From Wikipedia on cardinal numbers:
The oldest definition of the cardinality of a set $X$ (implicit in Cantor and explicit in Frege and Principia Mathematica) is as the class $[X]$ of all sets that are equinumerous with $X$.
My question is simple:
Who was the first to state explicitly that the length of a line segment $l$ is the class $[l]$ of all line segments that are equal to $l$ (in the sense of Euclid)? And who can be assumed to have known or considered this implicitly? Euclid himself?
Probably not the first but a very important author did state it like this:
(Hartshorne, Geometry: Euclid and beyond (1997), p. 3)