This may well be true, but it doesn't answer my original question. Let me
recapitualte it. In certain, very common, circumstances we wish to assign
an object to each equivalence class, such that distinct objects are
assigned to distinct equivalence classed (for example, if the equivalence
relation is ...parallel to --- then the new object is called `direction';
it the equivalnce relation is equinumerosity then the new object is called
`cardinal number').
The older practice was to introduce the required objects as new primitives.
(This procedure was called `abstraction'.) The usual *modern* practice is
to take the equivalence classes *themselves* as the required new objects.
Of course, this presupposes a set-theoretic ontology, in which infinite
classes can be regarded as objects. This modern procedure was, essentially,
followed by Frege in his definition of [cardinal] number.
My question was: who was the first to use this modern procedure.
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