Certainly not a fully-fledged theory of them. But he did seem to
have the idea that it made sense to calculate with such things in a simple
way. I have a photo-copy of the relevant pages (not the whole book), so
can quote how he introduces these formulae.
"Wenn man die Menge aller in einem und demselben reellen einfoermigen
Gebilde enthaltenen reellen Elemente durch n + 1 bezeichnet und mit
diesem Ausdrucke, welcher dieselbe Bedeutung auch in den acht folgenden
Nummern hat, wie mit einer endlichen Zahl verfaehrt, so ...."
Here's my crude translation, wide open to correction.
"If the set of all real elements in one and the same real uniform structure
is labelled n + 1, and this expression (which has the same meaning in the
next eight sections) is treated like a finite number, then ...."
(His "real uniform structure" is a technical term which he has just
introduced.) Notice particularly that he says the set of elements is
_labelled_ n + 1, which is then _treated_like_ a finite number. It's
also perhaps interesting that he used the words "Menge" (set) and
"Elemente" (elements) exactly as Cantor did later.
Ken Pledger.