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    I can’t read German however I don’t see any indication that the text is introducing a new notation.

    It should be remembered that calculus began with notion of infinitesimal and only gradually developed a rigorous development so the notion of “orders of infinity” may be hard to trace exactly.

    That said, I vaguely recall that “big O” is just a part of a system of orders of infinity developed by Paul du Bois-Reymond and I think there’s support for that contention here, say: http://www-personal.umich.edu/~tappen/McCartyonduboisreymond.pdf