"The statement is so frequently made that the differential calculus deals with continuous magnitude, and yet an explanation of this continuity is nowhere given; even the most rigorous expositions of the differential calculus do not base their proofs upon continuity but, with more or less consciousness of the fact, they either appeal to geometric notions or those suggested by geometry, or depend upon theorems which are never established in a purely arithmetic manner. ...It then only remained to discover its true origin in the elements of arithmetic and thus at the same time to secure a real definition of the essence of continuity. I succeeded Nov. 24, 1858."
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, Stetigkeit und irrationale Zahlen (1872) translated in Essays on the Theory of Numbers (1909) by Wooster Woodruff Beman, p. 2.
https://en.wikiquote.org/wiki/History_of_calculus
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History of calculus
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