 Cauchy chose to characterize the continuity of functions in terms of a rigorized notion of infinitesimal, which he defines in the Cours d’analyse as “a variable quantity [whose value] decreases indefinitely in such a way as to converge to the limit 0” (Kline 1972: 951). Here is his definition of continuity. Cauchy’s definition of continuity of \(f(x)\) in the neighborhood of a value \(a\) amounts to the condition, in modern notation, that \(\lim_{x\rightarrow a}f(x) = f(a)\). Cauchy defines the derivative \(f '(x)\) of a function \(f(x)\) in a manner essentially identical to that of Bolzano.