Eine wissenschaftstheoretische Analyse des Leibniz’schen calculus – das Beispiel des Krümmungsradius

Leibniz is one of the founders of calculus, a starting point of modern mathematics. A crucial point in the understanding of Leibniz’s calculus is the concept of differential, especially differential of higher order. In this article we discuss the first successful application of differentials of higher order, namely the determination of the radius of curvature. 1692 Jakob Bernoulli determined three formulas for this radius. Leibniz was not satisfied with the proofs of Bernoulli and published two years later a new elegant deduction. The article is a reconstruction of Bernoulli’s and Leibniz’s approaches showing the ingenious work of Leibniz in this field.