In the history of mathematics Leibniz as one of the scientists who developed the calculus of differentials has an outstanding position. However, it is difficult to reconstruct his theory in a consistent way. The main problem is the concept of differential. For an adequate understanding of this concept it is necessary to analyze how it is used. In this article we deal with the first systematic formulation of Leibniz' calculus, the Lectiones de calculo differentialium of Johann Bernoulli from 1691/92. It (...) will be proved that Leibniz's theory is consistent and can be reconstructed as an empirical theory - concerning physical curves - within the structuralist metatheory. The concept of differential is a theoretical one in respect to this theory. (shrink)

For an appropriate understanding of Leibniz's calculus the concept of differential is a crucial one. In Die Differentialrechnung nach Leibniz -eine Rekonstruktion (published in this journal in 2001) the calculus differentialis of Leibniz was analysed. In this paper we deal with the first systematic formulation of the calculus integralis, the Lectiones mathematicae de methodo integralium aliisque of Johann Bernoulli from 1691/92. It will be pointed out that Leibniz's theory is consistent and can be reconstructed as an empirical theory within the (...) structuralist metatheory. (shrink)