The calculus according to Leibniz - A reconstruction (Concept of differential)

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.