One of the most famous critiques of the Leibnitian calculus is contained in the essay “The Analyst” written by George Berkeley in 1734. His key argument is those on compensating errors. In this article, we reconstruct Berkeley's argument from a systematical point of view showing that the argument is neither circular nor trivial, as some modern historians think. In spite of this well-founded argument, the critique of Berkeley is with respect to the calculus not a fundamental one. Nevertheless, it highlights (...) central aspects of the calculus that are characteristic of modern scientific theories. (shrink)

Leibniz is one of the founders of calculus, a starting point of modern mathematics. A crucial point in the understanding of Leibniz' 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' approaches showing the ingenious work of Leibniz in this field. (shrink)