Leibniz at the peak of his mathematical fame

The article focusses on the decade between Leibniz's return from Italy in 1690 and the beginning of the public dispute over priority which was precipitated by Fatio's accusation of plagiarism in his Lineae brevissimi descensus investigatio geometrica of 1699. The prehistory of this decade, namely the discovery of differential and integral calculus and the absence of any real response, has been dealt with exhaustively in secondary literature. The same is true also of the later dispute between Continental and English mathematicians over the priority of the two great methods of modern analysis and the question of the possible dependency of the one upon the other. The aim of the present paper is to show how the widespread applications of Leibniz's calculus and its power to perform successfully were extended during the period under consideration. It shows also that while advocates of his method increasingly determined events, its ingenious discoverer was admired and held in high esteem. In view of such success on the Continent it was unavoidable that English mathematicians found themselves forced to assert the priority of Newton's method of fluxions and the supposed dependency of Leibniz's calculus on it. In the decade concerned both Leibniz and Newton tried to prevent a public dispute breaking out. However, they soon recognized that they themselves were not free from socio-political and scientific constraints.