Justification of the Differential Calculus

Justification of the Differential Calculus

This section presents several texts written by Leibniz in the context of the famous “Querelle des infiniment petits”, that agitated the French Académie royale des Sciences, after the attacks launched by Michel Rolle and Thomas Gouye in 1700. Leibniz first sent a letter which was published almost in extenso in the Mémoire de Trevoux [Leibniz 1701b]. However, this text raised a lot of perplexity, even amongst Leibniz’ supporters, since it contained a comparison between the various orders of differentials and fixed and finite entities such as a grain of sand and the sun (GM V 96). Being asked about these comparisons by Varignon, Leibniz replied in the famous letter of 2 February 1702, that it was a coarse way of speaking and that infinitesimals should not be seen as fixed entities (published in the Journal des Sçavans [Leibniz 1702]). The Justification was conceived as a follow up to this letter aimed specifically at critique coming from Rolle. It was sent again to Pinsson for Varignon for publication in the Journal des Sçavans, but the project did not succeed. The Cum Prodiisset, written at the same period, provides a different strategy for the foundation of the differential calculus (based not only on the law of continuity, but also on the use of varying ratios of finite quantities). The beginning of The Defense du calcul summarizes these various strategies and testifies to Leibniz’ pluralistic approach to the justification of his calculus.