Entre Varignon et Grandi : une proposition leibnizienne sur les plus qu’infinis
摘要
In April 1712, Leibniz published a note in the Acta eruditorum entitled: "Observation on the Fact that Ratios and Proportions Do Not Apply to Quantities Less Than Nothing." This text is famous for having initiated the quarrel with Jean Bernoulli over the logarithms of negative numbers. However, this fame has obscured some important aspects on which I intend to reflect in this study. The last lines of the article inform us that it was initially conceived as an intervention in a controversy that was raging at the time around the "more than infinite". This explains part of the title of Leibniz's article, often omitted when cited, yet significant: "on the true meaning of the infinitesimal method" (de vero sensu Methodi infinitesimalis). Indeed, if we consider his position not in relation to its aftermath, but in relation to its origin, we see that this article directly follows an intervention by Pierre Varignon published in the same journal, which itself responded to a work on the "infinities of infinities" published in 1710 by Guido Grandi. The aim of this article is to retrace this history in order to better identify the position that Leibniz advocated in this controversy.