Printing Leibniz's Calculus: Dating and Numbering the Editions of the Nova Methodus pro Maximis et Minimis (October 1684)

The textual history of the first work on infinitesimal calculus and differentiation in print—Gottfried Wilhelm Leibniz’s ‘Nova methodus pro maximis et minimis …’ in the October 1684 instalment of the Leipzig scientific journal Acta Eruditorum—remains unstudied. Consequent to this inattention, extant copies of Leibniz’s article have been assigned to a single edition and a single press, despite evidence of substantive variation among them. This article examines the typographic and bibliographical evidence across multiple copies of the October 1684 instalment of the Acta to demonstrate that these extant copies in fact represent three separate editions printed on multiple presses over many years. This evidence, in turn, casts new light on both the complex printing history of the Acta Eruditorum in its first decade of publication (1682–93) and the distribution of learned periodicals in the seventeenth century.

Activities in the Secondary School

In this chapter there is the presentation of a vertical path on the main topics of arithmetic-algebra-infinitesimal calculus and numerical methods, which are an object of study in the secondary school. Naturally, the attention will be focused on the “virtual” phase, that is the applications with the computer and the MatCos 3.X environment, both as graphical-numerical experimentation, of intuitive support to the understanding of the concepts, that as a necessary moment for the actual calculation in the applications. It presents a TLS based on a real problem, from which the whole presented methodology shines through: from problem solving, to mathematical and numerical modeling, to the formulation of the solving algorithm and its implementation in the MatCos 3.X environment.

The Indivisibles of the Continuum

This chapter considers some significant developments in seventeenth-century mathematics which are part of the pre-history of the infinitesimal calculus. In particular, I examine the “method of indivisibles” proposed by Bonaventura Cavalieri and various developments of this method by Evangelista Torricelli, Gilles Personne de Roberval, and John Wallis. From the beginning, the method of indivisibles faced objections that aimed to show that it was either conceptually ill-founded (in supposing that the continuum could be composed of dimensionless points) or that its application would lead to error. I show that Cavalieri’s original formulation of the method attempted to sidestep the question of whether a continuous magnitude could be composed of indivisibles, while Torricelli proposed to avoid paradox by taking indivisibles to have both non-zero (yet infinitesimal) magnitude and internal structure. In contrast, Roberval and Wallis showed significantly less interest in addressing foundational issues and were content to maintain that the method could (at least in principle) be reduced to Archimedean exhaustion techniques.