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

In 1974 Edwin Wolf noticed that the Library Company of Philadelphia’s copy of the October 1684 instalment of the Leipzig scientific journal Acta Eruditorum contained a form of the ‘Nova Methodus pro maximis et minimis’¹ that belonged to ‘a completely different printing of Leibnitz’s [sic] classic article on calculus than that reproduced by Harrison Horblit, One Hundred Great Books of Science (New York, 1964)’. Wolf further observed that this second printing remained unrecorded and suggested that the sequence or priority of the two was unknown: ‘That there were two printings of this [instalment] of the Acta has not previously been stated. Which was the first has not been determined.’² This article examines the bibliographical and typographic evidence to establish the sequence and dates of publication of these two editions (Wolf characterizes them as ‘printings’, i.e. ‘impressions’); it also describes a third, unrecorded edition of Leibniz’s ‘Nova Methodus’ for the first time.³

The existence of three unrecognized editions of one of the most significant papers in the history of mathematics—each of which conveys a substantively variant form of Leibniz’s text—is worthy of note. In what follows, I illustrate and characterize each of these three editions to aid in their identification, differentiation, and study. The printing evidence and the evidence of distinctive or damaged type I describe here also demonstrates the erratic nature of the production of the Acta Eruditorum (the first learned journal to be published in German-speaking Europe) in its first decade and therefore hints at the intricacies of scholarly periodical publication when the genre was new. In interpreting this evidence, I conclude the article by forwarding some preliminary theories about the printing, reprinting, and distribution of the Acta Eruditorum in its first fitful years of publication.

Scholars have long recognized the bibliographical complexities inhering in Leibniz’s paper. Clara Silvia Roero, for instance, has characterized the printing history of the ‘Nova Methodus’ as ‘enigmatic’.⁴ One cause of the confused nature of its printing was likely Leibniz’s interest in establishing the priority of his work on the calculus at a relatively early date. Heinz-Jürgen Hess observes that an article published in the May 1683 instalment of the Acta Eruditorum by Ehrenfried Walter von Tschirnhaus (1651–1708) put Leibniz at risk of losing out on his claim to priority.⁵ That Leibniz’s paper appeared in the following volume of the Acta speaks to one of Leibniz’s motives—precedence. However, while the cause of the erratic printing of Leibniz’s ‘Nova Methodus’ has been subject to some debate, the progress of Leibniz’s calculus through the press, and any errors introduced due to the ostensibly hurried nature of its printing have yet to be fully examined.

The question of bibliographic unit

The bibliographic unit treated here is not the annual volume (or Jahrbuch) of the Acta Eruditorum for 1684, but rather the single monthly instalment for October that contains Leibniz’s ‘Nova Methodus’. This selective focus is in part consequent on the assortment of editions of monthly instalments that can make up any single annual volume of the journal. In other words, a first-edition January instalment was not necessarily joined by a first-edition May instalment when they came to be bound together. Identifying patterns in how the constituent instalments of annual volumes were assembled and bound would necessarily involve an examination of multiple copies of each annual volume—a task beyond the scope of this article. Suffice to say that the evidence suggests that copies of the various editions of monthly instalments were issued to subscribers and buyers somewhat haphazardly; any given subscriber might have received a first edition of a particular instalment in one month and a second edition instalment in the next. What’s more, this disregards the added complexity of back-issues of particular instalments ordered months, or even years after the date of initial publication, or second-hand copies acquired belatedly to fill out incomplete sets. Second...