Abstract
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.
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‐ Jurgen 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, I treat only the October 1684 instalment due to the fact that monthly instalments formed the basic bibliographic (or production) unit of the Acta Eruditorum; that is to say, the press was set up to print monthly instalments singly. The bibliographical implications of this fact should be spelled out: properly speaking, there are no distinct editions of the Acta’s annual volumes. Rather, each annual volume might contain various editions of its constituent monthly instalments. I return to this question below.
Distinguishing the three editions of the ‘Nova Methodus’
All three editions of Leibniz's ‘Nova Methodus’ were printed in Leipzig— the first and second editions by Christoph Gunther and the third edition by Christian Gotze (as shown below)—and comprise seven pages of the October instalment of the 1684 volume of the Acta Eruditorum.6 All instalments of the Acta Eruditorum in its first decade were edited by Otto Mencke and published by a consortium that comprised Leipzig booksellers Johann Grosse and Johann Friedrich Gleditsch.7 These monthly instalments were evidently assembled by subscribers over the course of a year and bound up into annual volumes only after the preliminaries had arrived with the December instalment.8 Each successive monthly instalment was paginated and signed in an uninterrupted sequence from January through December. The monthly instalments comprising the annual volume for 1684, for example, collate A‐4F4 with pagination [10] 1‐591 [7]. Singly, the October 1684 instalment collates 3K‐3P4 and is paginated 439‐486. Leibniz's article, appearing near the end of the October 1684 instalment, collates 3N3r ‐ 3O2r and is paginated 467‐473 in all three editions. Invariant in signing and pagination, then, the three editions of the ‘Nova Methodus’—and, by extension, the three editions of the October 1684 instalment in which the three editions of the ‘Nova Methodus’ appear—can be distinguished by the layout and typography of the first page of Leibniz's article (p. 467), as follows:
Page 467 of the first edition of the October, 1684 installment. Image courtesy of The Dibner Library of the History of Science and Technology (Washington, D.C.): Z1007 .A18 1684/5.
Page 467 of the second edition October, 1684 installment. Image courtesy of The Ohio State University Rare Books and Manuscripts Library: Z1007.A43 1684.
Page 467 of the third edition October, 1684 installment. Image courtesy of The Houghton Library, Harvard University: Houghton GEN BP 431.1.
Ordering the three editions: the evidence of errata
The first edition of the ‘Nova Methodus’ dates to October 1684 and was printed in September of that year by the Leipzig printer Christoph Gunther. As A. H. Laeven notes in his study of the Acta Eruditorum, each instalment of the journal was edited and printed to a monthly deadline and was typically ready for distribution on the first day of each month.9 While the date of the second edition is open to doubt, the sequence of the first and second editions is easily established. On the final leaf verso of the March 1685 instalment appears an errata notice correcting errors in Leibniz's then five‐month‐old article (Fig. 4).
The errata printed at the end of the March, 1685 instalment correcting errors in the ‘Nova Methodus’, p. 142; these corrections are incorporated into the second and third editions (see figs. 5a-c). Image courtesy of The Dibner Library of the History of Science and Technology (Washington, D.C.): Z1007 .A18 1684/5.
Notably, only the second and third editions of Leibniz's text incorporate these errata, suggesting that they were printed after the errors were discovered and the errata issued in March 1685 (see Figs. 5a‐c).10 These errata correct mistakes in Leibniz's formulae: the first moves ‘ydv’ in the first line of page 469 into the numerator; the second adds a derivative of x (‘dx’) to the ninth line of page 469; the third adds the phrase ‘inde ab ipso’ to the eighth line of page 471; and the final correction to page 472 replaces the variable m with the variable g in lines 11 and 12.
a. The uncorrected formula on page 469 of the first-edition October instalment. Image courtesy of Carnegie Mellon University Libraries Special Collections: Poster Memorial Collection QA304 .L45X 1684.
b. The partly corrected formula on page 469 of the second-edition October instalment (note the accidental omission of YY in the denominator and the missing crossbar above the second cross in the numerator). Image courtesy of The Ohio State University Rare Books and Manuscripts Library: Z1007 .A43 1684.
c. The fully corrected formula on page 469 of the third-edition October instalment (note the YY in the denominator). Image courtesy of Princeton University Library, Rare Books and Special Collections: 0958.113 1684/85.
While the sequence of the second and third editions—both of which convey the same, corrected form of Leibniz's text—is more difficult to determine, a set of corrigenda published at the end of the first index volume for the Acta Eruditorum provides another delimiting date (Fig. 6).11 This index volume, printed in Leipzig in May or June 1693 and titled Indices Generales Auctorum et Rerum Primi Actorum eruditorum quae Lipsiae publicantur Decennii [...], was the first decennial index for the Acta Eruditorum to be issued.12 Apparently submitted by Leibniz himself, these 1693 corrigenda are substantive: one calls for the deletion of an entire paragraph, and another for the revision of Leibniz's style of notation.13 None of the 1693 corrections are incorporated into any of the three editions of Leibniz's ‘Nova Methodus’, however. This suggests that the second and third editions of the October 1684 instalment were printed and issued prior to 1693—that is, before Leibniz submitted these final corrigenda. The date of the 1693 index volume consequently provides a tentative terminus ante quem for both the second and third editions of Leibniz's article: May 1693.
The 1693 Indices corrigenda correcting errors in Leibniz's ‘Nova Methodus.’ Image courtesy of The Dibner Library of the History of Science and Technology (Washington, D.C.): Z1007 .A18 Index 1693.
In addition to providing evidence useful in dating the second and third editions of the October 1684 instalment, these corrigenda are also significant, in that they reflect Leibniz's interest in refining mathematical notation to better suit typographic expression. To be sure, the inconsistent disposition of the mathematical content in all three editions of the ‘Nova Methodus’ (see Figs. 1‐3) may have influenced Leibniz's thinking on the matter and prompted some of the changes he submitted for publication in the 1693 Indices. In 1696, for instance, Leibniz suggested to the Swiss mathematician Johann Bernoulli that ratios be expressed with a colon—‘that a:b be the same as a/b’ due to the fact that it ‘is very easily typed [and] the spacing of the lines is not disturbed’.14 Later, in another letter to Johann Bernoulli, Leibniz observed that he endeavoured to mark mathematical operations in a manner that would ‘diminish the task of type‐setting’ and ensure that ‘the line of type is not broken, nor the spacing disturbed’—two problems that recur in all three editions of the ‘Nova Methodus’.15 One of Leibniz's 1693 corrigenda, altering the signa ambigua (±, 
) to ‘+’ and ‘_’, respectively, arguably fits with this interest in improving the clarity and economy of mathematical expression in type: the altered forms require no special characters and could be provisioned from a standard case of type. Leibniz plainly viewed these kinds of modification to mathematical notation as essential to the reformation and correct practice of mathematics: ‘[i]n signs one observes an advantage in discovery which is greatest when they express the exact nature of a thing briefly and, as it were, picture it; then indeed the labour of thought is wonderfully diminished’.16
Leibniz's quasi‐editorial work on the Acta Eruditorum and his involvement in its early planning and publication is well documented, but relatively little is known about what role, if any, Leibniz played in determining the design and typography of the journal. As Maria Rosa Antognazza notes, ‘as early as October 1668, and then again in 1669 and in 1670, Leibniz himself had proposed the establishment of a [...] journal’ akin to the Acta Eruditorum, titled Nucleus Librarius Semestralis.1718 With these early designs abandoned in 1681, Leibniz was enlisted as a willing participant in establishing a journal that would follow the model of the French Journal des Sfavans.18 This journal would become the Acta Eruditorum, with its first instalments appearing in 1682. Besides Leibniz's involvement in the early development of the Acta’s editorial programme, his correspondence suggests that he was also involved peripherally in the journal's design and typesetting. Heinz‐Jurgen Hess quotes from a letter sent to Leibniz from the Acta’s editor and publisher Otto Mencke describing the manufacture of mathematical symbols in small, letter‐sized woodblocks for inclusion in the apparently delayed ‘Nova Methodus’. In this same letter Mencke requests Leibniz's opinion on their practicality: ‘The brief treatise on the method of tangents, etc. will be found in the October instalment, as the printer has had to cut some characters in wood [einige characteres in Holtz schneiden] for this purpose. Whether it was done well I would like to hear.’19 The ‘characters’ Mencke refers to are most likely the crosses pattée (
) and radical signs or root symbols (√) used throughout Leibniz's article, as the variability of these symbols on the page suggests that they were cut in wood, rather than punched and cast in metal.
Evidently Leibniz's involvement in the printing of the ‘Nova Methodus’ and the Acta was considerable; and the corrigenda printed in the 1693 Indices volume demonstrate one form that this involvement took. Surprisingly, then, the 1693 corrigenda have only recently been treated as authorial in the literature on the infinitesimal calculus.20 While Carl Immanuel Gerhardt's still standard 1858 edition of the ‘Nova Methodus’ makes some of the corrections detailed in the 1693 corrigenda, most of the errors remain: for example, the paragraph Leibniz ultimately omitted and a formula the corrigenda sought to clarify are both left standing.21 The corrections that the 1858 edition does introduce are apparently the product of Gerhardt's own editorial intervention, made without recourse to the 1693 corrigenda, which Gerhardt does not acknowledge. More recently, both D. J. Struik's and Evelyn Walker's edited translations of Leibniz's ‘Nova Methodus’ fail to incorporate or acknowledge the 1693 corrigenda.22 Struik's and Walker's translations evidently derive from copies or transcriptions of the third edition, though they may also derive from Gerhardt's edited text. Heinz‐Jurgen Hess, Clara Silvia Roero, and Pascal Dupont are apparently the first to record the existence of the 1693 corrigenda and to argue for their authority in interpreting Leibniz's calculus.23 And while Hess and Malte‐Ludolf Babin incorporate and treat the 1693 corrigenda in their recent edition and translation into German of the ‘Nova Methodus’, none of these authors note the existence of variant editions of Leibniz's article, and the 1693 corrigenda are still often characterized as emendations of typographical errors and errors in presswork only.24 On the contrary, the 1693 corrigenda represent Leibniz's final work on the ‘Nova Methodus’ and constitute slight yet important revisions to its mathematics and formulary. The 1693 Indices consequently merits reexamination and should be viewed as a meaningful contribution to the early refinement of the calculus.
To return to the problem of dating the three editions of the ‘Nova Methodus’, the evidence presented thus far suggests that all copies of the October 1684 instalment of the Acta Eruditorum were printed between September 1684 and May 1693—that is, the first edition was printed in September 1684; the second edition sometime after the March 1685 errata; and the third edition sometime after March 1685 and before June 1693, when Leibniz's final corrigenda for the ‘Nova Methodus’ were issued at the end of the first decennial Indices volume. The questions that remain, then, are: when between 1685 and 1693 were the second and third editions of the October instalment printed; and why were two new editions warranted?
The date and printer of the third edition: the evidence of type
While the dates of the errata correcting errors in Leibniz's ‘Nova Methodus’ are suggestive, the evidence of distinctive and damaged type assists in dating the printing of the second and third editions empirically. In the first and second editions, for instance, the printer employs only the cross pattee in Leibniz's formulae, while the printer of the third edition uses both the long, or ‘Latin’ cross and the cross pattee indiscriminately (cf. Figs. 1, 2, and 3). The spacing of the mathematical content in the third edition also varies significantly more than it does in the first and second editions, suggesting a different (less rigorous) process of setting mathematical content in type. This difference in typesetting and type implies that the first and second editions were printed by the same printer, while the third edition was printed by a second printer, who perhaps did not have access to the customcut mathematical symbols referred to in Leibniz's correspondence with Mencke.
The printing history of the Acta provides a clue as to the origin of these variations in type. As A. H. Laeven notes, the Acta was primarily printed by three printers in its first decade: ‘until 1692 [...] all issues of the Acta were printed by Christoph Gunther [...]. However, in a letter to Leibniz dated 24 February 1692, Mencke wrote that he had had disagreements with the firm of Gunther and was looking for a new printer for the February issue.’25 While the details of these ‘disagreements’ are unknown, Gunther's death eventually led to the transfer of the printing of the Acta, first to Gunther's widow, then to the firm of Andreas Zeidler in 1692, though it is unclear if Zeidler printed any instalments of the Acta.26 Thereafter, the printing of the Acta was transferred again, with the May and June instalments for 1692 appearing simultaneously, printed cooperatively by Leipzig printers Johann Georg and Christian Banckmann.27 After the summer of 1692, printing of the Acta passed briefly to Christian Gotze, who printed the remaining instalments for 1692, all instalments for 1693 and 1694, and the index volume of 1693, which contained Leibniz's final corrigenda for the ‘Nova Methodus’. After Gotze's brief tenure, Johann Georg again became the printer of the Acta and remained so from 1695 until his death in 1701.28
The title of the third‐edition October, 1684 instalment, p. 439. Note the broken serif in the first U and the gaps between the stem and the bowl of the second R. Note, too, the printer's use of capital Us without tail serifs. Image courtesy of Princeton University Library, Rare Books and Special Collections: 0958.113 1684/85.
Given what we know about the printing of the Acta in its first decade, the change in type in the third edition suggests that it was printed after the production of the Acta was transferred from Christoph Gunther in 1692. Conclusive evidence supporting this theory was found in the distinctive type used in the titles that appear at the head of individual monthly instalments. Namely, on the title‐page for the third edition of the October 1684 instalment appears a broken uppercase U and a distinctive uppercase R. As seen in Fig. 8, the rightmost outer serif of the first U is almost entirely broken away, while the junctures closing the stem and the bowl in the first R are broken away or poorly inked, resulting in two slight gaps where there should be sutures. This same sequence of type—the broken‐serif U and the loosely‐connected R—appears in the titles of instalments for 1692 and 1693 at the Dibner Library, all of which belong to a uniformly bound set of the Acta that contains a copy of the first edition of the October 1684 instal‐ ment.29 Specifically, the distinctive U and R evidently first appear in the first edition instalment for November 1692, again in December, and recur thereafter until August 1693—a period during which Christian Gotze was solely responsible for the production of the Acta (see Fig. 9). This idiosyncratic series of type appears nowhere else in the first decade of the Acta’s publication, demonstrating that the third edition of Leibniz's article was printed sometime between November 1692 and August 1693 by Christian Gotze. This typographic evidence also testifies to Gotze's use of standing type for the titles of monthly instalments of the Acta Eruditorum. Combining this typographic evidence with the fact that the 1693 corrigenda were printed in May or June provides an even narrower range of possible printing dates for the third edition: that is, between November 1692 and April 1693.
The same title, including the distinctive U and R, in the first‐edition, November, 1692 instalment, p. 505. Image courtesy of The Dibner Library of the History of Science and Technology (Washington, D.C.): Z1007 .A18 1692/3.
Narrowing the date of the second edition
Typographic evidence in the second edition similarly allows us to more accurately date its printing, or at least narrow considerably the range of possible dates, currently delimited by the appearance of the March 1685 errata (incorporated into the text of the second edition), and the death of Christoph Gunther and subsequent transfer of the printing of the Acta to the printer of the third edition, Christian Gotze, in 1692. That the second edition was printed by the Acta’s first printer, Christoph Gunther, is again demonstrated by the type used in the October instalment's title. Fig. 7 shows the title of the third edition of the October 1684 instalment (printed by Christian Gotze and discussed in the previous section), while Fig. 9 shows the title of the second edition of the October 1684 instalment. As demonstrated above, the typography of the former is typical of Christian Gotze between November 1692 and August 1693, while the typography of the latter is typical of Christoph Gunther from 1682 to about 1690. The most obvious distinguishing characteristics of Gunther's titles include tail‐serifed Us and the less‐pronounced serifs of the tie in the E.
While the type and disposition of its title‐page confirms that the second edition of the October instalment was printed by Christoph Gunther, determining the date of the second edition more precisely required an examination of Gunther's headlines. These appear in two forms between 1685 and 1691 in first‐edition copies. Namely, in two separate periods (between January 1685 and January 1686 and between December 1688 and December 1690) the uppercase Us in the running title, ‘ACTA ERUDITORUM’, have tail serifs (see Fig. 10). In the intervening period (between February 1685 and November 1688) these same Us lack tail serifs (see Fig. 12). Figure 11 shows that the headlines in the second edition of the October 1684 instalment lack tail‐serifed Us; it is logical to infer, then, that the second edition was printed by Christoph Gunther during this intervening period: February 1685 to November 1688.
The title of the second‐edition October, 1684 instalment, showing the distinctive type used by Christoph Gunther in the title of each installment. Note the tail‐serifed Us in ERUDITORUM. Image courtesy of The Ohio State University Rare Books and Manuscripts Library: Z1007.A43 1684.
The running title used by Christoph Günther before January, 1686 on p. 314 of the 1684 volume. Note the tail‐serifed Us. Image courtesy of WP Watson Antiquarian Books, London, UK.
The typographic evidence most useful in dating precisely the second edition of the October 1684 instalment, however, was found in its headline on page 474 (see Fig. 11). This same headline reappears on page 226 of the first‐edition instalment for May 1686 (Fig. 12). These two headlines match in every particular: the squat I, the slightly loose spacing between the T and the O, the upward curl of the terminal serif in the second R, and the bowllike, inward‐slanting serifs of the final U. While this same running‐title appears periodically throughout the first‐edition February, March, August, and September instalments for 1686, the visual similarities are closest in these two instances, suggesting that the second edition of the October 1684 issue (and the second edition of Leibniz's ‘Nova Methodus’ along with it) was printed sometime between May and July 1686—two years after the appearance of the first edition. The repeated headline also demonstrates that Gunther employed a standing skeleton forme in printing successive monthly instalments. And more precisely, it shows that Gunther kept his press active by printing back‐issues of individual instalments during interruptions to his regular work on the Acta.
The running title on p. 474 of the second‐edition ‘Nova Methodus’. Image courtesy of The Ohio State University Rare Books and Manuscripts Library: Z1007.A43 1684.
The same running title in the first‐edition, May 1686 installment, p. 226. Imagecourtesy of The Dibner Library of the History of Science and Technology (Washington, D.C.): Z1007 .A18 1686/7.
The typographic evidence is unequivocal. Extant copies of Leibniz's ‘Nova Methodus’ represent three separate editions of the October instalment, each of which can be dated to three separate years (1684, 1686, and 1692/3) and assigned to two separate printers (Christoph Gunther and Christian Gotze). Besides establishing the priority of these three editions, the typographic evidence reveals that individual instalments from the first decade of the Acta Eruditorum were reprinted many times and over many years. I consider briefly the implications of this fact below.
The plate
First, a note regarding the engraved geometric figure that accompanies Leibniz's ‘Nova Methodus’ in all three editions: this engraving, labelled ‘Tab. XII.’, was found to be invariant in design and layout in all copies examined. In a single, privately held copy of the third edition, however, the month has been added to the caption in the upper left corner of the plate, following the page number. This variant of the plate caption reads, ‘TAB. XII. | ad. A. 1684. p:467. M. Oct.’. In all other copies examined, this caption reads, ‘TAB. XII. | ad A. 1684. p:467.’ While the origin of this expanded caption remains obscure, it is likely that the copper matrix plate had been stored after the printing of the third edition of the text was complete in 1692 or 1693. Perhaps to ease in its later retrieval and reuse, the plate was labelled with the month. Subsequently, Otto Mencke and his booksellers, finding that they had more copies of the third‐edition text on hand than they had copies of the accompanying engraving, ordered further impressions of the plate pulled to be bound with these supernumerary copies of the text. This is speculative, of course; more work needs to be done on the plate, and ideally more copies of the ‘Nova Methodus’ bearing this later state of the engraving will surface. Despite this one anomalous copy, however, the existence of only one form of the engraving argues for the fact that all three editions of Leibniz's article were authorized—each, after all, is illustrated by the authorized and original plate, to which unauthorized printers would not have had access. Finally, while the origin of the added caption remains obscure, its sole appearance in a third‐edition copy of Leibniz's article serves to reinforce the sequence of editions presented here. Put simply, a later plate adverts a later text. There is also the possibility that this modified plate in fact represents an earlier state, with the later state printed from the same copper plate matrix after the ‘M. Oct.’ had been removed via a kind of chal‐ cographic pentimento.30 I think this is unlikely, however, given that the modified plate accompanies a copy of the third edition and that other plates found throughout the first decade of the Acta are labelled with the month in the same manner.
Reprinting & distributing the Acta Eruditorum
Why a new edition of a single monthly instalment would have been required nearly a decade after its first appearance is a subject only for speculation: as subscriptions increased during the first years of the journal's publication, demand may have arisen for earlier instalments of the Acta to fill out incomplete sets on the shelves of fastidious subscribers. In his catalogue of the Loganian Library (now at the Library Company of Philadelphia), Edwin Wolf quotes from a 1743 letter sent by James Logan to John Whiston: ‘If the Acta Erudit. Lipsiae of wch. I have ye 7 first voll in Parchmt could be procured for me not above 6 Sh[illings] p[er] ann[um] I shod desire those from 1689 to 1700 wth their Supllemy Inclusion’.31 This letter shows Logan ordering volumes of the Acta some fifty years after their initial publication, hinting at a robust (even transatlantic) trade in secondhand copies well into the eighteenth century. There is further evidence in Logan's correspondence that suggests he got what he asked for: six years later, in 1749, Logan remarked to Thomas Osborn, ‘I have all the Acta Eruditorium [sic] from 1688 to 1727 except for three intermediate years between 1700 & 1710 & some Supplem[en]ta’.32 While Logan's copies of the Acta were almost certainly acquired second‐hand, there is nothing to suggest that this kind of completist collecting did not exist earlier, when there were copies of back issues of instalments still available for sale in book markets and stalls across Europe—until, of course, there were not. Lacking a supply to meet belated orders or subscriptions like Logan's, Otto Mencke may have had more copies printed intermittently as needed. There is also the possibility of piracy—the second and third editions may have been unauthorized printings of the first—, though I think this unlikely given the scale, speed, and complexity of the Acta’s production and distribution (on the question of piracy, see the preceding section above).
Why have these three editions gone unrecognized for so long? For one, as demonstrated by Figs 1, 2 and 3, they are difficult to distinguish. The compositors working on the Acta used copies of previous editions in setting the type for subsequent editions and evidently took pains to replicate the disposition and appearance of their copy‐texts: the type fonts and page layouts of all three editions are nearly identical, with similar patterns in line endings, pagination, headings, and signing maintained throughout. This was for good reason: as the twelve issues comprising each annual volume were signed and paginated in an uninterrupted sequence, altering the original imposition even slightly in subsequent printings would have had a cascading effect, leading to discrepancies in pagination and signing in later instalments. What's more, the role of the Acta’s later printers in resetting and reprinting the work of their predecessors was often well disguised. The annual title‐page of the 1684 volume at Princeton (containing a third edition of the October instalment), for example, carries the name of Christoph Gunther in the imprint, even though Gunther was dead and the volume's contents was in fact the work of Christian Gotze (see above). This same title‐page also carries the original 1684 dedication, addressed to that ‘most serene pair of brothers’, Johann Georg IV (1668‐1694) and Frederick Augustus I (1670‐1733), the sons and heirs of Johann Georg III, the elector of Saxony from 1680 until 1691—this despite the fact that at the time of printing, Johann Georg III had died and Johann Georg IV had acceded to the electorship. On a subsequent leaf augmenting this dedication, the elder Johann Georg is described as alive and well, while the son is still referred to as his father's ‘heir’. Clearly, in mimicking the typesetting, content, and even political context of the first edition, later editions of monthly instalments were meant to be passed off as copies of the first.
This typographic deception raises the question of whether subsequent editions of the Acta Eruditorum were produced instalment by instalment or in twelve‐instalment annual sets; in other words, were annual volumes reprinted at one time in their entirety (all of which exceed 500 pages [sixty‐ two sheets of paper], and thus would have required a significant investment of time and materials), or were out‐of‐print instalments reprinted singly and sold piecemeal as needed? The typographic evidence and common sense support the latter theory: unsubscribed‐for instalments of the Acta were likely kept on hand by the publisher, Otto Mencke, and/or his deputized booksellers, Johann Grosse and Johann Friedrich Gleditsch. As copies of the Acta were ordered or subscribed for, copies of individual instalments were either gathered indiscriminately into twelve‐instalment annual sets or distributed piecemeal, without accounting for the variety of editions on hand to be sold and shipped (after all, each new edition was designed to be indistinguishable from earlier editions, and all editions were thus interchangeable, likely for this reason). While this indiscriminate assembling of copies of monthly instalments would mean that later editions of individual instalments were more likely to be bound with later editions of adjacent instalments, such a system might also result in mixed annual volumes comprising both early‐ and late‐edition instalments. For similar reasons, standing subscribers to the Acta were more likely to receive first editions of each instalment, while subsequent subscribers or readers who purchased an individual instalment months or years after its initial publication were more likely to receive later editions—that is, after copies of the first edition had all been sold.
In conclusion, the typographic and printing evidence presented in this article demonstrates that the first edition of Leibniz's ‘Nova Methodus’ was printed in September 1684 by Christoph Gunther and issued in October of that year; the second edition, incorporating the errata printed in March 1685, was printed in the summer of 1686, also by Christoph Gunther; and the third edition, incorporating the March 1685 errata but omitting the June 1693 corrigenda, was printed between November 1692 and April 1693 by Christian Götze. This chronology alters significantly the abiding view that all three extant forms of Leibniz's article (previously and variously called ‘states’, ‘versions’, and ‘printings’) are to be dated to 1684 and assigned to a single press. Rather, they are distinct and disjunct documents, with the third edition postdating the first by nearly a decade—that is, long after the discovery of the calculus had ceased to be news.
I am grateful to the colleagues and friends who contributed to this article. I wish to thank, in particular, Rick Watson, Roger Gaskell, David Vander Meulen, Lilla Vekerdy, Ethan Henderson, Eric White, Niccolo Guicciardini, Siegmund Probst, Rebecca Jewett, and Neal D. Curtis. I also wish to thank the Friends of the Princeton University Library and the Bibliographical Society of the University of Virginia for supporting my research, as well as the staffs of the Houghton Library (Harvard University), the Dibner Library of the History of Science and Technology, and Princeton University Library Special Collections.
Footnotes
Full title: ‘Nova Methodus pro Maximis et Minimis, itemque tangentibus, quae nec fractas, nec irrationales quantitates moratur, & singulare pro illis calculi genus, per G.G.L’ [‘A new method for maxima and minima as well as tangents, which is impeded neither by fractional nor irrational quantities, and a remarkable type of calculus for them, by G.G.L.’]; hereafter, ‘Nova Methodus’. It has been suggested that Leibniz's decision to publish the ‘Nova Methodus’ under his initials reveals some unease about releasing his work at such an early stage of its development. This semi‐anonymizing tactic was also motivated by the fact that Leibniz was eager to establish priority, even while his work was still evolving. This concern about priority was warranted: as Clara Silvia Roero observes, after a period of collaborative work in Paris in 1675, Leibniz's erstwhile friend Ehrenfried Walter von Tschirnhaus began ‘publishing articles on current themes and problems using infinitesimal methods which were very close to those that Leibniz had confided to him’; in consequence, ‘Leibniz risked having his own invention stolen from him’; C. S. Roero, ‘Gottfried Wilhelm Leibniz, First Three Papers on the Calculus (1684, 1686, 1693)’, in Landmark Writings in Western Mathematics, 1640—1940, ed. by Ivor Grattan‐Guinness & Roger Cooke (Amsterdam: Elsevier, 2005), pp. 46—58 (p. 49). My thanks to one of the anonymous reviewers for this point. For a full account of the development and reception of Leibniz's calculus see Siegmund Probst, ‘The Calculus’, in The Oxford Handbook of Leibniz, ed. by Maria Rosa Antognazza (Oxford: Oxford University Press, 2018), pp. 212‐24.
A note on terminology: the periodical term ‘issue’ occasions some confusion in a bibliographical context. While a bibliographical issue refers to a discrete unit of a particular edition, a periodical issue refers to an instalment, or number (usually monthly) of a particular journal. To avoid any ambiguity, in this article I employ the term ‘instalment’ to refer to an issue in the periodical sense, and ‘issue’ to refer to its narrower, bibliographical meaning.
Edwin Wolf, The Library of James Logan of Philadelphia, 1674—1751 (Philadelphia, PA: The Library Company of Philadelphia, 1974), p. 4. See Harrison Horblit, One Hundred Famous Books in Science: Based on an Exhibition Held at The Grolier Club (New York, NY: The Grolier Club, 1964), 66a; see also Verne Roberts and Ivy Trent, Bibliotheca Mechanica (New York, NY: Jonathan Hill, 1991), pp. 5—6; and also Edwin Wolf, James Logan, 1674—1751: Bookman Extraordinary (Philadelphia, PA: The Library Company of Philadelphia, 1971), p. 36.
On the distinction between ‘printing’ (or ‘impression’) and ‘edition’, see Fredson Bowers’ classic treatment in Principles of Bibliographical Description (New Castle, DE: Oak Knoll, 2005), pp. 37‐39: ‘An edition is the whole number of copies of a book printed at any time or times from substantially the same setting of type‐pages’, p. 39. See also Philip Gaskell, A New Introduction to Bibliography (New Castle, DE: Oak Knoll Press, 1995), p. 313: ‘an edition [...] is all the copies of a book printed at any time (or times) from substantially the same setting of type, and includes all the various impressions, issues, and states which may have derived from that setting’. As the three editions treated here are the product of separate settings of type, I describe each as an edition rather than as an ‘impression’, or ‘printing’. Confusion may arise given the complexity of the bibliographical unit in question, that is, a monthly instalment (see section ‘The question of bibliographic unit’, below).
Roero, ‘Gottfried Wilhelm Leibniz’, p. 46.
See Heinz‐Jurgen Hess & James G. O’Hara, ‘Infinitesimalrechnung und andere Mathematica’, in Gottfried Wilhelm Leibniz, Mathematischer Naturwissenchaftlicher und Technischer Briefwechsel, Vierter Band, Juli 1683—1690, Samtliche Schriften und Briefe, 3, iv (Berlin: Akademie Verlag, 1995), xxiv—xxv: ‘Die leibnizsche Kommunikationsbereitschaft hatte das Ziel, kritische Anregungen zu erhalten sowie sich und seine Ergebnisse bekannt zu machen, um dadurch Prioritatsanspruche zu sichern’, xxv. See also n. 1, above.
On Christian Götze, see Christoph Reske and Josef Benzing, Die Buchdrucker des 16. und 17. Jahrhunderts im deutschen Sprachgebiet?: auf der Grundlage des gleichnamigen Werkes von Josef Benzing (Wiesbaden: Harrassowitz Verlag, 2007), p. 544; on Christoph Gunther, see p. 543.
A. H. Laeven observes that this consortium represented ‘the strongest conceivable publishing and bookselling combination in Leipzig at that time, with an international name’. Gleditsch, for his part, was ‘one of the most important book dealers anywhere in German territory’. Laeven notes, however, that ‘it is no longer possible to reconstruct from the available source material a picture of the part the booksellers played in the distribution of the Acta’. Augustinus Hubertus Laeven, The Acta Eruditorum under the Editorship of Otto Mencke (1644—1707): The History of an International Learned Journal between 1682 and 1707, trans. by Lynne Richards (Amsterdam: APA‐Holland University Press, 1990), pp. 42‐43. On Johann Friedrich Gleditsch, see Neue Deutsche Biographie [NDB], vi (Berlin: Dunker & Humblot, 1964), pp. 439‐40; On Johann Grosse see NDB, vii (Berlin: Dunker & Humblot, 1966), p. 148.
The annual preliminaries are always subscribed and dated December and are conjugate or printed with the December instalment.
See Laeven, The Acta Eruditorum under the Editorship of Otto Mencke, p. 68: ‘The issues, which were always dated the first day of the month, were in fact usually on their way to the regular readers within a few days of the date given, as we see from many of Mencke's letters’.
An alternative interpretation of this evidence, disproved below (see ‘Narrowing the date of the second edition’) is that the second and third editions could have been printed prior to the date of these errata, required by subscribers who had received an uncorrected, first‐edition copy.
The corrigenda extend to three pages and are printed beneath the heading, ‘Corrigenda in Schediasmatibus Leibnitianis, quae Actis Eruditorum Lipsiensibus sunt inserta’, in Indices generales auctorum et rerum primi Actorum Eruditorum quae Lipsiae publicantur decennii, nec non supplementorum tomi primi (Leipzig: Joh. Grossii Haeredes & J. F. Gleditschium, 1693), 2Q2—2Q3. The preface to the Indices is dated June 1693, suggesting that it was printed in May of that year.
The preface to this volume is subscribed, ‘Scribebamus Lipsiae Calendis Junii A. MDCXCIII’. A second index volume was printed in 1704, and a third in 1714.
On the importance of Leibnizian mathematical notation, see Florian Cajori, A History of Mathematical Notations (New York, NY: Dover Publications, 1993), pp. 180—96; see also, Maria Rosa Antognazza, Leibniz: An Intellectual Biography (Cambridge: Cambridge University Press, 2004), PP. 243‐45.
Quoted in Cajori, History of Mathematical Notations, p. 183.
ibid.
ibid., pp. 184—85. Leibniz's zeal for notational reform proved influential. As Cajori observes, ‘Among Leibniz's symbols which at the present time enjoy universal, or well‐nigh universal, recognition and wide adoption are his dx, dy, his sign of integration, his colon for division, his dot for multiplication, his geometric signs for similar and congruence, his use of the Recordian sign of equality in writing proportions, his double‐suffix notation for determinants’.
Antognazza, Leibniz: An Intellectual Biography, p. 239.
On Leibniz's peripheral involvement in founding the Acta Eruditorum, see also Laeven, The Acta Eruditorum under the Editorship of Otto Mencke, pp. 40—46; and pp. 10—20.
‘Das Schediasma de methodo Tangentium etc. wird M. h. Herr im Octobri finden, undt hat der buchdrücker deßwegen einige characters in Holtz schneiden lassen müssen. Obs so wol gerathen, verlange ich zu vernehmen’. Quoted in Heinz‐Jürgen Hess, ‘Zur Vorgeschichte der ‘Nova Methodus’ 1676—1684’, in 300 Jahre ‘Nova methodus’ von G.W. Leibniz: (1684—1984), ed. by A. Heinekamp (Stuttgart: Steiner, 1987), p. 64. My thanks to the anonymous reviewer for improving my translation.
Thanks to Professor Niccolo Guicciardini and Professor Siegmund Probst for clarifying this point.
Carl Immanuel Gerhardt (ed.), Leibnizens mathematische schriften, v (Halle: H.W. Schmidt, 1858), 220—33. See also Gustav Eneström, ‘Über Die Erste Aufnahme Der Leibnizschen Differntialrechnung [On the First Appearance of the Leibnizian Differential Calculus]’, Bibliotheca Mathematica IX (September 1908), 309—20. Enestrom notes the presence of ‘misprintings’ in Leibniz's article, but was, like Gerhardt, apparently unaware of the 1693 corrigenda.
Dirk Jan Struik, A Source Book in Mathematics, 1200—1800 (Cambridge, MA: Harvard University Press, 1969), pp. 271—80; and ‘Leibniz on the Calculus, Translated from the Latin by Evelyn Walker’, in David Eugene Smith, A Source Book in Mathematics (New York: Dover Publications, 1959), pp. 619—26. Struik provides a photograph of the first page of the ‘Nova Methodus’ from a copy of the third edition, evidently his source.
Hess, ‘Zur Vorgeschichte der ‘Nova Methodus’’, pp. 64—102; Pascal Dupont & Clara Silvia Roero, Leibniz 84: il decollo enigmatico del calcolo differenziale (Rende: Mediterranean Press, 1991); see also Roero, ‘Gottfried Wilhelm Leibniz’, pp. 46—58.
‘Kapitel 8: Nova methodus pro maximis et minimis’, in Gottfried Wilhelm Leibniz, Die mathematischen Zeitschriftenartikel, ed. by Heinz‐Jürgen Hess and Malte‐Ludolf Babin (Zürich: Georg Olms Verlag, 2011), pp. 51—62. See, in particular, nn. 1 (p. 51), 5 (p. 53), 12 (p. 55), 13 (p. 56), 16 and 18 (p. 58), for an explanation of their editorial programme and a justification for the incorporation or omission of the 1693 corrigenda.
Laeven, The Acta Eruditorum under the Editorship of Otto Mencke, p. 66.
On Zeidler, see Christoph Reske, Die Buchdrucker des 16. und 17. Jahrhunderts im deutschen Sprachgebiet auf der Grundlage des gleichnamigen Werkes von Josef Benzing (Wiesbaden: Otto Harassowitz, 2007), p. 275.
On Georg, see Josef Benzing, Die Buchdrucker des 16. und 17. Jahrhunderts im deutschen Sprachgebiet, 2nd edn (Wiesbaden: Otto Harassowitz, 1982), p. 288; on Banckmann, see Reske, Die Buchdrucker, p. 543.
Laeven, The Acta Eruditorum under the Editorship of Otto Mencke, pp. 66‐68.
The Dibner Library of the History of Science and Technology (Washington, DC): Z1007 .A18 1692/93.
My thanks to Terry Belanger for this point.
Quoted in Wolf, Library of James Logan of Philadelphia, p. 4.
ibid.
