Alexander Savérien’s Dictionnaire universel de mathématique et de physique: The First Mathematical Dictionary in French

Jeff Loveland

The first mathematical dictionaries in the vernacular appeared successively in English, German, and Dutch. Joseph Moxon’s Mathematicks Made Easie (1679) had already gone through three editions in English by 1705. Similarly, Christian Wolff’s Mathematisches Lexicon (1716)—the century’s most influential mathematical dictionary—had gone through three editions in German by 1747, and it had also been translated and adapted in Dutch (1740). In French, Jacques Ozanam had published a Dictionaire mathématique in 1691, but it was ordered pedagogically, not alphabetically. It was not, consequently, a dictionary in the modern sense of the word, a sense that had solidified enough by Ozanam’s time to elicit an apology: “Je n’ay pas suivi l’ordre Alphabetique, que l’on observe ordinairement en de semblables livres.”1 Nonetheless, in a concession to a rising fortunes of alphabetical order during the period, Ozanam included a sixty-seven page index. This would be a boon for future compilers of mathematical dictionaries, notably the undertakers of the English-language Mathematical Dictionary […] Abridg’d from Monsieur Ozanam, and Others (1702).

Explaining France’s late entry into the production of mathematical dictionaries is hard, since France was a leader in publishing specialized and general encyclopedias in the late seventeenth and early eighteenth centuries. Two factors probably contributed.

First, despite the destabilizing effects of the many Francophone presses outside of France, the market for French books was both relatively centralized (in comparison with the market for German ones) and governmentally controlled (in comparison with the market for English ones). Any author planning to publish a book had reason to negotiate ahead of time with the governmentally appointed director of the book-trade. During his tenure as the director from 1750 to 1763, Chrétien-Guillaume de Lamoignon de Malesherbes received dozens of requests from potential dictionary-writers, with various outcomes. Regardless, the language of the supplicants suggests that permission to publish was not taken for granted and that it hinged on complex considerations of public utility, literary property, and the contemporary landscape of dictionaries on the same or similar subjects2.

Second, the publication of the Encyclopédie (1751-72), a large, collaborative general encyclopedia edited by Denis Diderot Jean D’Alembert, may have had a discouraging effect on the production of other encyclopedias, whether general or specialized. Personal circumstances were probably the deciding factor in Samuel Formey’s decision to stop work on his philosophical dictionary and sell the manuscript for incorporation into the Encyclopedie, but the development of the latter work did deprive him of the services of his chosen publisher3. Similarly, André Morellet’s abandonment of his dictionary of commerce after decades of work may have owed something to the saturation of the French market with cheap editions of the Encyclopédie4.

In the case of mathematical dictionaries, the only known interference from the Encyclopédie produced an ambiguous result. In 1743, Charles-Antoine Jombert—already experienced as a publisher of both dictionaries and mathematical works—acquired a license to publish a translation and adaptation of the Mathematisches Lexicon among other works. Two Maurists, François de Brézillac and Antoine-Joseph Pernety, collaborated on the project, expanding it in the direction of the indeterminate field of “physics.” Jombert advertised the resulting Nouveau dictionnaire de mathématique et de physique in 1746-47 but—intimidated by the forthcoming publication of the Encyclopedie, and unable to muster support from the government—decided to rethink it5. In the end, he seems to have hired Alexandre Savérien to narrow the work’s scope and complete it, a way of lessening his risks—an effort that gave rise to a new prospectus (1749) and then the two-volume Dictionnaire universel de mathématique et de physique in 17536. Some of the material in the dictionary was recent—at one extreme, a report on Thomas-François Dalibard’s experiments with lightning in May 17527—but Wolff’s influence remained considerable. In the first twenty pages, for instance, the brief articles “Acamptes,” “Aderaimin,” “Adhil,” “Alcor,” “Algeneb,” “Algethi,” “Algorithme,” and “Almageste” all appear to have been translated from the Mathematisches Lexicon8.

In an age in which specialization was increasingly valued, Savérien must have struck Jombert as a better figure than the Maurists to advertise on the title page of a mathematical dictionary. As the title page in fact indicated, he was a member of the Société Royale de Lyon. More importantly, he was a naval engineer, and one who had published abundantly on his specialty, including the Discours sur la navigation et la physique expérimentale (1742), Recherches historiques sur l’origine et le progrès de la construction des navires des anciens (1747), and Description et usages des globes célestes et terrestres (1752). As this list suggests, his interests in mathematics were practical and historical rather than theoretical and abstract.

Even if Savérien’s encyclopedia was narrower and smaller than the one the Maurists were working towards, it was bigger and more expensive than any mathematical dictionary to date. It had almost 800 illustrations, grouped together in 101 plates at the back of the volumes. Through the first third of the eighteenth century, illustrations in mathematical dictionaries were usually printed from woodcuts, which allowed them to be placed alongside articles, but favor for copperplates grew over time. As the mathematician Abraham Gotthelf Kästner pointed out, copperplates had two disadvantages: their expensiveness relative to woodcuts and the fact that they had to printed on separate pages, which meant the reader might have to switch back and forth between pages 9.

The copperplates in Savérien’s Dictionnaire contributed to its relatively high price of 33 livres10. Another factor was its format of quarto. All but two of Europe’s previous mathematical dictionaries had been published in octavo, a smaller format. Books in smaller formats were less prestigious but cost markedly less and had the advantage of portability. Thus, soon after publishing his mathematical dictionary, Savérien chose to publish his Dictionnaire historique, théorique et pratique de marine (1758) as a duodecimo to “rassembler toutes ces matieres en deux volumes portatifs, pour la commodité des navigateurs.”11

A final factor contributing to the price of Savérien’s Dictionnaire was its simple size. Published in two volumes, it was Europe’s first multi-volume mathematical dictionary, and it contained some 772,000 words, almost twice as many as the previous record-holder among mathematical dictionaries.

In two respects, Savérien seems to have modeled his dictionary on Diderot and D’Alembert’s Encyclopédie. First, undoubtedly thinking of D’Alembert’s “Discours préliminaire,” he began with a preface presenting mathematics in an expansive philosophical context12. He even complemented it with a diagrammatic “Systême figuré des sciences mathematiques” clearly recalling the “Systême figuré des connoissances humaines” in the Encyclopédie13. Second, he took pleasure in mocking and denouncing what he considered superstition, and he occasionally went so far as present organized religion in a negative light. In “Chiromancie,” for example—making use of the first person, as he often did toward the end of longer articles—he apologized for covering chiromancy: “Sincerement je demande pardon au Lecteur de l’avoir entretenu d’un sujet aussi pitoïable.” Still, Savérien argued, his coverage had been necessary insofar as the practice had been supported by religious authorities. He then quoted a statement, dated 1652, from two ecclesiastics who pronounced a book on chiromancy compatible with religious doctrine14. Diderot, one imagines, would have been delighted to sign such an article.

On the average, entries in Savérien’s Dictionnaire were some 700 words long, in keeping with the tendency toward long entries among mathematical dictionaries after 1750, but they varied widely among themselves. At one extreme, a great many entries were either mere cross-references or brief definitions. The article “Congé,” for example, occupied only two lines: “CONGE'. Terme d’Architecture civile. Voïez APOPHYGE.” By contrast, some entries were long. The following are the ones occupying part or all of six or more pages.

As this table indicates, Savérien conceived mathematics broadly, stretching it into what we see as physics, instrumentation, or engineering, but he was hardly unusual in this respect among eighteenth-century mathematical dictionary-writers. Toward the end of the century, Gottfried Erich Rosenthal published four volumes of an Encyklopädie der reinen Mathematik (1794-1803), but even here, under a ostensibly unambiguous title, he covered surveying and measuring instruments as well as such practical matters as “forest geometry” and “forest taxation.”15

Savérien’s Dictionnaire appears to have been received favorably16. It did not, however, follow Wolff’s Mathematisches Lexicon in going into further editions. Indeed, at the time of his death in 1784, Jombert still had 81 unsold copies17. The work’s price, which restricted ownership to the higher ranks of the middle class and those above, undoubtedly played a role. In France, moreover, the heritage of mathematical reference leading from the Diderot and D’Alembert’s Encyclopédie to the Encyclopédie méthodique (1782-1832) was probably too strong to allow Savérien to establish much of a heritage of his own.