#### Elaborately Stencilled Throughout;

Unpublished

# Manuscript on paper, entitled: “Du Calcul de l’Infini ou Theorie & Usages de l’Analise des Infiniment-Petits. Ex lib. Bicquilley,” written in a fine professional hand, with a number of authorial corrections in what is certainly the hand of Bicquilley.

Five folding hand-drawn plates & much stencilling of chapter headings, decorative initials, and mathematical symbols. 160; 185 pp. Two vols. in one. Large 4to (295 x 245 mm.), cont. mottled calf (upper joint cracked but strong), spine gilt, red morocco lettering-piece on spine. From the manuscript title-page: “Paris: M.D.CC.LXX.”

The re-discovered manuscript fair copy, written in a fine hand and laid-out to be sent to the printer for typesetting, of a hitherto unknown work by Bicquilley (1738-1814), a mathematician who made important contributions to probability theory and mathematical economics. Our manuscript, which is completely unknown, precedes Bicquilley’s first published work, Du Calcul des Probabilités (1783) by many years.

This is a remarkable manuscript in several ways including the method of production (see near the bottom). While the manuscript is not signed by Bicquilley, we make the attribution to him based on these factors: the style of writing here — concise, neat, clear, and modern — is typical of Bicquilley’s other mathematical writings, “in the form of a manual ready for teaching…a systematic study” (Crépel, p. 33). This concision is very different from other treatises of the time. Furthermore, the author of this text is obviously influenced by the mathematical work of Cousin (see the preface), and we know that Bicquilley corresponded with Cousin. The several corrections in the text closely resemble Bicquilley’s handwriting. This manuscript also comes from the library of Bicquilley and has his bookplate and a stencilled ex libris on the title. It would seem that Bicquilley had this fair copy manuscript prepared to send to the printer but did not, and so it entered his own library.

Unheralded until recently, Bicquilley is now best known for his work on commerce and probability; however, very few details of his mathematical background in differential and integral calculus are available today. From this manuscript, we learn of Bicquilley’s previous communication with the mathematician Jacques Antoine Joseph Cousin (1739-1800), whom he praises and thanks in the preface. The earliest letter between the two that the historian of science Pierre Crépel has found dates from 1776. With the scarcity of documentation, the first half of Bicquilley’s life is very difficult to reconstruct. The present manuscript offers considerable insight into his early years as a skilled mathematician.

Bicquilley was born into a family of magistrates in the commune of Toul, a small town near Nancy in northeastern France. He was a law student at the University of Pont-à-Mousson, where he also likely taught mathematics. His service in the military starting at the age of 26 introduced him to the engineer Didier Grégoire Trincano. It was Trincano who very probably exposed Bicquilley to the joys of mathematical research, and his influence appears throughout Bicquilley’s published work. Bicquilley joined the Freemason Loge des Neufs-Soeurs of Toul in the early 1780s; cf. Pierre Crépel, “Mathematical Economics and Probability Theory: Charles-François Bicquilley’s Daring Contribution,” in Studies in the History of French Political Economy: From Bodin to Walras, ed. Gilbert Faccarello (1998), pp. 84-87.

Bicquilley’s Du Calcul des Probabilités (Toul: 1783) was his first published book; it had considerable success, with a “new edition” issued in Paris in 1805 and a translation into German in 1788. His extremely rare Théorie Elémentaire du Commerce (Toul: 1804), has been the subject of research conducted by Crépel, who writes (in trans.): “The work is remarkable in more than one respect: (1) it is a mathematics book, constructed as such in terms of definitions, theorems, and corollaries; (2) it is written for a wide public in a particularly clear and comprehensible style; (3) it contains a mathematical determination of prices very similar to N.F. Canard’s in his work Principes d’économie politique, although manuscript analysis proves that Bicquilley’s formulation is without doubt the earlier of the two; (4) unlike the mathematical economic theories published in subsequent decades, Bicquilley’s theory also uses probability theory.”–ibid., p. 78. Also, see Prof. Stephen Stigler’s “Postface” (pp. 229-32) for another account of Bicquilley’s works in mathematics, including the introduction of the calculus of probability to speculation: his “extension of the application of probability beyond games to risky investments was exceedingly novel at the time.”

In the preface (pp. vii-viii) of our manuscript, Bicquilley states that a significant portion of the first book is based on Cousin’s research and teachings (in trans.): “A part of the contents which it offers is already known; I owe the other matters to the insight of M. Cousin, several theories belong to him entirely; from this number are the integration of polynomials, the summation of infinite sequences, the theory of tautochrones, and the theory of central forces. The little that I was able to present is the fruit of his lessons.”

The production of this handsome manuscript utilizes a remarkable amount of stencilling throughout. The person who wrote this manuscript has employed stencilling for the large decorative initials and head- and tailpieces, portions of chapter headings, and many of the capital letters used in formulae.

In a fine state of preservation. Bicquilley’s woodcut bookplate, executed by “Zapouraph 1773,” is found on the front paste-down. Zapouraph (n.d.) was a wood engraver active in Toul, by whom at least six bookplates are known (see Archives de la Société des collectionneurs d’ex-libris et de reliures historiques, Vol. 12 [1905], pp. 87-91, especially p. 89, where Bicquilley’s bookplate is illustrated and discussed). The author of the article, Dr. L. Bouland, speculates that the wood engraver is the Vicomte Nicolas François de Curel, “officier du génie, chimiste, écrivain.”

❧ Théorie Elémentaire du Commerce, ed. Pierre Crepel (1995). N.B.G., Vol. 12, cols. 250-51 (Cousin).

Price: $12,500.00

Item ID: 6833