BERNOULLI, Jakob I (1654-1705). Ars conjectandi, opus posthumum. Accedit tractatus de seriebus infinitis, et epistola Gallic scripta de ludo pilae reticularis. Edited by Nicolaus I Bernoulli (1687-1759). Basel: Thurneisen Brothers, 1713.
4 (209 x 165mm). Woodcut device on title, folding woodcut diagram, 2 folding letterpress tables, several woodcut diagrams in text. (Title with small worm track in blank area, repaired with paper on verso, K1 recto with slight soil mark, a few quires browned.) Modern vellum-backed marbled boards, uncut and partly unopened.
FIRST EDITION of Jakob Bernoulli's most celebrated work, edited by his nephew Nikolaus I after being left incomplete at his death. The Latin word "conjectandi" in the title can be taken to refer literally to the throwing or casting of dice, though the "art of conjecturing" or "doctrine of chances" is implied equally strongly. It was the first great work on this subject, so important to the devlopment of 18th-century mercantile theory, in particular money-lending and insurance. The first part forms a commentary on Huygens's De ratiociniis in aleae ludo which had been published as an appendix to Schooten's Exercitationes mathematicae (1657); in dealing with the theory of combinations in the second part, Bernoulli assesses the contributions made by van Schooten (1657), Leibnitz (1666), Wallis (1685), and Jean Prestet's Elmens de mathmatique (1675; second edition, 1689) and himself introduces the term "permutations" for the first time; the third part gives twenty-four examples of the expectation of profit in various games of chance; while 'the fourth part contains the philosophical thoughts on probability that are especially characteristic of Bernoulli: probability as a measurable degree of certainty; necessity and chance; moral versus mathematical expectation; a priori and a posteriori probability; expectation of winning when the players are divided according to dexterity; regard of all available arguments, their valuation, and their calculable evaluation; law of large numbers; and reference to the Art de penser (Logique de Port Royal, Antoine Arnauld and Pierre Nicole, eds., 1662). The last section contains a penetrating discussion of "jeu de paume"': DSB p. 50; Dibner Heralds of Science 110; Grolier/Horblit 12; Norman 216; PMM 179.