Beschreibung:

BERNOULLI, Jakob (1654-1705). Ars conjectandi, opus posthumum. Accedit tractatus de seriebus infinitis, et epistola gallicè scripta de ludo pilae reticularis . Edited by Nicolaus I. Bernoulli (1687-1759). Basel: Thurneisen Brothers, 1713. 4 o (201 x 153 mm). Woodcut device on title, folding sheet with woodcut diagrams, 2 folding letterpress tables, some woodcut diagrams in text, woodcut decorations and initials. (Title and preliminaries lightly evenly browned, scattered spotting, mostly marginal.) Contemporary calf, the spine gilt (rebacked, preserving original spine). Provenance : A. ?Negenrode (contemporary purchase inscription on title); Ch. Roulleau de la Roussière (19th or early 20th-century bookplate on verso of free endpaper). FIRST EDITION OF THE "ESTABLISHMENT OF THE FUNDAMENTAL PRINCIPLES OF THE CALCULUS OF PROBABILITIES" (Grolier/Horblit). Bernoulli's posthumous treatise was edited by his nephew and is considered the first significant book on probability theory. The title refers to conjectandi , or "casting," as in the casting of dice. The Ars conjectandi "was the first systematic attempt to place the theory of probability on a firm basis and is still the foundation of much modern practice in all fields where probability is concerned--insurance, statistics and mathematical heredity tables" (PMM). The work is divided into four parts: the first a commentary on Huygens' De ratiociniis in aleae ludo (1657), the second a treatise on permutations and combinations (the former Bernoulli's own term), the third an application of the theory of combination to various games of chance, and the final, and most important, part containing Bernoulli's philosophical thoughts on probability as a measurable degree of certainty, necessity and chance, on moral versus mathematical expectation, and on a priori and a posteriori probablility. It also contains his theorem, an application of probability to statistics. Dibner Heralds of Science 110; Grolier/Horblit 12; Norman 216; PMM 179.