The Doctrine of Chances: or, A Method of Calculating the Probability of Events in Play

MOIVRE, Abraham de

Published by W[illiam]. Pearson for the Author, London, 1718

THE FOUNDING WORK OF THE FIELD OF PROBABILTY AND STATISTICS. First edition of this classic on the theory of probability, the first original work on the subject in English. "De Moivre s book on chances is considered the foundation for the field of probability and statistics" (Tomash). "De Moivre s masterpiece is The Doctrine of Chances" (DSB). "His work on the theory of probability surpasses anything done by any other mathematician except P. S. Laplace. His principal contributions are his investigations respecting the Duration of Play, his Theory of Recurring Series, and his extension of the value of Daniel Bernoulli s theorem by the aid of Stirling s theorem" (Cajori, A History of Mathematics, p. 230). "He was among the intimate friends of Newton, to whom this book is dedicated. It is the second book devoted entirely to the theory of probability and a classic on the subject" (Babson 181). De Moivre s interest in probability was raised by Pierre-Rémond de Montmort s Essay d analyse sur les jeux de hazard (1708), the first separately-published work on probability. "The [Doctrine] is in part the result of a competition between De Moivre on the one hand and Montmort together with Nikolaus Bernoulli on the other. De Moivre claimed that his representation of the solutions of the then current problems tended to be more general than those of Montmort, which Montmort resented very much. This situation led to some arguments between the two men, which finally were resolved by Montmort s premature death in 1719 … De Moivre had developed algebraic and analytical tools for the theory of probability like a new algebra for the solution of the problem of coincidences which somewhat foreshadowed Boolean algebra, and also the method of generating functions or the theory of recurrent series for the solution of difference equations. Differently from Montmort, De Moivre offered in [Doctrine] an introduction that contains the main concepts like probability, conditional probability, expectation, dependent and independent events, the multiplication rule, and the binomial distribution" (Schneider, p. 106). Provenance: Charles Meynell (early engraved bookplate). The modern theory of probability is generally agreed to have begun with the correspondence between Pierre de Fermat and Blaise Pascal in 1654 on the solution of the Problem of points . Pascal included his solution as the third section of the second part of his 36-page Traité du triangle arithmétique (1665), which was essentially a treatise on pure mathematics. "Huygens heard about Pascal s and Fermat s ideas [on games of chance] but had to work out the details for himself. His treatise De ratiociniis in ludo aleae … essentially followed Pascal s method of expectation. … At the end of his treatise, Huygens listed five problems about fair odds in games of chance, some of which had already been solved by Pascal and Fermat. These problems, together with similar questions inspired by other card and dice games popular at the time, set an agenda for research that continued for nearly a century. The most important landmarks of this work are [Jakob] Bernoulli s Ars conjectandi (1713), Montmort s Essay d'analyse sur les jeux de hazard (editions in 1708 and 1711 [i.e., 1713]) and De Moivre s Doctrine of Chances (editions in 1718, 1738, and 1756). These authors investigated many of the problems still studied under the heading of discrete probability, including gamblers ruin, duration of play, handicaps, coincidences and runs. In order to solve these problems, they improved Pascal and Fermat s combinatorial reasoning, summed infinite series, developed the method of inclusion and exclusion, and developed methods for solving the linear difference equations that arise in using Pascal s method of expectations." (Glenn Schafer in Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (1994), Grattan-Guiness (ed.), p. 1296). "De Moivre s earliest book on probability, the first edition. Seller Inventory # 5803

Bibliographic Details

Title: The Doctrine of Chances: or, A Method of ...
Publisher: W[illiam]. Pearson for the Author, London
Publication Date: 1718
Binding: Hardcover
Edition: First edition.