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

First edition, and an important association copy, of the first original work on probability 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” (Landmark Writings in Western Mathematics, p. 106). Provenance: Philip Stanhope (1714–1786), second Earl of Stanhope (bookplate on front paste-down). "Stanhope worked on probability problems and it is likely that he was responsible for getting [Thomas] Bayes interested in probability theory. The general theme of Stanhope's work in probability is to find alternate and simpler solutions to the more challenging probability problems of his day and to provide tables that would ease the burden of calculation. His work in probability is mainly derivative of Abraham De Moivre's (1667–1754) The Doctrine of Chances and Pierre Rémond de Montmort's (1678–1719) Essay d'analyse sur les jeux de hazard, and to a lesser extent of Thomas Simpson's (1710–1761) The Nature and Laws of Chance. Stanhope's work was solid but not highly original; he does not have the brilliant insight of someone like De Moivre. Standing below De Moivre and Simpson, Stanhope was at or near the top of the remaining group of British probabilists of that era . Early in life Stanhope expressed interest in studying mathematics, but was held back by his uncle Philip Dormer Stanhope (1694–1773), fourth Earl of Chesterfield . Once he came of age and became independent of his uncle, Philip Stanhope followed his mathematical interests . Philip Stanhope's name appears in a list of De Moivre's students given in the latter's biography by his friend Matthew Maty (1718–1776)" (Bellhouse, 'Lord Stanhope's papers on the Doctrine of Chances,' Historia Mathematica 34 (2007), pp. 173-186). Stanhope assisted De Moivre with the publication of the third edition of the Doctrine of Chances (1756). Babson/Newton 181; ESTC T33065; Goldsmiths'-Kress 05509.2-1; Norman 1529; Tomash M114. Large 4to, pp. [iv], xiv, 175, [1, blank]. Engraved vignette on title and engraved head- & tailpieces. Contemporary panelled calf with red-lettering piece on spine (rebacked with original spine laid on).…