'De Mensura Sortis, seu, de Probabilitate Eventuum in Ludis a Casu Fortuito Pendentibus,' pp. 213-264 in Philosophical Transactions, Vol. XXVII. For the Years 1710, 1711, and 1712

MOIVRE, Abraham de

Edité par Printed for H. Clements ? and W. Innys ? and D. Brown, London, 1712

A propos de cet article

THE FOUNDATION OF THE DOCTRINE OF CHANCES . First edition, contained in a complete volume of the Phil. Trans., of de Moivre's first published work on probability, and the first original work on the subject published in Britain, a precursor to his Doctrine of Chances which appeared seven years later. "[De Moivre's] work on the theory of probability surpasses anything done by any other mathematician except 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, p. 245). "The only systematic treatises on probability printed before 1711 were Huygens' De ratiociniis in ludo aleae (1657) and Pierre Rémond de Montmort's Essay d'analyse sur les jeux de hazard (1708). Problems which had been posed in these two books prompted de Moivre's earliest work and, incidentally, caused a feud between Montmort and de Moivre on the subject of originality and priority" (DSB). "Nearly all of De Mensura Sortis was later incorporated into de Moivre's book The Doctrine of Chances (1718, 1738, 1756), which was the most important textbook on probability theory until the publication of Laplace's Théorie Analytique des Probabilités (1812). In the preface de Moivre states that he began his work on probability theory at the exhortation of Francis Robartes, who asked him to solve the division problem for two gamesters playing bowls and also to find the probability of getting certain given faces as the outcome of a given number of throws with a die. He also states that he had previously read the books by Huygens and Montmort 'but these distinguished gentlemen do not seem to have employed that simplicity and generality which the nature of the matter demands.' Furthermore he writes that 'while they suppose that the skill of the gamesters is always equal, they confine this doctrine of games within limits too narrow.' Finally his remarks about Montmort may be read as if Montmort had used only the method of Huygens on some new examples. These rash remarks naturally provoked a dispute with Montmort" (Hald 1984, pp. 230-1). "The most remarkable of de Moivre's contributions [in De mensura sortis] are his derivation of the ruin probability in Huygens' fifth problem; his use of the Poisson approximation to solve the binomial equation B(c, n, p) = ½ with respect to n; his solution of the occupancy problem by means of the method of inclusion and exclusion, and the algorithm for the continuation probability in the duration of play for the ruin problem. Furthermore, he gives without proof the probability of getting a given number of points by throwing any given number of dice and the probability of ruin when one of the players has infinitely many counters. The only contemporary evaluation of these impressive results is the critical review given by Montmort in a letter of 5 September 1712 to Nicholas Bernoulli, about a month after Montmort had received a copy of the paper from de Moivre . [Montmort] recognizes de Moivre's priority to the Poisson approximation, to Robartes' problem, and to the algorithm for finding the continuation probability in the problem of the duration of play" (Hald 2003, pp. 403-4). No copies in auction records. Provenance: Toft Hall in Cheshire, England, seat of the Leycester family since the 14th century (bookplate on front paste-down). De Moivre's interest in probability was awakened by Francis Robartes (1649-1718), Member of Parliament and scion of an aristocratic family. In 1692, Robartes wrote a manuscript on two probability problems that he presented to the Royal Society but never published, and in the following year he succeeded in publishing another paper on probability. In 1710 Robartes helped John Harris with his article entitled "Play" in Harris's scientific dictionary Lexicon Technicum. Robartes devised an algorithm that Harris used to extract the appropriate terms in a.

N° de réf. du vendeur 6431

Détails bibliographiques

• Titre: 'De Mensura Sortis, seu, de Probabilitate Eventuum in Ludis a Casu Fortuito Pendentibus,' pp. 213-264 in Philosophical Transactions, Vol. XXVII. For the Years 1710, 1711, and 1712
• Éditeur: Printed for H. Clements ? and W. Innys ? and D. Brown, London
• Date de parution: 1712
• Édition: First edition.
• Catalogues du vendeur:
  • Statistics, Probability Theory