doctrine chances method calculating von moivre abraham (23 Ergebnisse)

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Facsimile reprint of 3rd edn. 8vo. Original gilt lettered blue cloth (VG), no dustwrapper. Pp. xi + 368, illus with tables (no inscriptions).

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(27,5 x 21,5 cm). (4) XIV (2w) 258 (1) S. Mit Titelvignette und 6 (3 gestochenen) Kopf- bzw. Schlußvignetten. Lederband der Zeit. Gegenüber der ersten Ausgabe von 1718 um über 80 Seiten vermehrt. - "The first textbook for the calculus of probabilities. It constitutes the results of the activities of its author as a private instructor of mathematics. It was based on the concept of probability and its classical measure; it contained in an introductory theoretical part the main rules, extended the mathematical methods for the solution of its problems by analytical tools, and offered from the second edition on an approximation of the binomial by the normal distribution. A second edition (1738) contained his normal approximation to the binomial distribution, which he had found in 1733. De Moivre's greatest mathematical achievement is considered a form of the central limit theorem, which he found in 1733 at the age of 66. He understood his central limit theorem as a generalization and a sharpening of Bernoulli's 'Theorema aureum', which was later named 'the law of large numbers' by S. D. Poisson" (Landmark writings). - "De Moivre's masterpiece is 'The Doctrine of Chances'. A Latin version appeared as 'De mensura sortis' in 'Philosophical Transactions of the Royal Society'. He was able to dedicate his first book, 'The Doctrine of Chances', to Newton; and the aging Newton would, it is said, turn students away with 'Go to Mr. De Moivre; he knows these things better than I do'" (DSB). - Exlibris. Stempel mit Elephant auf Titel. Vereinzelt gering fleckig. Vorsätze erneuert und Rücken sorgsam restauriert. Insgesamt wohlerhalten. - DSB 9, 452; Landmark writings in western mathematics S. 105; Kress 4395; vgl. Norman 1529 (EA).

4to, pp.[4], xiv, 175, [1]; copper-engraved ornament to title-page, woodcut and engraved head- and tailpieces; occasional stains and light foxing, otherwise a handsome copy on fine paper in contemporary Cambridge-panelled calf, gilt red morocco lettering-piece to spine; skilfully rebacked and recornered with the original spine relaid, spine worn and covers scuffed; armorial bookplate of Sir Alfred Sherlock Gooch to front pastedown, early ink inscription to front free endpaper (see below), two minor annotations in ink to pp.7 and 36.First edition, a very good copy with likely Virginian provenance, of this classic on the theory of probability and game theory, inscribed in multiple hands aboard the sixty-gun warship HMS Dunkirk, a human moment of indulgence stolen between the drudgery and danger of life aboard a Royal Naval ship. The Doctrine of Chances is dedicated to Sir Isaac Newton, President of the Royal Society, and personal friend of de Moivre. 'The principal contributions to our subject from de Moivre are his investigations respecting the Duration of Play, his Theory of Recurring Series, and his extension of the value of Bernoulli's Theorem by the aid of Stirling's Theorem . it will not be doubted that the Theory of Probability owes more to [de Moivre] than to any other mathematician, with the sole exception of Laplace' (Todhunter, A History of the mathematical Theory of probability from the time of Pascal to that of Laplace (1865), p.193). Our copy records a rare and fleeting moment of levity on deck: the inscription to the front free endpaper, written in multiple hands, reads 'Mr. Mollet & Mr Dobby playing at Backgamon | 29May 1740 under the awning on Board His | Majisties Ship Dunkirk Capt. Bolling | & Mr Stafford first Lieutenant looking on'. Ship's logs show that on 29 May 1740, the HMS Dunkirk was at sea off the Isles of Scilly, and travelled thirty-two miles in stormy weather; an unlikely time to play backgammon on deck. Furthermore, we can find no record of a Captain Bolling or any of the other officers named in British Army or Royal Navy lists for 1740. Could the year 1740 have been written in error instead of 1741, perhaps by force of habit in the early months of the new year (prior to the adoption of the Gregorian calendar in 1752, the year began on 25 March)? Circumstance seems to support this: on 29 May 1741 the conditions were decidedly different: the HMS Dunkirk was moored in fair weather at the mouth of the Magdalena River in Colombia, one of a fleet of British warships patrolling the north coast of South America in the aftermath of Admiral Vernon's disastrous attack on Cartagena earlier that year, which inflicted over ten thousand fatalities on British forces. The Dunkirk's manoeuvres off Cartagena provide a compelling clue to the possible identities of our officers and to the connection between the 1740s owner of this book and the later Gooch family provenance. In autumn 1740, SirWilliam Gooch (16811751), Lieutenant Governor of Virginia, led a regiment of some 3500 Virginian militiamen (known as 'Gooch's American Foot') to Jamaica; they would then take part in the failed attack on Cartagena. Gooch was excluded from the British council of war, and his men were disdained by the officers. At the start of 1741, many of Gooch's men were made deckhands on undermanned British ships, fifty-one of them embarking to the Dunkirk on 24 January 1741 as supernumeraries. In March, they sailed as de facto members of the Royal Navy, and 'a majority of the American troops never returned, being kept as conscripted sailors on the ships to which they had been abducted' (Slaughter, Independence: The Tangled American Revolution). Where we find no Captain Bollings in the UK, we find a plethora of them in Virginia, all members of the local militia. The Captain Bolling mentioned in the inscription is likely the Virginian John Bolling Jr (17001757), great-great-grandson of Pocahontas and John Rolfe and later colonel of the W.

Hardcover. First edition. 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 of the Doctrine of Chances, was an expansion of a long (fifty-two pages) memoir he had published in Latin in the Philosophical Transactions of the Royal Society in 1711 under the title 'De mensura sortis' (literally, 'On the measurement of lots'). De Moivre tells us that in 1711 he had read only Huygens' 1657 tract De Ratiociniis in Ludo Aleae and an anonymous English 1692 tract based on Huygens' work (now known to have been written by John Arbuthnot). By 1718 he had encountered both Montmort's Essay d'analyse sur les jeux de hazard (2nd ed., 1713) and Bernoulli's Ars Conjectandi (1713), although the latter had no pronounced effect on De Moivre at that early date" (Stigler, p. 71). The Doctrine consists of an introduction with definitions and elementary theorems, followed by a series of numbered problems. "De Moivre begins with the classical measure of probability, 'a fraction whereof the numerator be the number of chances whereby an event may happen, and the denominator the number of all the chances whereby it may either happen or fail'. He gives the summation rule for probabilities of disjunct events explicitly only for the case of the happening and the not happening of an event. Expectation is still on the level of Huygens defined as the product of an expected sum of money and the probability of obtaining it, the expectation of several sums is determined by the sum of the expectations of the singular sums. He defines independent and dependent events and gives the multiplication rule for both. But whereas today the criterion for independence of two events is the validity of the multiplication rule in the [Doctrine], the multiplication rule follows from the independence of the events, which seems to be a self-evident concept for De Moivre "With these tools 'those who are acquainted with Arithmetical Operations' (as De Moivre remarked in the preface) could tackle many problems, in part already well known but which he gradually generalized. Because the majority of.

First edition of the author's masterpiece, an early and important contribution to the calculus of games of chance and probability theory, setting out "a series of algebraic and analytic tools for the theory of probability. which foreshadowed Boolean algebra" (ODNB) and other concepts. His introduction contains an overview of main concepts such as probability, conditional probability, expectation, dependent and independent events, the multiplication rule, and the binomial distribution. The book is dedicated to Sir Isaac Newton, whose priority in the dispute between Newton and Leibniz over the development of infinitesimal calculus de Moivre had defended. Babson 181; E STC T33065; Honeyman 2240. Quarto (255 x 195 mm). Engraved vignette on title page, engraved and woodcut initials, head- and tailpieces. Contemporary calf, rebacked with original spine laid down, orange label, gilt in compartments, marbled endpapers, brown speckled edges. Slight rubbing, patch of loss and abrasion to front cover, scattered very light foxing. A very good copy.