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LINCOLN ABRAHAMABAA

The Gettysburg Address of Abraham Lincoln

DE MOIVRE Abraham 1667a1754.ABAA

The Doctrine of Chances: Or a Method of Calculating Probabilities of Events in Play. The third edition Fuller Clearer and more Correct than the Former.

1756S13188London:: A. Millar 1756. 1756. Quarto. 4 xi 1 errata 348 pp. Portrait medallion vignette on title; mild foxing but barely noticeable. Original full calf red gilt-stamped leather spine label; hinges repaired with calf inner joints strengthened corners worn all preserving original spine. Bookseller's ticket: "Sold by Carpenter & Co. 14 Old Bond Street" London. Early ownership ink signature of Th. Spencer; penciled initials of F.N.D. see below. Very good. A KEY WORK BY THE FATHER OF PROBABILITY THEORY. Third edition. This is a key work by the father of probability theory in which major steps in the measurement of uncertainty were achieved. De Moivre is "best known in statistical circles for his famous large-sample approximation to the binomial distribution whose generalization is now referred to as the Central Limit Theorem. De Moivre was one of the great pioneers of classical probability theory." Bellhouse-Genest p.1. It is the first systematic treatment of probability in English. Abraham De Moivre became with Edmund Halley a founder of English actuarial science. The author's dedicatory letter is address to Lord George Carpenter 1702-1749 the first edition had been dedicated to Newton where the author states emphatically "that this Doctrine is so far from encouraging Play that it is rather a Guard against it. . ." DNB vol. 38 p.116. / "The first edition of this work contains 175 pages the second edition 258 pages and the third 348 pages. The following list will indicate the parts which are new in the third edition: the Remark pages 30/33 and pages 48 & 49 the greater part of the second Corollary pages 64/66 the Examples page 88; the Scholium page 95 the Remark page 149 and pages 151/159 the fourth Corollary page 162 the second Corollary pages 176/179 the note at the foot of page 187 the Remark pages 251/254. The part on life annuities is very much changed. The Introduction is very much fuller than the corresponding part of the first edition. In his third edition De Moivre draws attention to the convenience of approximating to a fraction with a large numerator and denominator by continued fractions which he calls "the Method proposed by Dr. Wallis Huygens and others". He gives the rule for the formation of the successive convergents. This third edition contains 74 problems exclusive of those relating to life annuities in the first edition there were 53 problems. The pages 220/229 contains one of De Moivre's most valuable contributions to mathematics namely that of Recurring series. Pages 261/328 are devoted to Annuities on lives ; an Appendix finishes the book occupying pages 329/348 : this also relates principally to annuities but it contains a few notes on the subject of probability." :: Todhunter. A very full account of the above third edition will be found in Todhunter's History of the theory of probability. / "De Moivre's first book on probability was based upon a short memoir entitled De mensura sortis published in the 1711 volume of the Philosophical Transactions. The 1718 first edition is essentially a gambler's manual giving a systematic presentation of the arithmetic principles upon which are based the solution of problems concerning the advantage of players and size of wager which may be lain in a wide variety of games of chance. Walker. It does not contain De Moivre's work on the normal approximation of the binomial probability distribution which ranks as the most memorable of his discoveries; this discovery was first printed in its entirety in 1733 in a Latin pamphlet which was later translated into English and incorporated in successively expanded versions in the second 1738 and posthumous third 1756 edition of The doctrine of chances." Norman. / In terms of mathematics applied to the human actuarial lifespan "De Moivre French Huguenot mathematician and demographer formulated the hypothesis that among a body of persons over a certain age the successive annual decreases by death are nearly equal." Garrison & Morton. / "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 Bernouilli's theorem by the aid of Sterling's theorem". Cajori. / De Moivre born at Vitry received a varied education and settled in London as a Huguenot refugee in 1688. In England he continued his study of mathematics while working as a tutor. He is said to have acquired and read a copy of Newton's Principia and even to have carried loose sheets around with him to study at every available moment. This method of study worked so well that not only did he become one of England's foremost mathematicians but Newton in old age was in the habit of referring questions about the Principia to De Moivre. De Moivre's Doctrines of Chance is in fact a revised and expanded translation of his essay De Mensura Sortis which had been published in Latin in the Philosophical Transactions in 1711. In its Latin form it thus preceded Jacob Bernoulli's Ars Conjectandi 1713 by a full two years. / De Moivre was a French mathematician famous for De Moivre's formula which links complex numbers and trigonometry and for his work on the normal distribution and probability theory. He was elected a Fellow of the Royal Society in 1697 and was a friend of Isaac Newton Edmund Halley and James Stirling. Among his fellow Huguenot exiles in England he was a colleague of the editor and translator Pierre des Maizeaux. / Shafer points out that De Moivre one of Jacob Bernoulli's successors was among those who were applying Huygens' theories to both games and economies p. 11. He points out that the 1718 first edition was influenced by Bermoulli in that he used the word "probability" which was a word he did not use in his De mensura sortis. He continues: "We should not exaggerate De Moivre's importance in the eighteenth century. In retrospect he represents the pat that mathematical probability followed but he was hardly a philosopher of Jacob's caliber and Jacob retained a strong influence throughout the century among those who wanted to understand probability philosophically. Jacob's and Hooper's rules survived the whole course of that century in the works of philosophically sophisticated writers such as Lambert and Diderot. They disappeared only after Bayesian alternatives were developed by Laplace." pp. 13-14. Steve Stigler and Lorraine Daston expand on the use of the word "probability" in the eighteenth century. / Theodore Porter UCLA writes that De Moivre introduced the astronomer's law error to probability theory p. 93. "Like most early probability mathematics it first arose in the context of games of chance; it appeared as the limit of the binomial distribution. Because of its usefulness in combination and permutation problems the binomial had become the heart of the doctrine of chances. . . De Moivre then showed in a paper of 1733 reprinted in 1738 in the second edition of his Doctrine of Chances that the exponential error function gave a very good approximation to the distribution of possible outcomes for problems like the result of 1000 coin tosses Now for the first time it was practicable to apply probability theory to indefinitely large numbers of independent events." / PROVENANCE: I Thomas Spencer undetermined. II F.N.D. :: Florence Nightingale David 1909-1993 also known as F. N. David was an English statistician born in Ivington Herefordshire England. She was named after Florence Nightingale who was a friend of her parents. David did not like her forenames and thus always referred to herself as "F. N. David". She attended the Bedford College for Women in London earning her degree in mathematics in 1931. She then joined University College London to work with Karl Pearson who obtained a scholarship for her working as his research assistant resulting in a doctorate received in 1938 Pearson died in 1934. In 1938 her first book was published Tables of the Correlation Coefficient. During that period she was working with Jerzy Neyman. "During World War II she served as Experimental Officer in the Ordnance Board for the Ministry of Supply Senior Statistician for the Research and Experiments Department for the Ministry of Home Security Member of the Land Mines Committee of the Scientific Advisory Council and as Scientific Advisor on Mines to the Military Experimental Establishment. Her work during this time ranged from the study of bombing patterns and damage to the problem of discovering the placement of enemy land mines and a methodology for randomly placing land mines so as to avoid the semblance of any pattern in their placement." Garber et.al. After WWII she came back to University College London and was appointed professor in 1962. Five or six years later she took a position at the University of California Riverside becoming head of the Department of Statistics in 1970. Retiring in 1977 she came to Berkeley and continued her research. this book bears her initials on the Francis Galton Laboratory bookplate; she gave her books to Margaret Stein of Stanford University. See: M. J. Garber D. V. Gokhale J. M. Utts R. J. Beaver Chair "Florence Nightingale David Statistics: Riverside." Obituary; "A conversation with F.N. David" Statistical Science Vol. 4 No. 3235-246 by Nan Laird; J. Utts "Florence Nightingale David 1909-1993: Obituary" Biometrics 1993 49 1289-1291; Norman L. Johnson & Samuel Kotz eds. Leading Personalities in Statistical Sciences from the Seventeenth Century to the Present Wiley 1997 pp. 91-92. / REFERENCES: Babson 181 1st ed.; Ball A short account of the history of mathematics pp. 383-4; BM Readex Vol. 17 p. 751; Cajori History of Mathematics pp. 229-30; DNB vol. 38 p.116; Kress S.2793; Institute of Actuaries 1935 p. 39; Mansutti 504; Norman 1529 1st ed.; Pearson The History of Statistics in the 17th & 18th Centuries. . . pp. 155-60 165-66; Smith Source book in mathematics pp. 440-54; Stigler The History of Statistics: The Measurement of Uncertainty before 1900 1986 p. 70; Todhunter History of the theory of probability; Walker pp. 12-13; Wellcome IV p. 149; Westergaard pp. 104-5. Not in Goldsmiths or Hanson. / See: Raymond Clare Archibald "Abraham de Moivre"; David F.N. Games Gods and Gambling; The origins and history of probability and statistical ideas . . . 1962 pp. 161-178. A. Millar, 1756. hardcover books

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