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4 
DE MOIVRE, Abraham (1667–1754). 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. London: A. Millar, 1756. Quarto. 348 pp. Portrait medallion vignette on title. Original full calf; joints repaired. Fine. 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 LARGESAMPLE 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.” [BellhouseGenest, 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 (17021749) (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 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. ¶ 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 1,000 coin tosses Now, for the first time, it was practicable to apply probability theory to indefinitely large numbers of independent events.” ¶ REFERENCES: Babson 181 (1st ed.); Ball, A short account of the history of mathematics, pp. 3834; BM Readex Vol. 17, p. 751; Cajori, History of Mathematics, pp. 22930; 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. 15560, 16566; Smith, Source book in mathematics, pp. 44054; Stigler, The History of Statistics: The Measurement of Uncertainty before 1900 (1986), p. 70; Todhunter, History of the theory of probability; Walker pp. 1213; Wellcome IV, p. 149; Westergaard pp. 1045. 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. 161178. [PLEASE CONTACT DIRECT FOR FURTHER INFORMATION]. First Edition.
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6 
ELDERTON, W. Palin. Frequencycurves and correlation. London: Charles & Edwin Layton, [1906]. 8vo. xiii, 172 pp. Illus., tables, index. Original green cloth; spine ends chipped, inner hinges cracked. Ex library rubber stamp and ownership signature on title. Very good. FIRST EDITION. This work is a detailed description of the basis and practical application of modern statistical methods associated with Professor Karl Pearson. It explains frequencycurves using illustrations of their use based on actuarial data. First Edition.
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10 
PEARSON, Karl (18571936) & Margaret MOUL. "The mathematics of intelligence. I. The sampling errors in the theory of a generalised factor." In: Biometrika, Vol. XIX, Parts I and II, July, 1927. 8vo. Pages (246)291. [Entire volume: v, 442 pp.] 2 diagrams, tables; a few pages (in contents pages) expertly repaired. Later black buckram, gilt spine. Ex library copy, paper spine label removed. Very good. FIRST EDITION. This volume includes a number of papers by Karl Pearson, most notably a piece on "The mathematics of intelligence," which is an attack on Charles Spearman. See: DSB, X, pp. 447473; Stigler, The History of statistics, passim. First Edition.
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300.00 USD

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11 
PEARSON, Karl (18571936). "On a criterion which may serve to test various theories of inheritance." In: Proceedings of the Royal Society of London, Vol. LXXIII. London: Harrison and Sons, 1904. 8vo. Pages 262280. [Entire volume: viii, 548 pp.] 2 diagrams, tables. Original blindstamped navy cloth, gilt spine; rebacked, new endleaves. Ex library copy, paper spine label removed. Fine. FIRST EDITION. Francis Galton was influenced by Darwin's belief that inheritance is conditioned by a blending mechanism. Galton propounded his law of ancestral heredity, which set the average contribution of each parent at 1/4, of each grandparent at 1/16, and so forth. Pearson and his colleagues pursued the notion in a series of sophisticated researches, but Galton's law received withering criticisms after the rediscovery, in 1900, of Mendel's work on particulate inheritance. Here Pearson proposes a variability criterion between contending theories of inheritance. See: DSB, X, pp. 447473. First Edition.
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12 
POISSON, SiméonDenis (17811840). Recherches sur la probabilité des jugements en matière criminelle et en matière civile, précédées des règles générales du calcul des probabilités. Paris: Bachelier, 1837. 4to. [4], ix, [3], 415, [1] pp. Half title; light foxing within. Original quarter dark green giltstamped calf, marbled boards; extremities worn. Very good. PROVENANCE: SIGNATURE OF KARL PEARSON (18571936). KARL PEARSON’S COPY WITH HIS BOLD SIGNATURE. First edition of the work that presented Poisson’s ‘Law of large numbers.’ “He improved Laplace’s work by relating it explicitly to Jacob Sernoulli’s fundamental theorem and by showing that the invariance in the prior probabilities of mutually exclusive events is not a necessary condition for calculating the approximate probabilities. It is also from Poisson that we derive the study of a problem that Laplace had passed over, the case of great asymmetry between opposite events, such that the prior probability of either event is very small.” – DSB (p. 489). ¶ “Poisson’s major work on probability was a book, Recherches sur la probabilité…, published in 1837. The book was in large part a treatise on probability theory after the manner of Laplace, with an emphasis on the behavior of means of large numbers of measurements. The latter portion (p. 318415) dealt with the subject matter of the title. Some of this material was taken from memoirs Poisson published in the two preceding years. Only a charitable modern reading could identify a new concept in the work; yet the book contains the germ of the two things now most commonly associated with the Poisson’s name. The first of these is the probability distribution now commonly called the Poisson distribution… In a section of the book concerned with the form of the binomial distribution for large numbers of trials, Poisson does in fact derive this distribution in its cumulative form, as a limit to the binomial distribution when the chance of a success is very small. The distribution appears on only one page in all of Poisson’s work (see p. 206). Although it is given no special emphasis tis brief notice did catch the eye of Cournot, who republished it in 1843 with calculations demonstrating the effectiveness of the approximation (Cournot, 1843 …). The second most common appearance of Poisson’s name in modern literature is in connection with a generalization of the Bernoulli law of large numbers.” – Stigler. ¶ “[This work is] significant for the author’s participation in an important contemporary debate. The legitimacy of the application of the calculus to areas relating to the moral order, that is to say within the broad area of what is now called the humanistic sciences, was bitterly disputed beginning in 1820 in politically conservative circles... Poission was bold enough to take pen in hand to defend the universality of the probabilistic thesis and to demonstrate the conformability to the order of nature of the regularities that the calculus of probability, without recourse to hidden causes, reveals when things are subjected to a great number of observations.” –DSB (pp. 489). LAID WITHIN THIS VOLUME ARE FIVE PAGES (ON FOUR LEAVES) OF MATHEMATICAL NOTATIONS IN FRENCH, SUGGESTING AN OWNERSHIP (UNKNOWN) PRIOR TO PEARSON. Karl Pearson (18571936) “was a major player in the early development of statistics as a serious scientific discipline in its own right. He founded the Department of Applied Statistics (now the Department of Statistical Science) at University College London in 1911; it was the first university statistics department in the world. The present departments of Statistical Science and Computer Science, as well as the Genetics and Biometry group in Biology and the physical side of Anthropology are all part of his legacy to UCL.” A major proponent of eugenics, Pearson was also a protégé and biographer of Sir Francis Galton. ¶ REFERENCES: F. Fraunberger, within DSB, XV, Supple., I, pp. 480491; Dodge, Yadolah, The Concise Encyclopedia of Statistics, (2008), p. 427; Stigler, The History of Statistics, pp. 1823. See: Pearson, E.S., Karl Pearson: an appreciation of some aspects of his life and work. Cambridge University Press, (1938). [PLEASE CONTACT DIRECT FOR FURTHER INFORMATION]. First Edition.
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14 
SIMPSON, Thomas (17101761). The Nature and Laws of Chance. Containing, among other Particulars, The Solutions of several abstruse and important Problems... the whole after a new, general... London: Printed by Edward Cave, 1740. Signed First edition. 8vo. [2], iv, 85, [1]; [2], iv, [5]216; [v], x, “[liv]”, [2]; 103, [1] pp. Frontispiece (Stuart), 3 folding engraved plates – the three folded plates are signed: “J. Mynde sc.”; the frontispiece is signed “I Fayram inven. deli et sculp.”; small stabholes deep in gutter (center) pp. 95216 (Fluxions). Modern full calf with giltextra tooled spine and compartments, black title label, preserving original endleaves. Early armorial bookplates of Thomas Salwey, L.L.D. [ca.174060] of Richard’s Castle [motto: “Crucem gerentes salvaegentes”], Salop; J.W.L. Glaisher, Sc.D., Trinity. Bookplate of The Francis Galton Laboratory for National Eugenics (Jan. 1930); initials “F.N.D.” for Florence Nightingale David of University College London. David presented this book to statistician Margaret Stein (married to fellow statistician Charles Stein). EXTREMELY RARE COLLECTION. SAMMELBAND ON BRITISH PROBABILITY, DIFFERENTIAL CALCULUS AND MEDICINE ALLUDING TO A SYSTEM OF NEWTONIAN PHILOSOPHY. All first editions and each are rare on the market. The lead work is Simpson’s response to and challenge towards Abraham de Moivre’s (16671754), Doctrine of Chances, issued in a second edition in 1738. Simpson’s work in the preface directly addresses Mr. De Moivre, “I should be poorly ambitious of appearing the Author of a Performance, that would, was every Bird to claim his own Feather, be stript as naked as the Jay in the Fable.” See also: Karl Pearson, (edited by Egon Sharpe Pearson), History of Statistics in the 17th and 18th Centuries, (1978), pages 169, 1712. ¶ Stephen Stigler describes how this book and the author’s 1742 title, The Doctrine of Annuities and Reversions, irritated De Moivre. Both titles were based on the work of De Moivre, whom Stigler indicates was intellectually the superior to Simpson. – (Stigler, p. 88). De Moivre’s second edition of his Annuities book is scathing of Simpson’s work, saying he “mutilates my Propositions.” The two exchanged barbs and accusations as evidenced in their own writings. Stigler observes that Simpson as a mathematicianwriter tends to the reactionary and chooses to point out the distribution of errors and not on the mean observation. “Even though the position of the body observed might be considered unknown, the distribution of errors was, for Simpson, known.” (p. 91). ¶ [ALSO BOUND WITH:] SIMPSON. A New Treatise of Fluxions: wherein the direct and inverse method are demonstrated ... also the doctrine of infinite series ... are amply explained, ... together with a variety of new and curious problems. London : Printed by Tho. Gardner… ; For, and are to be had of, the author …, 1737. First edition. [WITH:] STUART, Alexander (16731742). Three Lectures on Muscular Motion Read before the Royal Society in the Year MDCCXXXVIII … William Croone … Being a supplement to the Philosophical Transactions … London: Printed for T. Woodward; and C. Davis … 1739. See: Russell, K.F. British anatomy (2nd ed.), 782. First edition. [WITH:] LANGRISH, Browne (d.1759). A New Essay on Muscular Motion. Founded on Experiments, Observations, and the Newtonian Philosophy. London: Printed for A. Bettesworth and C. Hitch, 1733. First edition. ¶ PROVENANCE: Rev. Thomas Salwey (ca.1705 after or on 1759), of Ludlow, L.L.D. * Salwey was Rector of Richard’s Castle. He married Constance (only daughter of Francis Biddulph) in 1742. PROVENANCE: James Whitbread Lee Glaisher, Sc.D. (18481928), Fellow of Trinity College, was a prolific English mathematician and astronomer. PROVENANCE: Francis Galton Laboratory. Karl Pearson In the twentieth century Francis Galton and Karl Pearson led the way in developing statistics into a mathematical discipline. PROVENANCE: F.N.D. Florence Nightingale David (19091993), also known as F. N. David was an English statistician, born in Ivington, Herefordshire, England. ¶ See: Blanco, Mónica. “Thomas Simpson: Weaving fluxions in 18thcentury London.” Historia Mathematica, vol. 41 (1) (2014), pp. 38—81. “The main part of this historical paper deals with a comparison of Thomas Simpson’s 1737 and 1750 treatises on fluxions, and with their place in the exposition and development of Newtonian calculus in the 18th century. The author highlights some of the differences in emphasis and content between the two works, explaining several of those differences in helpful detail.” – Douglas Bridges, Christchurch, New Zealand. REFERENCES: ESTC [Simpson, Laws of Chance] T78204; [Simpson, Fluxions] N7839; [Stuart, Three lectures] N14306; [Langrish] T65047. See: Theodore M. Porter, Karl Pearson: The Scientific Life in a Statistical Age, (2010), page 2901: “Simpson … was a scoundrel, supporting himself by converting De Moivre’s great discoveries into textbook routines.” Lowndes p. 1685. FULL TITLE [I]: The Nature and Laws of Chance. Containing, among other Particulars, The Solutions of several abstruse and important Problems... the whole after a new, general, and conspicuous manner, and illustrated with a great variety of examples. [SAMMELBAND WITH FOUR WORKS]. [PLEASE CONTACT DIRECT FOR FURTHER INFORMATION]. First Edition.
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