An essay towards solving a problem in the Doctrine of Chances

London: L. Davis and C. Reymers, 1764

First edition of Thomas Bayes's extremely influential work on the concept of "inverse probability", the basis of modern statistical inference.

Bayes's paper marked “a truly Copernican revolution in statistical concept ... [It] served to embed his name in what has become ... one of the most widely known eponyms in all of science, Bayesian inference ... The ideas this essay contains have been of vast influence” (S. M. Stigler, The History of Statistics).

''Bayes, a Nonconformist minister, published only two works during his lifetime: Divine Benefits (1731), a religious treatise; and Introduction to the Doctrine of Fluxions (1736), in which he responded to Bishop Berkeley's attack on the logical foundations of Newton's calculus. For the latter work he was elected a member of the Royal Society in 1742. In 1763, two years after Bayes's death, Richard Price, a fellow Nonconformist minister, economist, and actuary to whom Bayes had bequeathed his papers, found Bayes's Essay and submitted it to the Royal Society for publication. The arguments in Bayes's paper were adopted by Laplace, who saw in them the basis for statistical inference; they were later challenged by George Boole in his Laws of Thought.

“Bayes’s Essay contains the first statement of Bayes's Theorem for calculating 'inverse probabilities', which forms the basis for methods of decision analysis, statistical learning machines, and Bayesian networks. Bayesian networks are complex diagrams that organise the body of knowledge in any given area by mapping out cause-and-effect relationships among key variables and encoding them with numbers that represent the extent to which one variable is likely to affect another. Programmed into computers, these systems can automatically generate optimal predictions or decisions even when key pieces of information are missing. Bayesian or subjective decision theory is arguably the most comprehensive theory of decision-making; however, until the late 1980s, it had little impact due to the stupefying complexity of the mathematics involved. The rapid advances in computing power and the development of key mathematical equations during the late 1980s and early 1990s made it possible to compute Bayesian networks with enough variables to be useful in practical applications" (Hook & Norman).

With the advent of the Internet, Bayesian networks have been applied extensively to fundamental search structures. "Search giant Google and Autonomy, a company that sells information retrieval tools, both employ Bayesian principles to provide likely (but technically never exact) results to data searches. Researchers are also using Bayesian models to determine correlations between specific symptoms and diseases, create personal robots, and develop artificially intelligent devices that 'think' by doing what data and experience tell them to do" (Michael Kanellos, "18th-century theory is new force in computing").

Only one other mathematical contribution of Bayes has come down to us, which appears on pp. 269-71. It is referred to by Price on p. 401 of the Essay in connection with the evaluation of factorials needed for the second rule. In this paper Bayes considers the series for log n! given by Stirling and de Moivre. He makes the important observation that "at length the subsequent terms of this series are greater than the preceding ones, and increase in infinitum, and therefore the whole series can have no ultimate value whatsoever" (p. 270). This was contrary to de Moivre's view that the series "converged, but slowly". Bayes was, in fact, the first to appreciate the asymptotic character of Stirling's series: there is now an extensive theory of such 'asymptotic series'. The present volume also contains a paper by Ferguson on the anticipated 1769 transit of Venus, which prompted Captain Cook's voyage to Tahiti, and led to the first accurate measurement of the sun's distance, illustrated with a fine large folding engraved plate.

An essay towards solving a problem in the Doctrine of Chances. By the late Rev. Mr. Bayes F.R.S. Communicated by Mr. Price in a Letter to John Canton, A.M. F.R.S. in Philosophical Transactions, Vol. LIII (1763), pp. 370-418. London: L. Davis and C. Reymers, Printers to the Royal Society, 1764. With 26 engraved plates, mostly folding. Quarto, contemporary full calf rebacked. The entire volume, #53 for 1763 offered. "Belfast Society" in gilt on front board. Moderate wear to contemporary boards with renewed corners and edges; interior fine.

$8,750

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Bryan and Darrow at Dayton: The Bible Evolution Trial

FIRST EDITION. Contains full record (with commentary) of the famous Scopes Monkey Trial.“The Eugenics Society officially endorsed sterilization in June 1926. Prior to this it had been nominally neutral on the issue, although in practice firmly supporting sterilization. By 1926 the scene was set for a more aggressive push. Leonard Darwinʼs big book The Need for Eugenic Reform came out in that year. It was an earnest work that comprehensively set out the wide gamut of arguments for and against eugenics, and sterilization, and it had a generally good reception.” –David Paul Crook, Darwinʼs Coat-Tails: Essays on Social DarwinismOctavo, original green cloth.

$75

Almagestum seu magnae constructionis mathematicae opus [Almagest]

FIRST EDITION of the first Latin translation from the original Greek text. The Almagest, written in about 150 AD, "served as the basic guide for Islamic and European astronomers until about the beginning of the 17th century. Its original name was Mathematike Syntaxis (“The Mathematical Arrangement”); Almagest arose as an Arabic corruption of the Greek word for greatest (megiste). It was translated into Arabic about 827 and then from Arabic to Latin in the last half of the 12th century. Subsequently, the Greek text circulated widely in Europe, although the Latin translations from Arabic continued to be more influential."The Almagest is divided into 13 books. Book 1 gives arguments for a geocentric, spherical cosmos and introduces the necessary trigonometry, along with a trigonometry table, that allowed Ptolemy in subsequent books to explain and predict the motions of the Sun, Moon, planets, and stars. Book 2 uses spherical trigonometry to explain cartography and astronomical phenomena (such as the length of the longest day) characteristic of various localities. Book 3 deals with the motion of the Sun and how to predict its position in the zodiac at any given time, and Books 4 and 5 treat the more difficult problem of the Moon’s motion. Book 5 also describes the construction of instruments to aid in these investigations. The theory developed to this point is applied to solar and lunar eclipses in Book 6."Books 7 and 8 mainly concern the fixed stars, giving ecliptic coordinates and magnitudes for 1,022 stars. This star catalog relies heavily on that of Hipparchus (129 bc), and in the majority of cases Ptolemy simply converted Hipparchus’s description of the location of each star to ecliptic coordinates and then shifted these values by a constant to account for precession over the intervening centuries. These two books also discuss the construction of a star globe that adjusts for precession. The remaining five books, the most original, set forth in detail geometric models for the motion of the five planets visible to the naked eye, together with tables for predicting their positions at any given time."Commissioned by Pope Nicholas V (1446-1455), translated from Greek into Latin by Georgius Trapezuntius (1396-1472), edited by Luca Gaurico (1476-1558). An earlier Latin version had appeared in 1515, but was translated from the Arabic. Norman 1760; See Stillwell 97; Wellcome 5281.Venice: Lucantonio Giunta, 1528. Tall folio (313 x 218 mm), 18th-century full vellum with ink notation on spine. Collation: A6 a-s8 (s8 blank); 149 leaves (of 150, without a blank). Title printed in red and black. Printed in Roman, Gothic and Greek types with woodcut mathematical diagrams in margins throughout. Occasional light staining, mostly to margins; small hole in q8 (affecting border of table, a likely paper flaw); repairs to hinges. A beautiful wide-margined copy.

$15,500

Island Life: Or, the Phenomena and Causes of Insula Faunas and Floras, Including a Revision and Attempted Solution of the Problem of Geo- logical Climates

FIRST EDITION of one of Wallace's most important works. Wallace's treatment of the general distribution of island plant and animal life and the influence of the glacial epochs of these distribution patterns. Included is the first theory of continental glaciation, a discussion of island classification, and a survey of worldwide island faunas and floras.Octavo. Original green cloth. 3 maps (1 chromolithograph, 2 tinted); numer wood-engraved text illustrations throughout. A clean copy throughout; very minor rubbing at extremities. A very desirable copy.

$1,400

Hydrodynamica, sive de viribus et moribus fluidorum

FIRST EDITION of Bernoulli's masterpiece, the foundational work for hydrodynamics (a term Bernoulli invented).Bernoulli's "reputation was established in 1738 with Hydrodynamica, in which he considered the properties of basic importance in fluid flow, particularly pressure, density, and velocity, and set forth their fundamental relationship. He put forward what is called Bernoulli’s principle, which states that the pressure in a fluid decreases as its velocity increases. He also established the basis for the kinetic theory of gases and heat by demonstrating that the impact of molecules on a surface would explain pressure and that, assuming the constant, random motion of molecules, pressure and motion increase with temperature" (Britannica)."Besides introducing the first hydraulic theory of fluid flow, this book is the most remarkable general work in theoretical and applied mechanics written in the pre-Langrangean period of the 18th century, based on a deep physical understanding of mechanical phenomena and presenting many new ideas for the following scientific progress" (Mikhailov, in Landmark Writings in Western Mathematics, 1640-1940).With 12 folding engraved plates and 86 illustrations. Quarto, contemporary full calf rebacked with the original spine laid-down.

$17,000

Introductio in Analysin Infinitorum

FIRST EDITION of Euler's foundational work on mathematical analysis. "In his 'Introduction to Mathematical Analysis' Euler did for modern analysis what Euclid had done for ancient geometry. It contains an exposition of algebra, trigonometry and analytical geometry, both plane and solid, a definition of logarithms as exponents, and important contributions to the theory of equations. He evolved the modern exponential treatment of logarithms, including the fact that each number has an infinity of natural logarithms. In the early chapters there appears for the first time the definition of mathematical function, one of the fundamental concepts of modern mathematics. From Euler's time mathematics and physics tended to be treated algebraically, and many of his principles are still used in teaching mathematics" (PMM 196). Without the engraved portrait of the dedicatee Jean-Jacques Dortous de Mairan, possible indicating that this is an early issue. Titles in red and black with engraved vignettes, frontispiece by Soubeyran after De la Monce; with directions to the binder and 40 folding engraved plates in rear (largely unopened), woodcut initials, head- and tailpieces and chapter vignettes. Quarto, original blue wrappers with paper labels; custom cloth box. Two volumes. A few leaves with light dampstaining in outer margin, otherwise a fine, crisp uncut copy; extremely rare in original wrappers.

$12,000

Mechanique Analitique

FIRST EDITION, a foundational work in modern mechanics. "Joseph-Louis Lagrange (1736-1813) continued the work of the earlier half of the century on the calculus; he extended mathematical analysis and the theory of equations; and in 1788 he published his Mechanique Analitique, a work second only to Newton's Principia in the history of mechanics" (Goodwin, The New Cambridge Modern History). "With the appearance of the Mechanique Analitique in 1788, Lagrange proposed to reduce the theory of mechanics and the art of solving problems in that field to general formulas, the mere development of which would yield all the equations necessary for the solution of every problem... [it] united and presented from a single point of view the various principles of mechanics, demonstrated their connection and mutual dependence, and made it possible to judge their validity and scope" (DSB)."Lagrange produced his greatest work, Mecanique analytique (1788; Analytical Mechanics), in Paris. This summarized the research in mechanics since Isaac Newton, based on Lagrange's own calculus of variations, and finally placed the mechanical theory of solids and fluids on a rigorous and analytical foundation" (Biographical Encyclopedia of Scientists). Dibner 112.Quarto, contemporary mottled calf, gilt-decorated spine with morocco label. Spine ends and corners a little worn, otherwise fine.

$14,500

[Conics] Conicorum Libri Quattuor. Una Cum Pappi Alexandrini Lemmatibus, et Commentariis Eutochii Ascalonitae

FIRST EDITION of the first four books of Apollonius's Conics; the first printing of any of his work. "Of the school of Euclid in Alexandria, Apollonius applied to conic sections the discipline that Euclid had given to geometry" (Dibner 101).Apollonius was “known by his contemporaries as ‘the Great Geometer,’ whose treatise Conics is one of the greatest scientific works from the ancient world. Most of his other treatises are now lost, although their titles and a general indication of their contents were passed on by later writers, especially Pappus of Alexandria (fl. c. AD 320). Apollonius's work inspired much of the advancement of geometry in the Islamic world in medieval times, and the rediscovery of his Conics in Renaissance Europe formed a good part of the mathematical basis for the scientific revolution.“The first four books of the Conics survive in the original Greek, the next three only from a 9th-century Arabic translation, and an eighth book is now lost. Books I–IV contain a systematic account of the essential principles of conics and introduce the terms ellipse, parabola, and hyperbola, by which they became known" (Britannica).Beautifully printed with diagrams on nearly every page. Bound with: SERENUS OF ANZI (fl. 4th century). Libri duo. Unus de sectione cylindri, alter de sectione coni. All texts translated from Greek into Latin and edited by Federico Commandino (1509-1575). Bologna: Alessandro Benacci, 1566. Bologna: Alessandro Benacci, 1566, Folio, early full vellum with silk ties, old tape repair to top of spine, some soiling to binding, ties frayed, evidence of signature removal at top of title, bookplate of Franz Joseph, Count of Kuenberg. Text exceptionally clean with wide margins.

$14,000

The Expression of the Emotions in Man and Animals

FIRST EDITION, SECOND ISSUE. “One batch of material proved too bulky for incorporation in the Descent of Man and Darwin held it over for separate treatment. This derived from his research into human and animal expressions...Though much of his analysis has been superseded, and was for modern scientific purposes marred by much unconscious anthropomorphism, he was convinced that an evolutionary continuity existed between the expressions (and hence mental life) of animals and humans, and that animals experience traces of every human emotion, including the moral feelings. In this sense,The Expression of the Emo- tions in Man and Animals completed his great cycle of evolutionary writings.” –Oxford Dictionary of National BiographyOctavo. Original green cloth. First edition, second issue with ʻhtatʼ for ʻthatʼ at top of page 208. Publisherʼs ads dated Nov. 1872. Spine ends rubbed, corners bumped; split at inner hinge. Clean throughout. An attractive copy.The Expression of Emotions describes how humans and animals express and signal their emotions to others. Darwin based his conclusions on worldwide questionnaires, photographs of actors, babies, and “imbeciles” in an asylum, as well as his own observations based on the grief expressed following a family death.

$800

Earth In the Balance: Ecology and the Human Spirit

"A global environmental crisis threatens to overwhelm our children's generation. Mitigating the crisis will require a planetary perspective, long-term thinking, political courage and savvy, eloquence and leadership––all of which are in evidence in Al Gore's landmark book."–Carl SaganFIRST EDITION, SIGNED AND INSCRIBED BY AL GORE: "For the grandchildren of Sally and Paul Robinson". A fine copy in the original dust jacket.

$225

Nova Stereometria doliorum vinariorum

SCARCE FIRST EDITION of one of the most significant works in the prehistory of calculus. With the rare errata leaf present in two variant states."The task of writing a complete treatise on volumetric determination seems to have been suggested to Kepler by the prosaic problem of determining the best proportions for a wine cask. The result was the Nova stereometria, which appeared in 1615. This contains three parts, of which the ﬁrst is on Archimedean stereometry, together with a supplement containing some ninety-two solids not treated by Archimedes. The second part is on the measurement of Austrian wine barrels, and the third on applications of the whole" (Boyer, The History of the Calculus).Kepler's basic method was to regard the circle as a polygon with an inﬁnite number of sides and its area as being composed of an inﬁnite number of inﬁnitesimal triangles with vertex at the centre of the circle and base one of the sides of the polygon. Similarly, the volume of a sphere was made up of an inﬁnite number of pyramids, the cone and cylinder of inﬁnitely thin circular discs or of inﬁnitesimal wedge-shaped segments radiating from the axis. "Kepler then extended his work to solids not considered by the ancients. The areas of the segments cut from a circle by a chord he rotated about this chord, obtaining solids which he designated characteristically as apple or citron-shaped, according as the generating segment was greater or less than a semi-circle... Kepler's Doliometha... exerted such a strong inﬂuence in the inﬁnitesimal considerations which followed its appearance, and which culminated a half century later in the work of Newton, that it has been called [by Moritz Cantor] the source of inspiration for all later cubatures" (Boyer).Kepler's book on integration methods also contains the germ of the differential calculus. "The subject of the measurement of wine casks had led Kepler to the problem of determining the best proportions for these. This brought him to the consideration of a number of problems on maxima and minima ... he showed, among other things, that of all right parallelepipeds inscribed in a sphere and having square bases, the cube is the largest, and that of all right circular cylinders having the same diagonal, that one is greatest which has the diameter and altitude in the ratio of [square root of 2]:1. These results were obtained by making up tables in which were listed the volumes for given sets of values of the dimension ... He remarked that as the maximum volume was approached, the change in volume for a given change in the dimensions became smaller" (Boyer). Kepler had noted, in modern terms, that when a maximum occurs the rate of change becomes zero, a basic principle of the differential calculus that is usually credited to Fermat later in the century.Nova Stereometria doliorum vinariorum, in primis Austriaci, ﬁgurae omnium aptissimae; et usus in eo virgae cubicae compendiosossimus & plane singularis. Accessit Stereometriae Archimedae Supplememtum. Folio, contemporary calf sympathetically rebacked. With two errata leaves, woodcut on H3v shaved at foot as usual, ocassional foxing, small closed tears to final leaf; a very good crisp copy. RARE.

$45,500

On a New Series of Organic Bodies Containing Metals

"From novel and highly obscure compounds he had discovered one of the great principles of all chemistry, which came to be known as valency. Although others, particularly August Kekulé, claimed priority for this discovery, Frankland was certainly the first to articulate the concept of what he called ‘combining power’. The results he later communicated to the Royal Society, and they were read to the society's meeting on 10 May 1852. This important paper was subsequently published as ‘On a new series of organic bodies containing metal’ (PTRS, 142, 1852, 417–44)" (Oxford Dictionary of National Biography). Frankland's research on "combining power" revolutionized modern structural chemistry and established his reputation as one of the most important theoretical chemists in the world.IN: Philosophical Transactions of the Royal Society of London 142 pp. 417-444, 1852. First edition. Fine extract bound beautifully in aged leather and boards.

$500

Ondes et Mouvements [Waves and Motions]

FIRST EDITION IN ORIGINAL WRAPPERS of de Broglie’s presentation of his revolutionary theory of the wave-particle duality of matter. PMM 417.De Broglie’s work “served as the basis for developing the general theory nowadays known by the name of wave mechanics, a theory which has utterly transformed our knowledge of physical phenomena on the atomic scale.”Octavo, original printed wrappers; custom cloth box. Modest bookplate on inside front wrapper; tape repair to initial blank. Minor discoloration to wrapper edges; an excellent copy.

$2,500

BAYES, THOMAS