Science

FIRST EDITION of Huygens's masterpiece; an outstanding copy with noted provenance."A work of the highest genius which has influenced every science through its mastery of the principles of dynamics. It is second in scientific importance perhaps only to Newton's Principia, which is in some respects based on it" (Singer, A Short History of Science to the Nineteenth Century)."Important as Huygens's clock was from both a practical and a scientific point of view (it could be used by astronomers), the Horologium ('The Oscillating Clock') is a general work on dynamics and especially a mathematical analysis of pendulum motion. It was the most original work of this kind since Galileo's Discorsi" (PMM 154)."Although others had suggested the pendulum as part of a timing mechanism, it remained for Huygens to apply his keen mathematical sense to the problems of the clock. In this work, of which the first and fifth books are devoted to the pendulum, he treated many problems of dynamics of bodies in motion. He determined the tautochronous character of the cycloid and applied it to invent an isochronous pendulum clock. To the theory of curves he added the theory of evolutes, the fall of bodies along curves, and determined the first value of the force of gravity by using a compound pendulum. At the end are listed 13 theorems that relate to the theory of centrifugal force in circular motion, a theory that aided Newton in determining universal gravitation" (Dibner 145). Provenance: Eprit Flechier (1632-1710), Bishop of Nimes from 1687 to 1710, and well-known for his published sermons and histories. Indentified by The Catholic Encyclopedia as "one of the greatest sacred orators of his century". His library was sold in London on January 25, 1726.Horologium Oscillatorium. Sive de Motu Pendulorum ad Horologia aptato Demonstrationes Geometricae. Paris: F. Muguet, 1673. Folio, contemporary full speckled calf , elaborately gilt-decorated spine, gilt arms on boards of Eprit Flechier, Bishop of Nimes. With full page woodcut and numerous in-text woodcuts and tables. Repairs to spine and corners, text with occasional light browning. A beautiful, fine copy with wide margins.

EXTREMELY RARE FIRST EDITION of Fermat's Collected Works, containing the first publication of most of his work. "Fermat shares with Descartes the innovation of analytical geometry by applying algebra to geometry. He, independently, represented a curve by an equation defining its characteristic properties. He published little but, in the manner of his times, announced his discoveries in letters to other mathematicians. Among his discoveries was a general method of solving questions of maxima and minima, a method he used in 1629 and one in use today. He contributed basic concepts in the theory of numbers and probability. The above [Varia Opera], published after his death, first presented his work and correspondence" (Dibner 108). Provenance: the Inner Temple Library, with small ink stamp on title and a few other leaves; English mathematician Francis Maseres's (1731-1824) copy with his signature on front flyleaf and annotations in text. Folio, contemporary calf rebacked. With five engraved folding plates; engraved head and tailpieces, diagrams in text. Scarce portrait not present, as often. Occasional light browning and foxing. A very good copy. 

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.

FIRST EDITION. Hofmeister describes the fundamental structures and processess of the cell, and gives the first account of what later became known as chromosomes. Hofmeister's work inspired Mendel to begin the research on plant hybridization that led to Mendel's discoveries on the inheritance of traits. Large octavo. Early quarter-calf over pebbled cloth. Spine lightly rubbed; stamp at title, generally clean. A sound, attractive copy. 

FIRST EDITION.Octavo, original maroon cloth.The Scientific Basis of Evolution documents a series of lectures that Morgan gave at Cornell University in 1931 on the topic of the biology of evolution. A year later, Morgan was awarded the 1933 Nobel Prize in Physiology or Medicine.

"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. 

FIRST EDITION of Halley's important paper detailing his unprecedented mathematical description of the relationship between barometric pressure and altitude above sea level.  In addition, Halley may have been the one to coin the term "barometer" in this paper.  This issue of Philosophical Transactions also includes Cassini's discovery of two new Saturnian satellites.  While much of Aristotelian theory had been firmly discarded by the 17th century, Aristotle's idea that meteors were an atmospheric phenomenon perservered.  "The first serious challenge to Aristotle's meteor hypothesis was proposed by Edmund Halley, Astronomer Royal. Unlike Aristotle, Halley continually tried to measure quantities. The height of the Earth's atmosphere is a typical example… In [his Discourse] he calculated that the atmosphere only extended to a height of some 40 to 45 miles. So if meteors were ignited exhalations, they had to occur below this height" (Physicists Look Back: Studies in the History of Physics, ed. John Roche). IN: Philosophical Transactions of the Royal Society of London, Issue No. 181 pp. 104-116. London: Royal Society of London, 1686.  The complete issue, no. 181, pp. 77-123. Small quarto, sympathetically rebound in modern three quarter calf over marbled boards. A few spots to text, generally fine condition.

FIRST AMERICAN EDITION. In this work, Darwin first proposed his theory of pangenesis as the mechanism of heredity. The theory holds that body cells shed “gemmules” that collect in the reproductive organs, thus transmitting their characteristics to the next generation. Mendelʼs theory of genetics supplanted this theory in the early 1900s. Octavo, two volumes. Original green cloth. Light wear at head of both volumes; light spotting to spine of volume II. Cloth generally clean. An attractive set.

FIRST EDITION. "Hofmeister was a man of penetrating insight. He not only observed the constant changes in size, form and complexity that attended any embryological development: he also carried out physiological experiments and he constantly inquired: Hod does the observed form come to be? Here he had in mind the need to formulate explanations or interpretations, in general terms, incorporating mathematics and the physical sciences. These studies, which disclosed a new approach to morphology, were presented in ... Allgemeine Morphologie der Gewächse" –Claude Wilson Wardlaw, Essays on Form in Plants. Octavo, quarter cloth over original wrappers mounted on boards. (Bound upside-down and backwards). Generally clean. An attractive copy in original boards., 

"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.

SECOND AMERICAN EDITION. Lyell uses the evidence of fossil remains to place the age of the human race in the context of other historical artifacts such as glaciers and extinct species of animals. This was much longer than previously supposed. Lyell also comments on the ideas of species and race, and on the evolution theories of Lamarck, Chambers, Darwin, and Wallace.“Though written by a single author, Antiquity of Man was substantively and symbolically the work of all the human antiquity investigators. It drew extensively on Prestwichʼs and Evansʼs work in the Somme Valley, Pengellyʼs excavation of Brixham Cave, Flaconerʼs investigations of caves throughout Europe, and a variety of recent archaeological stud- ies... His knowledge of post-Tertiary geology and his reputation as theorist meant that, in expressing his belief in men among the mammoths, he tacitly spoke for all the geolo-gists working on the human antiquity question.” - A. Bowdoin Van Riper, Men Among the Mammoths: Victorian Science and the Discovery of Human PrehistoryOctavo. Original pebbled cloth. An attractive copy in original cloth. Generally clean throughout; spine ends frayed with loss, corners rubbed, gilt somewhat dulled. Generally a handsome and sound volume. 

FIRST EDITION IN ENGLISH of Weismann's Studien zur Descendez-Theorie (1875-1876).Weismann described the seasonal dimorphism of butterflies and then first proposed his theory of the mechanism of heredity. This theory is now called “blastogenesis”. This theory holds that inheritance takes place exclusively through the germ plasm and that none of the other cells of the body pass genetic information to germ cells. This means that the characteristics acquired during life are not transmitted onto the next generation. This is in direct conflict with Lamarckian evolutionary theory and Darinʼs earlier theory of “pangenesis”. Charles Darwin was very supportive of Weismannʼs work and wrote the introduction to this book.Octavo. Two volumes, early half-calf over brown boards.

FIRST AMERICAN EDITION.  “In paleontology, catastrophism reached an apogee in Georges Cuvierʼs... ʻEssay on the theory of the earth.” Cuvier did not present his Essay as a textbook of catastrophism, but as a statement about the roles that paleontology and geology should play in unravelling the history of the earth. Nonetheless, Cuvierʼs Essay exposes all characteristic features of catastrophism as a science, and illustrates the incompatibility of this geologi- cal approach with Darwinʼs prerequisites for natural selection as a chief agent of macro-evolutionary pattern.” - Stephen Jay Gould, The Structure of Evolutionary TheoryOctavo. Complete with half-title and 8 engraved plates. Modern 1/4 calf over early marbled boards. Scattered foxing; glean throughout. A handsome copy. 

FIRST EDITION (precedes the English edition of the same year). “Huxley wages his struggle [in favor of Darwinʼs theory of evolution] in the pages of his book--in its metaphors and myths, in its rhythms and repetitions, in its images and instructions. ʻThe difference between Man and Ape is less than the difference between Ape and Monkeyʼ--over and over the lesson is repeated, like on of the slogans in the Brave New World of Huxleyʼs grandson Aldous.” –Misia Landau, Narratives of Human Evolution Small 8vo. Original cloth, original spine lablel. Spine ends chipped, spine label and extremities lightly rubbed. Clean throughout. A very attractive copy. Synthesis of the anatomic and embryological evidence of human evolution. Contains a precursor to the “man evolved from apes” theory, noting the resemblance of manʼs skeleton to that of an ape. This predated Darwinʼs Descent of Man by 8 years.

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.

Feynman's path integral formulation of quantum mechanics.  Also contains "A Generalized Theory of Gravitation" by Albert Einstein (pp. 35-39).Volume beautifully bound in cloth and boards in pristine condition inside and out.

FIRST EDITION of the famous Many Worlds interpretation of quantum mechanics. “Many worlds” is an alternative to the Copenhagen interpretation that creates a special role of the observer by postulating the collapse of the universal wave function at every observation.  Instead, Many Worlds proposes that the wave function never collapses, and views reality as a many-branched tree in which every possible outcome is realized through a splitting of reality into alternate universes – hence “many worlds.”In: Reviews of Modern Physics, vol. 29, no. 3, July, 1957, pp. 454-62, the entire issue in original orange printed wrappers offered here. Spine toned, owner signature on front wrapper, the word 'Gravitation' written in block letters at top of spine. A fresh, attractive copy.

FIRST EDITION. Contains a series of Wallaceʼs essays on the topic of natural selection, some original and some reprinted (including the two papers he published prior to Origin of Species). This is Wallaceʼs first writing on the topic of natural selection with respect to man. His thesis was that natural selection alone cannot explain the evolution of man.Octavo, recent half-calf over marbled boards. Library stamps on recto and verso of title. A handsome copy. 

FIRST EDITION. "The first statement of the theory of natural selection and an almost complete anticipation of Darwin's theory" – Garrison Morton"[What was done for animals artificially] seems to be done with equal efficiency, though more slowly, by nature, in the formation of varieties of mankind, fitted for the country which they inhabit. Of the accidental varieties of man, which would occur among the first scattered inhabitants, some one would be better fitted than the others to bear the dis- eases of the country. This race would multiply while the others would decrease, and as the darkest would be the best fitted for the [African] climate, at length [they would] be- come the most prevalent, if not the only race."Wells presented “An Account of a Female of the White Race...” to the Royal Society in 1813 but the work was not published until 1818, after his death, as a paper in the volume entitled Two Essays. In this paper, Wells describeshow the natural selection process applies to skin color in humans.Octavo.

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.

FIRST EDITION of Whiston's famous description of the earth's creation and great flood.  Beautifully rebound in period style full leather.  A fine copy.

FIRST EDITION of Jevons's explanation of his "logical piano"; a landmark in computer science.To the reader of the preceding paper it will be evident that mechanism is capable of replacing for the most part the action of thought required in the performance of logical deduction. Mental agency is required only in interpreting correctly the grammatical structure of the premises, and in gathering the purport of the reply... The machine is thus the embodiment of a true symbolic method or Calculus... Jevons invented a "logical piano" (so named because it resembled a small upright piano) that could perform, through a sequence of switches, various types of logical calculations. In doing so, he became "the first person to construct a machine with sufficient power to solve a complicated problem faster than the problem could be solved without the machine's aid" (Goldstine). "On the Mechanical Performance of Logical Inference," a paper Jevons read before the Royal Society on January 20, 1870, is his most detailed description of this early prototype of the modern computer. The logical piano now stands in the Museum of the History of Science in Oxford.In: Philosophical Transactions of the Royal Society of London for the year 1870, pp. 497-518, Vol. 160, Part II (the complete volume). London: Taylor and Francis, 1870. Quarto, modern half-calf over marbled boards, with the original wrappers bound-in. A fine copy.

First printings of three important papers demonstrating the universal validity of Newton's laws of gravity and motion. Extracted from Philosophical Transactions 93, pt2; 94, pt. 2; 114, pt. 3.Isaac Newton developed the laws of physics (motion and gravity) from observations on earth and the motions of the moon and planets within the solar system, and though scientists believed these laws to be universal, it was more than 100 years before they were demonstrated to hold outside the solar system. William Herschel published the results of a 25 year program of measuring the motion of binary stars in in two parts, in 1803 and 1804. He was able to demonstrate that orbital motion of these double stars obeyed Newton’s law of gravity and motion, thus providing the first scientific evidence of the validity of the laws of physics outside our solar system. More than 20 years later in 1824, William Herschel’s son John Frederick William Herschel (1792–1871) published an even larger study of the motion of double stars (360 in all) that supported his father’s earlier work. “Account of the Changes that have Happened, During the Last Twenty-five Years, in the Relative Situation of Double-Stars, with an Investigation of the Cause to which they are Owing” by William Herschel (Philosophical Transactions of the Royal Society of London 93 Part 2 pp. 339-382, 1803)“Continuation of an Account of the Changes That Have Happened in the Relative Situation of Double Stars” by William Herschel (Extract from Philosophical Transactions of the Royal Society of London 94 Part II pp. 353-384, 1804)“Observations of the Apparent Distances and Positions of 380 Double and Triple Stars, Made in the Years 1821, 1822, and 1823, and Compared with Those of Other Astronomers; Together with an Account of Such Changes as Appear to Have Taken Place in Them Since Their First Discovery. Also a Description of a Five-Feet Equatorial Instrument Employed in the Observations” by John Herschel (Philosophical Transactions of the Royal Society of London 114 Part 3, 1824) Very good condition. The first and third extracts are untrimmed and bound in early paper wraps; the second is a more recent extract and lacks wrappers. All are housed in an attractive custom clamshell box. 

FIRST EDITIONS OF THOMSON'S PAPERS ON THE DISCOVERY OF THE ELECTRON.  The two papers  demonstrated the discovery of the electron. In 1897, J. J. Thomson completed measurements of cathode rays and announced on April 30, 1897 that they are comprised of corpuscles with a charge to mass ratio (e/m) roughly one thousand times that of the hydrogen ion. Because he thought that the charge of the corpuscle might be the same as the hydrogen ion measured in electrolysis, he speculated that the mass of the negatively charged corpuscle could be as little as one thousandth of the hydrogen atom.  This was printed in the famous paper "Cathode Rays."  In the following two years, Thomson conducted additional experiments to determine (rather than just infer) the charge of the corpuscle and improve the precision of his measurements of e/m.  He also performed  these measurements on corpuscles generated through other  mechanisms (e.g., ions created by X-rays) and found that the results were the same regardless of source.  In 1899, in the second of these papers, Thomson concluded that the corpuscle was a subatomic particle with a mass 1/1000 of the mass of the hydrogen atom, thus confirming the discovery of the electron. "On the Charge of Electricity carried by the Ions produced by Röntgen Rays" (The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 46 pp. 528-545, 1898) and “On the Masses of the Ions in Gases at Low Pressures,” (The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 48 pp. 547-567, 1899).Two volumes. Quarto. Both volumes beautifully bound in leather and boards.  Back of title pages strengthened.  Otherwise fine.

Dinsdale's Seeing by Wire or Wireless was the first book entirely devoted to subject of television.  Dinsdale gives and account of the demonstration of John Baird's successful television system in January 1926, details similar previous experiments, and describes the mechanics of television.  Overall, the history of television is well-documented in Dinsdale's work, and Baird's system paved the way for future developments in television, leading to the first high-definition broadcasting system in 1936. First edition.  Original wraps, no dust cover; in clamshell box.

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.

FIVE FIRST EDITIONS DOCUMENTING THE INTRODUCTION AND DEVELOPMENT OF WEGENER'S THEORY OF CONTINENTAL DRIFTIf we are to believe in Wegener’s hypothesis we must forget everything which has been learned in the last 70 years and start all over again –Alexander du Toit, Our Wandering Continents (1937).From the mid-1920s to the mid-1960s most geologists worked within Permanentist or Contractionist frameworks. Few adhered to Drift. From the mid-1950s, two developments took place. First, some groups of geologists concentrated on new phenomena and geophysical data which had come to light since Wegener. Second, new versions of Drift were put forward... By the early 1970s the ‘modern revolution’ in geology was complete: the plate tectonics version of Drift, in which the surface of the earth was composed of slowly-moving slabs of crust, was firmly entrenched as the new orthodoxy.  –Homer Eugene LeGrand, Drifting Continents and Shifting Theories Wegener, Alfred. "Die Entstehung der Kontinente" (Mitteilung aus Justus Perthes’ geographischer Anstalt 58 pp. 185–195, 253–256, 305–309, 1912)WITH: "History of Ocean Basins" by Harry H. Hess (Petologic studies: a volume in honor of A. F. Buddington. Geologic Society of America pp. 599-620, 1962)WITH: "Evidence from Islands on the Spreading of Ocean Floors" by J. Tuzo Wilson (Nature 197 no. 4867 pp. 536–538, 9 February 1963) WITH: "A new Class of Faults and their Bearing on Continental Drift" by J. Tuzo Wilson (Nature 207 no. 4995 pp. 343–347,24 July 1965)WITH: "Did the Atlantic close and then re-open?" by J. Tuzo Wilson (Nature 211 no. 5050 pp. 676–68, August 13, 1966); and "Seismology and the New Global Tectonics" by Jack Oliver et al. (Journal of Geophysical Research 73 No. 18 pp. 5855-5899, 1968).

Second edition of Galileo's collected works; an important edition containing a wealth of material (nearly all of volume 3) not included in the 1655-56 first collected edition. The first two volumes are essentially a reprint of the 1655-56 Bologna edition, while the third volume contains previously unpublished material. Sometimes referred to as  the "first complete edition", although this edition does not include the Dialogo nor the Letter to the Grand Duchess Cristina, both of which were still on the Index Prohibitorum. Edited by Tommaso Buonaventuri.Quarto, contemporary full vellum with leather labels; edges speckled red. Three volumes. With engraved frontispiece portrait of Galileo, engraved vignette with view of Florence on first title page with title page printed in red and black, woodcut initials, head- and tailpieces, woodcut diagrams, folding engraved plate. A few cosmetic cracks to vellum at joints. Faint evidence of stamp removal on title pages, two small spots of dampstaining on top margin of first few leaves of vol 1; tiny worming on first few leaves of vol 3. Text extremely clean with wide margins. A beautiful set.

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.

RARE FIRST EDITION of books V-VII of Apollonius’s hugely influential Conics, containing his most original work. 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. Although most of Books I–II are based on previous works, a number of theorems in Book III and the greater part of Book IV are new. It is with Books V–VII, however, that Apollonius demonstrates his originality. His genius is most evident in Book V, in which he considers the shortest and the longest straight lines that can be drawn from a given point to points on the curve. (Such considerations, with the introduction of a coordinate system, lead immediately to a complete characterization of the curvature properties of the conics.)” (Britannica). With: Archimedes’s Liber Assumptorum following the Apollonius. Complete with half-title. Folio, contemporary full calf rebacked with original gilt-decorated spine laid down. Some scuffing to binding. Text clean with wide margins. 

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.

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. 

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.

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.

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.

FIRST EDITION of Bernoulli's foundational work on probablility theory.Jakob Bernoulli's "great treatise (conjectandi means literally 'casting, sc. dice) was published posthumously. It was the first systematic attempt to place the theory of probability on a firm basis and is still the foundation of much modern practice in all fields where propability is concerned - insurance, statistics and mathematical heredity tables" (PMM 179)."Jakob Bernoulli’s pioneering work Ars Conjectandi (published posthumously, 1713; “The Art of Conjecturing”) contained many of his finest concepts: his theory of permutations and combinations; the so-called Bernoulli numbers, by which he derived the exponential series; his treatment of mathematical and moral predictability; and the subject of probability—containing what is now called the Bernoulli law of large numbers, basic to all modern sampling theory" (Britannica).Small quarto, contemporary full calf rebacked with original spine laid down; elaborately gilt-decorated spine; marbled endpapers, edges dyed red. Bookplate of Ch. Roulleau de la Roussiere on front free endpaper. Neat small contemporary ownership inscription on title. Light occasional foxing generally to margins, foxing heavier on first few and last few leaves. A very good copy in handsome contemporary binding. 

FIRST EDITION of the first announcement of differential calculus. "The controversy with Newton on priority of invention of the calculus does not detract from the superiority of Leibniz' method of notation, one retained in modern use. He applied his new method to the solution of the cubic parabola and the inverse methods of tangents and many problems left unsolved by Descartes. Fifteen years after Newton's first work in fluxions and nine after his own independent discovery, Leibniz published [Nova Methodus], his first announcement of the differential calculus" (Dibner 109). "Leibniz was an almost universal genius whose place in the history of mathematics depends on his being an independent inventor of the infinitesimal calculus and on his contributions to combinatorial analysis which foreshadowed the development of modern mathematical analysis... The Acta Eruditorum was established in imitation of the French Journal des Scavans in Berlin in 1682 and Leibniz was a frequent contributor. Another German mathematician (E.W. Tschirnhausen) having published in it his paper on quadratures, based on researches that Liebniz had communicated to him, Leibniz at last decided in 1684 to present to the world the more abstruse parts of his own work on the calculus. His epoch-making papers give rules of calculation without proof for rates of variation of functions and for drawing tangents to curves... "The infinitesimal calculus originated in the 17th century with the researches of Kepler, Cavalieri, Torrecelli, Fermat and Barrow, but the two independant inventors of the subject, as we understand it today, were Newton and Leibniz... Although both Newton and Leibniz developed similar ideas, Leibniz devised a superior symbolism and his notation is now an essential feature in all presentation of the sibject.... With the calculus a new era began in mathematics, and the development of mathematical physics since the 17th century would not have been possible without the aid of this powerful technique" (PMM 160).IN: Acta Eruditorum, 1684-1685, pp. 467-73. The full volume offered, with volume title, index, and addenda. Thick quarto, contemporary half-calf with elaborately gilt-decorated spine; edges dyed red. Corners on binding bumped and worn. Text generally very clean with only ocassional light browning.

FIRST PUBLISHED EDITION of one of the rarest and most important papers of modern science: Oersted's discovery of the connection between electricity and magnetism. Preceded only by the legendarily rare privately-printed pamphlet (of which only a few copies are known to exist, only one in private hands), the first journal printing is exceedingly scarce.  Text in the original Latin."The 'Experimenta...' opened a new epoch in the history of physics. From it followed the creation of electrodynamics by Ampere and Faraday's 'Experimental Researches in Electricity" (DSB)."It was after lecturing to students in his own rooms in the Noerragade, Copenhagen, in 1819 or 1820 that [Oersted] invited a few of them to stay on to witness an experiment- the possible deflection of a compass -needle by an adjacent electric current. The experiment was successful; but only just; and Oersted repeated it many times before venturing on 21 July to proclaim the identity of magnetism and electricity in this four-page paper entitled 'Experiments relative to"The 'Experimenta...' opened a new epoch in the history of physics. From it followed the creation of electrodynamics by Ampere and Faraday's 'Experimental Researches in Electricity" (DSB). the Effect of the Contiguity of Electricity to a Magnetic Needle'."The results were as important as they were widespread. Oersted's paper was within the year reprinted in England, France, Germany, Italy and Denmark. In 1823 Ronalds and in 1833 Gauss and Weber constructed the first practical electric telegraphs. Faraday's momentous experiments with the sequels by Clerk Maxwell, Hertz and others bore further witness to its significance" (Printing and the Mind of Man, 282).Printed in the July, 1820 issue of Schweigger's Journal für Chemie und Physik. Less than a year later, "in 1821, volume 31 of the prestigious Journal für Chemie und Physik opened with an editorial announcing a change in format 'in part because a new epoch in chemistry and physics appears to have begun with Ørsted's important discoveries on the connection between magnetism and electricity.' A contributor wrote: 'Orsted's experiments regarding magnetism are the most interesting ones performed in more than a thousand years'" (Physics in Denmark, nobelprize.org).WITH: Neuere electro-magnetische Versuche, Oersted's succeeding paper on the interactions between an electric current and a magnetic field. In: Journal für Chemie und Physik. Hrsg. v. Schweigger u. Meinecke, Vol. 29, pp. 275-281 (Oersted in July issue);  Neuere electro-magnetische Versuche, pp. 364-369. Nuremberg: Schrag, 1820. The whole volume offered. Octavo, contemporary three-quarter green morocco, marbled boards. Some wear to edges of binding, text clean.  Provenance: with library and de-accession stamps on series title from the prestigious Gmelin Institute (after 1996, part of the Max Planck Institute). SCARCE.

FIRST EDITION of Bacon’s argument for and development of the scientific method. PMM 119.Bacon “insisted on experiment in determining truth in nature and the above book is a proposed method for the assessment of all knowledge. The accumulation of observation and fact must be the basis of a new philosophy and not the authority of Aristotle or anyone else... Bacon’s inspiration led directly to the formation of the Royal Society. The famous engraved title-page showing a ship boldly sailing beyond the Pillars of Hercules (the limits of the old world) is interpreted to represent the bold spirit of adventure and research of the new age of science” (Dibner 80). “Bacon conceived a massive plan for the reorganization of scientific method an gave purposeful thought to the relation of science to public and social life. His pronouncement ‘I have taken all knowledge to be my province’ it he motto of his work... The frontispiece to his magnum opus shows a ship in full sail passing through the Pillars of Hercules from the old to the new world. It symbolizes the vision of its author whose ambitious proposal was: ‘a total reconstruction of sciences, arts and all human knowledge... to extend the power and dominion of the human race... over the universe’” (PMM 119). Second issue (as usual) with “Billium” only (omitting Bill Norton) in colophon and added errata. With engraved title by Simon van de Passe. Folio, contemporary full calf rebacked with original spine laid-down; custom box. Some soiling to binding and repairs to corners. Title page with early signature and notation in top margin, a few scattered rust spots, tiny tear to corner of B2. Overall, text extremely clean and crisp with wide margins.

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.