## LE VERRIER, Urbain Jean Joseph

# Recherches sur les mouvements de la planète Herschel

Bachelier, Paris: 1846

- $3,500

THE PREDICTION OF THE EXISTENCE OF NEPTUNE: THE RARE OFFPRINT. First edition, second offprint issue, very rare, of Le Verrier's mathematical prediction of the existence of Neptune, "undeniably one of the major scientific events of the nineteenth century" (Lequeux, p. 22). "Neptune, whose existence was visually confirmed in 1846, was the first planet to be discovered by mathematical rather than observational means. The discovery of Neptune not only represents the greatest triumph for Newton's gravitational theory since the return of Halley's Cometin 1758,but it also marks the point at which mathematics and theory, rather than observation, began to take the lead in astronomical research . The discovery of Neptune resulted from the need to develop a theory explaining the motion of the solar system's seventh planet, Uranus, the movements of which could not be completely accounted for by the gravitational effects of Jupiter and Saturn. Several astronomers since the planet's discovery in 1781 had suggested that the perturbations in Uranus's orbit could be caused by an as yet unknown trans-Uranian planet. However, the complex mathematics required for proving this hypothesis was so daunting that no one had attempted the task . Le Verrier had begun his own work on the Uranus problem in the summer of 1845, encouraged by François Arago, who by then had become France's leading astronomer. On November 19, 1845 Le Verrier published his first brief paper on the subject in the Comptes rendus de l'Académie des sciences, following it with three more equally brief papers published on June 1, August 31 and October 5, 1846. These short papers, totaling only 34 pages, were preliminary to the full and detailed account Le Verrier gave of his results in [the present work]; on p. 5 of that work Le Verrier referred to the Comptes rendus papers as 'publications partielles'" (). Le Verrier communicated the result of his investigations to several astronomers who had powerful instruments at their disposal. Among them was J. G. Galle, at the Berlin observatory, who was notified by Le Verrier on 23 September. Two days later he wrote to Le Verrier, announcing that he had observed the planet within 1° of Le Verrier's predicted position. "During the time that Le Verrier was conducting his research on the movements of Uranus, the English astronomer J. C. Adams was independently arriving at the same conclusions, which he communicated to the Astronomer Royal, George Biddell Airy. Adams's paper remained unpublished until 1847" (Norman 1343). OCLC lists nine copies of this issue; no copy listed on ABPC/RBH. "In his celebrated treatise on celestial mechanics, Pierre Simon de Laplace had developed mathematical expressions for the mutual perturbations exerted by the planets as a result of their gravitational attraction. Using these expressions, one could carry out numerical calculations to produce tables of the positions of the planets over time. The responsibility for doing so was claimed by the Bureau of Longitudes, headed by Laplace himself, though the work of actually performing these backbreaking calculations was distributed among several astronomers at the Bureau, including Delambre, Alexis Bouvard, and Burckhardt. Bouvard, Laplace's student, was assigned the most thankless task. In 1821, he began the laborious calculation of tables predicting the movements of the three giant planets: Jupiter, Saturn, and Uranus. The calculation of the tables of Jupiter and Saturn proved to be relatively straightforward. Uranus, however, proved to be highly intractable. Even after taking into account the perturbations exerted by the other planets, Bouvard could not derive a set of orbital elements that would successfully account for the movements of Uranus during the entire period over which it had been observed . "Resigned to defeat, Bouvard wrote in the introduction of his Tables of Uranus in 1821 that it would remain the task of future investigators to determine whence arose the difficulty in reconciling these two data sets: whether the failure of the observations before 1781 to fit the tables was due to the inaccuracy of the older observations or whether they might depend on 'some foreign and unperceived source of disturbance acting upon the planet' . It seems, then, that Alexis Bouvard himself had been the first to speculate that the anomalous motion of Uranus could be occasioned by the gravitational action of a new planète troublante (disturbing planet) . Following Alexis Bouvard's death in 1843, his nephew Eugène was charged by the Bureau of Longitudes to work on new tables of the planets. He submitted his results to the Academy of Sciences on September 1, 1845, but they were never published. By then he had come to regard the discrepancies between observation and theory as irreconcilable without adding another factor, and personally found 'entirely plausible the idea suggested by my uncle that another planet was perturbing Uranus.' "Arago evidently hoped that the problem of Uranus would be taken up at the Paris Observatory, but he lacked confidence in Eugène Bouvard, whose measurements at the eclipse expedition of 1842 had been of poor quality. Since there was no one else at the observatory he deemed capable of tackling such a difficult problem, he turned to Le Verrier (1811-77). He had great faith in Le Verrier's mathematical abilities, and so, at Arago's request, Le Verrier abandoned the investigation of comets in which he was then involved and devoted himself to Uranus . "Le Verrier scrupulously examined all the available observations up until 1845, notably those made recently at the Paris Observatory, which Arago put in his hands, and which were of excellent quality; and also those made at Greenwich which were sent by the director, Airy. He also examined carefully Alexis Bouvard's calculations (he seems not to have considered those of his nephew, Eugène). He discovered that certain terms had been neglected unjustifiably, and he al

More from Sophia Rare Books

## Die Mechanik in ihrer Entwickelung, historisch-kritisch dargestellt

MACH, Ernst Waldfried Josef Wenzel MACH'S PRINCIPLE. First edition, a copy with outstanding provenance, of "Mach's most important work, in which he presents his criticism of the epistemological and methodological basis of scientific inquiry. In his analysis of the conceptual basis of Newtonian physics, he introduces what Einstein later named the 'Mach principle': the inertia of an isolated body can have no meaning and can be expressed only by its relationship to the inertial frame. This critique of Newtonian mechanics influenced the development of Einstein's gravitational theory. The work is divided into five parts, the development of the principles of statics, development of the principles of dynamics, the application of the principles, formal development of mechanics, and mechanics and other sciences. An appendix lists the most significant practitioners of mechanics and their works" (Bibliotheca Mechanica, p. 208). Einstein wrote of Mach's influence on his own work on several occasions. In a letter to Carl Seelig (April 8, 1952), he recalled that "My attention was drawn to Ernst Mach's Science of Mechanics by my friend Besso while a student, around the year 1897. The book exerted a deep and persisting impression upon me . owing to its physical orientation toward fundamental concepts and fundamental laws" (quoted in Holton, Thematic Origins of Scientific Thought: Kepler to Einstein, 1973). In his obituary of Mach (Physikalische Zeitschrift, 1916), Einstein paid him this tribute: "I can say with certainty that the study of Mach and Hume has been directly and indirectly a great help in my work." "Published in 1883 and widely read ever since, [the present work] argues fiercely for the primacy of empirical facts and the need to understand the contingent historical nature of progress in science. Mach was strongly antimetaphysical and questioned the foundations of all knowledge. Physical concepts are not immutable and should always be based on universally observed connections within phenomena. Newton had given a circular definition of mass; Mach replaced it with an operational definition based on the observed accelerations that interacting bodies impart to each other. Einstein recognized the key importance of Mach's approach in his own celebrated operational definition of simultaneity in the special theory of relativity in 1905" (Encyclopedia of Philosophy). 'Mach's principle' was so called by Einstein, who "found the hypothesis helpful in formulating his theory of general relativity-i.e., it was suggestive of a connection between geometry and matter-and attributed the idea to Mach, unaware that the English philosopher George Berkeley had proposed similar views during the 1700s. (Berkeley had argued that all motion, both uniform and nonuniform, was relative to the distant stars.) Einstein later abandoned the principle when it was realized that inertia is implicit in the geodesic equations of motion and need not depend on the existence of matter elsewhere in the universe" (Britannica). RBH lists only three copies in the last half-century. Provenance: Richard Dedekind (1831-1916), German mathematician (signature on front flyleaf). Dedekind made important contributions to number theory, abstract algebra, the axiomatic foundations of arithmetic, and the definition of the real numbers through the notion of 'Dedekind cut'; Herbert McLean Evans (1882-1971), American anatomist, embryologist, and book collector (bookplate); Bern Dibner (1897-1988), electrical engineer, industrialist, and historian of science and technology (bookplate); donated by Dibner to the Burndy Library (bookplate). "Austrian physicist Ernst Mach (1838-1916) is best known for his 1883 book Die Mechanik in ihrer Entwickelung (The Science of Mechanics), a work widely credited with helping instigate a reconsideration of the Newtonian worldview that led to the formulation of special and general relativity in the early 20th century. Mach's first critiques of mechanics had been published as early as 1868 and 1872 in studies of mass and inertia. But the section in The Science of Mechanics in which Mach attacks Isaac Newton's concept of absolute space develops a line of thought begun in 1879. There, Mach responds to Newton's primary argument for absolute space, the rotating-bucket experiment. "If a bucket of water is set spinning, the walls of the bucket at first rotate relative to the stationary water, and the surface of the water remains level. Then the water starts to rotate also, and it rises toward the walls. When the spinning bucket and water are at rest relative to each other, the water surface is concave. Interactions between water and walls can't explain the deformation, and Newton argued that the surface concavity demonstrated the bucket's absolute rotation in space. For Newton, absolute space remained similar and immovable, without regard to anything external, but the experiment showed that the absolute rotation of water could be measured. "In 1883 Mach wrote that Newton's experiment merely shows that the relative rotation of the water with respect to the sides of the vessel produces no noticeable centrifugal forces and that such forces are instead produced by its relative rotation with respect to Earth and the other celestial bodies. Referring to a situation he seems to have first sketched in a notebook entry in 1879, Mach added, 'No one is competent to say how the experiment would turn out if the sides of the vessel increased in thickness and mass till they were ultimately several leagues thick.' He went on to argue that when we say that a body retains its direction and velocity in space, that expression is an abbreviated reference to the entire universe. "Over time, Mach's attack on absolutes and his discussion of the bucket experiment became the most celebrated features of his account of mechanics. Indeed, for many years Albert Einstein saw the demand to provide an account of inertial mass that depends on the masses of the universe as one of the central cri- $1,500

- $1,500

## Hemisphaerium dissectum opus geometricum: in quo obiter tractatur de maximix inscriptibilibus & minimis circumscribentibus: ratio etiam discutitur quare aliquæ propositiones non admittant solutionem per media plana vel Euclidis elementa: cum methodo novâ geometricâ quâ ad aequationem reducitur propositio de sectione hemisphærij in ratione datâ: accessit appendix de inscriptione in sphaæra coni scaleni & de superficie eius: demum cubatio cuiusdam partis cylindri dissectæ plano

WHITE, Richard COMMENTARY ON ARCHIMEDES' ON THE SPHERE AND CYLINDER . First edition of this rare Galileianum, an explication and extension of the two books of Archimedes' On the sphere and the cylinder, which gave the first exact determination of the area and volume of a curved figure. They "are, of course, exceptional masterpieces. According to a testimony by Cicero, whom there is no reason to doubt, Archimedes' tomb had inscribed a sphere circumscribed inside a cylinder, recalling the major measurement of volume obtained in [the first book]: if so, either Archimedes or those close to him considered [this book] to be somehow the peak of his achievement. The reason is not difficult to find. Archimedes' works are almost all motivated by the problem of measuring curvilinear figures, all of course indirectly related to the problem of measuring the circle . Measuring the sphere is the closest Archimedes, or mathematics in general, has ever got to measuring the circle. The sphere is measured by being reduced to other curvilinear figures. Still, the main results obtained - that the sphere as a solid is two thirds the cylinder circumscribing it, its surface four times its great circle - are remarkable in simplifying curvilinear, three-dimensional objects, that arise very naturally" (Netz, p. 19). Archimedes' proof is extraordinarily ingenious. "A circle with a polygon inscribed within it is imagined rotated in space, yielding a sphere with a figure inscribed within it. The inscribed figure is made of truncated cones . Furthermore, with the same idea extended to a circumscribed polygon yielding a circumscribed figure made of truncated cones, proportion inequalities come about involving the circumscribed and inscribed figures . such proportion inequalities can be manipulated to combine with the measurements of the inscribed and circumscribed figures, reaching, indirectly, a measurement of the sphere itself" (ibid., pp. 20-21). In this, probably White's only published work, he uses Archimedes' techniques to study other solids that can be inscribed in, and circumscribed about, a hemisphere. He also studies the relation between the areas and volumes of parts of a hemisphere and corresponding parts of a cylinder or a cone. White was personally acquainted with Galileo and he and his younger brother Thomas were instrumental in bringing Galileo's discoveries and opinions to the attention of British scientists, notably Francis Bacon. In the preface White praises Galileo as the outstanding investigator of the heavens above, the waves below (a reference to the tidal theories of the Dialogo - see below), and mechanics on Earth, "though it was published in Rome under license during a period in which many Italian writers found it prudent to forgo any favourable reference to Galileo in their published works. White also conducted some elaborate experiments concerning specific gravities and made accurate observations of Halley's comet" (Drake, p. 245). Richard White was elected a fellow of the Royal Society in 1661. OCLC lists Columbia, Harvard, Huntington and Linda Hall in US. RBH lists four copies since 1931. Richard White (1590-1682) was born to a prominent Catholic family in Essex; his mother was the daughter of the celebrated jurist Edmund Plowden. In his preface, White explains how the urge 'to cross the furious ramparts of the ocean which surround Britain' led him through France to Florence in the company of one James Clayton (probably a member of another Recusant family). He lived for most of his life in Italy: he tells us that he first studied Aristotle in Florence (beginning with the Organon and thence to the Physics), where he came into contact with Galileo and his circle, especially Benedetto Castelli, who taught him Euclid, and Bonaventura Cavalieri, famous for his Geometria indivisibilibus (1635), which introduced the method of indivisibles, an important precursor of calculus. Richard was joined by his brother Thomas in Italy who encouraged him to study Archimedes' writings on the sphere and cylinder, resulting in the present work. Its publication, some years later, was partly at the urging of Michelangelo Ricci. Thomas White, a Jesuit, was a prolific writer. He was acquainted with prominent British intellectuals, including Thomas Hobbes and Sir Kenelm Digby, and belonged to the Mersenne circle in Paris in the 1640s. Richard White was instrumental in correcting a statement made by Galileo in his theory of the tides, 'Discorso sul flusso e it reflusso del mare,' which he submitted in the form of a private letter to Cardinal Orsini in 1616. Galileo believed that the tides were the result of the differential motions of different regions of the Earth, according to whether in a particular region the diurnal rotation of the Earth around its axis was in the same or the opposite direction as its annual rotation around the Sun; he used the analogy of a vase containing water - when the vase undergoes irregular motion the water itself acquires a motion relative to the vase. In the 1616 letter Galileo stated that the tides at Lisbon were half as frequent as those on the Mediterranean, which he explained from the fact that the Atlantic Ocean is twice as wide as the Mediterranean. These statements were omitted from the printed version in the Fourth Day of the Dialogo (1632), because in 1619 Richard White had informed Galileo that his data on the Lisbon tides were incorrect. In the same year White brought to England copies of Galileo's books and manuscripts, leaving them with Francis Bacon. This probably led to Bacon omitting from his Instauratio magna (1620) his essay on tides, 'On the ebb and flow of the seas,' written about 1611 and sent to Galileo in 1618. Bacon's essay had explained the tides as the effect on the oceans of the daily east-west motion of the Earth relative to the heavens, in opposition to Galileo's conclusion in the Orsini letter. According to some sources (e.g., Encyclopaedia Britannica, Vol. 20 (1842), p.- $2,500

- $2,500

## De magnete, seu rota perpetui motus, libellus

PEREGRINUS, Petrus (Pierre de MARICOURT) [GASSER, Achilles Pirmin (ed.)] THE DISCOVERY OF THE COMPASS - THE EARLIEST PRINTED BOOK ON THE MAGNET . First edition, of the greatest rarity, of "one of the most impressive scientific treatises of the Middle Ages . the first extant treatise on the properties and applications of magnets" (DSB), containing the earliest description of the pivoted compass - this work was published more than four decades before William Gilbert's De magnete(1600), and written centuries earlier. The work also shows Peregrinus to have been a pioneer of the experimental method. This is a wonderful copy, in an exquisite strictly contemporary dated binding, bound with three rare 16thcentury works on astronomy and astrology (see below). Couched as a letter to a friend in Picardy, dated 8 August 1269, this is "considered the earliest known European work of experimental science, and the foundation of the study of electricity and magnetism" (Norman). "The thirteen chapters into which the letter is divided form the most original, extensive and important treatise on the magnet prior to Gilbert's [in 1600]" (Wheeler Gift). This work was edited by the Lindau physician Achilles Gasser, famous for contributing the preface to Rheticus'sNarratio Prima(1540), the first published account of heliocentrism. In his introduction to the present work, which he dedicates to Emperor Ferdinand I, Gasser discusses Magellan's circumnavigation of the world, the history of Arab and Western seafarers, and the benefits of the marine compass for navigation and future exploration, which are described here for the first time. Peregrinus's latter is divided into two parts: the first is theoretical, presenting the laws of magnetic attraction, the polarity of the lodestone and every magnet (called 'polus' for the first time), experiments with separate lodestones, the attraction and magnetization of iron, and more. Part two applies these theories, presenting various devices that use magnetic attraction - the compass floating on water common at the time, an alternative compass without the use of water, as well as perpetual motion devices for clock and wheel, all four here pictured in woodcuts commissioned by Gasser. "Not only did Peregrinus bring together virtually all the relevant, contemporary knowledge on magnetism, but he obviously added to it and, of the greatest importance, organized the whole into a science of magnetism. He formulated rules for the determination of magnetic polarity, which then enabled him to enunciate rules for attraction and repulsion, all of which would today form the basis of an introductory lesson on magnetism. As the two magnetic compasses and perpetual motion devices for clock and wheel testify, Peregrines was also seriously concerned with the practical application of magnetic force. The subsequent influence of his treatise was considerable. The existence of at least thirty-one manuscript versions of it bears witness to its popularity during the Middle Ages. Of greater significance, however, was its eventual impact on Gilbert, who, in his famousDe magnete(1600), not only mentioned Peregrinus by name, but also drew upon the Epistolato build upon and add to the solid empirical rules on magnetic polarity and induction formulated by Peregrinus more than three centuries earlier" (DSB). This is a superb copy of a book that collectors will probably have at most one opportunity to acquire. Bern Dibner wrote in his Heralds of Science, in which Peregrinus is no. 52, that "Twenty copies of this book are known". RBH lists no copy since Honeyman, and none before that since Quaritch offered a copy in 1934. The Honeyman copy made £11,000 in 1978 (to Quaritch) - for comparison, Honeyman's three copies of the first editionPrincipiamade £12,500, £8,000 & £7,000. Provenance: 1) Johannes Delicasius (Theilenkäs) (1513-63) (blindstamp 'Joann. Delicasii LL. Doct. Origine Posonien. Sive Prespurgensis MDLXI' to upper cover, full page of annotations probably in his hand). Johannes Delicasius came from Poszony near Pressburg (Pezinok near Bratislava/Slovak Republic). He enrolled at the University of Vienna in the summer semester of 1513, obtained the title of Baccalaureus Artium on October 13, 1515 and four years later, on February 22, 1519, that of Licentiatus Artium. In the winter semester of 1529 he enrolled at the University of Ingolstadt, where he acquired the title of Doctor of Civil Law in 1549. From 1528 to 1537 he was procurator general and from 1549 to 1562 vicar general. Before he came to Regensburg, he was the first town clerk and mayor in Straubing, was ordained a priest and accepted into the Straubing Priestly Fraternity. Appointed to the Regensburg episcopal court, he familiarized himself with ecclesiastical law and fought with all means possible the introduction of the new doctrine in the city. He opened the Regensburg Synod of 1548 as commissioner of the vicariate. On March 18, 1549 he was admitted to the Regensburg Cathedral Chapter. At the Reichstag in Augsburg in 1547/48 he represented the two women's monasteries of Obermünster and Niedermünster. In 1557, the abbess of Obermünster, Barbara von Sandizell, sent him as a representative to the Reichstag in Augsburg. Johann Delicasius was a close friend of the famous historian Aventinus and in 1534 donated his tombstone on the west wall of the vestibule of St. Emmeram. 2) Manó Wagner (1857-1929), city councillor in Pest and Hungarian Royal Chief Advisor, with his library stamp on the title-page and on p. 121 of Al-Qabisi'sLibellus Isagogicusand his library label with shelfmark to inside upper cover. 3) Dr. Eszter Tóth (1948-2022), Hungarian physicist and educator who worked with the Hungarian Nobel laureate Eugene Wigner in the 1980s and was in close contact with Edwin Teller in the 1990s (cf. Register to the ET papers, Hoover Institution Library and Archives). Her textbooks on nuclear physics were widely published and saw numerous Chinese and Japanese editions. Acquired by the previous owner directly from her d- $400,000

- $400,000

## Chymista scepticus vel dubia et paradoxa chymico-physica, circa spagyricorum principa, vulgo dicta hypostatica, Prout proponi & propugnari solent à Turba Alchimistarum. Cui pars premittitur, alterius cujusdem dissertationis ad idem argumentum spectans

BOYLE, Robert THE FOUNDING WORK OF MODERN CHEMISTRY. First Latin edition, published one year after the first English edition, of this milestone in the history of chemistry. "His most important work [where he] set down his corpuscular theory of the constitution of matter, which finally freed chemistry from the restrictions of the Greek concept of the four elements, and was the forerunner of Dalton's atomic theory" (Sparrow). "The 'Sceptical Chymist' is one of the great books in the history of scientific thought, for it not only marks the transition from alchemy to modern chemistry but is a plea, couched in most modern terms, for the adoption of the experimental method. Boyle inveighed against the inaccurate terminology of the 'vulgar spagyrists' and the 'hermetick philosophers,' as he termed the alchemists who refused to define their terms . He predicted that many more [elements] existed than had been described, but insisted that many substances, then thought to be elemental, were, in fact, chemical compounds. He set forth the modern distinction between a compound and a mixture, pointing out that a true chemical compound possessed properties entirely different from either of its constituents" (Fulton). "The importance of Boyle's book must be sought in his combination of chemistry with physics. His corpuscular theory, and Newton's modification of it, gradually led chemists towards an atomic view of matter . Boyle distinguished between mixtures and compounds and tried to understand the latter in terms of the simpler chemical entities from which they could be constructed. His argument was designed to lead chemists away from the pure empiricism of his predecessors and to stress the theoretical, experimental and mechanistic elements of chemical science. The Sceptical Chymist is concerned with the relations between chemical substances rather than with transmuting one metal into another or the manufacture of drugs. In this sense the book must be considered as one of the most significant milestones on the way to the chemical revolution of Lavoisier in the late eighteenth century" (PMM). "Boyle's most celebrated book is his Sceptical Chymist . It contains the germs of many ideas elaborated by Boyle in his later publications . Boyle has been called the founder of modern chemistry, for three reasons: (1) he realized that chemistry is worthy of study for its own sake and not merely as an aid to medicine or alchemy - although he believed in the possibility of the latter; (2) he introduced a rigorous experimental method into chemistry; (3) he gave a clear definition of an element and showed by experiment that the four elements of Aristotle and the three principles of the alchemists (mercury, sulphur and salt) did not deserve to be called elements or principles at all, since none of them could be extracted from bodies" (Partington II, pp. 496-7). This Latin edition is the second edition overall. There are two issues, published at Rotterdam and London (no priority established). Curiously, this copy has the title pages of both issues. RBH lists one copy of the Rotterdam issue and none of the London issue. OCLC lists six copies of the Rotterdam issue and four of the London issue in the US. The first English edition now commands a very high price - the last complete copy at auction sold for £279,800 in 2023 - so that this first Latin edition is the earliest form of Boyle's greatest work that is accessible to the majority of collectors. Provenance: Ink stamp A*G* on Rotterdam title. "Robert Boyle was one of the most significant of British scientists. More than anyone else, he invented the modern experimental method. His profuse published findings on pneumatics, chemistry and many other scientific topics were widely influential in providing empirical support for a mechanical view of nature. He also wrote books on the philosophical aspects of science, and on religion. He was a founding member of the Royal Society, and was the doyen of that body in its formative years. "Boyle was born on 27 January 1627, youngest son of Richard Boyle, 1st Earl of Cork by his second wife, Catherine. After spending two years at Eton, he travelled on the continent and received further education in Geneva from a Huguenot intellectual, Isaac Marcombes. In 1644 he returned to England and settled at Stalbridge in Dorset, where his career as an author began. At this point, his writings were on moral and literary topics rather than scientific ones, but in 1649 he 'discovered' experimental science, and this was to dominate his entire subsequent career, in conjunction with an overriding religious commitment. From the early 1650s, he began to write treatises on scientific topics and to carry out experiments. This activity accelerated and became more focused following his move to Oxford in 1655-6 to join the group of group of natural philosophers there, and the late 1650s saw an intense burst of activity on Boyle's part, including such classic experiments as that illustrating the redintegration of saltpetre, or (in 1658-9) the series using an air-pump or vacuum chamber . "The years that Boyle spent at Oxford, prior to his move to London in 1668, also saw an extraordinarily intense programme of writing on his part. It was at this time that he began or completed the numerous books on different aspects of natural philosophy which set the pattern for his subsequent intellectual career, and on which, when he began to publish on a sustained scale from 1660 onwards, his later fame was based. These included his New Experiments Physico-Mechanical, Touching the Spring of Air and its Effects (1660), Certain Physiological Essays (1661), The Sceptical Chymist (1661), Some Considerations touching the Usefulness of Experimental Natural Philosophy (1663, 1671), Experiments and Considerations touching Colours (1664), New Experiments and Observations touching Cold (1665), Hydrostatical Paradoxes (1666) and The Origin of Forms and Qualities (1666)" (Robert Boyle Project).- $16,500

- $16,500

## Institutiones Calculi Differentialis cum eius usu in Analysi Finitorum ac Doctrina Serierum

EULER, Leonhard THE SECOND PART OF EULER'S GREAT TRILOGY ON THE CALCULUS . First edition, rare, of the second part of Euler's monumental trilogy on analysis, "the first textbook on the differential calculus which has any claim to be regarded as complete" (Rouse Ball, p. 368). "In 1755 Euler published another masterwork in mathematics, his two-part Institutiones calculi differentialis, the second part of his trilogy on calculus. The book was probably begun around 1727, but it was mostly finished by 1748 and completed two years later, when Euler was forty-three. For the previous decade, he had worked on it steadily. Institutiones calculi differentialis is the first textbook to organize systematically the hundreds of important discoveries made since the time of Leibniz and Newton. Today it is mainly remembered for the definition of the concept of a function, which stressed not the role of formulae but the more general idea of a formal correspondence between two sets of numbers. This new definition, which looked forward to the modern concept of a mapping between two sets, was probably motivated by the controversy with d'Alembert and Daniel Bernoulli over the vibrating string. The book began with the first didactic presentation of the calculus of finite differences when the differences become 'infinitely small'. This was a sound idea, but Euler did not possess a formal theory of limits, so . [he] had to resort to the idea that the differential, an infinitely small quantity, is 'a true zero' and to formalize differential calculus as a 'calculus of zeroes' . His vague definition of infinitesimals as quantities smaller than any fixed number looked back to the ideas of Johann I Bernoulli, and it would remain the accepted formulation of calculus for several decades . The second part of the Institutiones calculi differentialis contains an impressive array of important results, many of them found by Euler himself. Chapters 5 and 6 elaborate his summation formula for the Basel Problem [finding an exact formula for the sum of the reciprocal squares of the integers] and what would later be called the Euler-Maclaurin Formula. The results on the Bernoulli numbers were many, starting from their generating formula and going on to their application to the summation of power series and connection with the Riemann zeta function. Euler found several properties of these numbers, which had applications in many fields of mathematics, and their computation provides a challenging problem even today. With them Euler obtained exact sums of power series of even reciprocals. Among the equations which Euler studied in chapter 6 are the partial sums of the harmonic series, the Euler constant Î , the value of Ï, and approximate formulae for large factorials. The book was extremely influential and is now regarded as one of the most important scientific texts of the eighteenth century" (Calinger, pp. 395-6). "[Euler] thoroughly elaborated formulas of differentiation under substitution of variables; revealed his theorem on homogeneous functions, stated as early as 1736 ., deduced the necessary condition for an exact differential; applied Taylor's series to finding extrema [of functions of a single variable]; and investigated extrema of [functions of two variables]" (DSB). Copies in good condition in contemporary bindings are rare on the market. The Norman copy, in modern binding with library stamps, realized $3450 in 1998. Euler "He started to write this book already in Saint Petersburg and finished it around 1750 in Berlin, where it was published under the auspices of the Saint Petersburg Academy of Sciences. The existence of an early Latin manuscript 'Calculi differentialis', conserved in the Archives of the Russian Academy of Sciences in Saint Petersburg, shows that Euler worked over a very long period to present his modern view of the differential calculus. An account of his scientific manuscripts dated this one to the 1730s, while A.P. Yushkevich considered that it was written even earlier, around 1727. We consider that its comparison with the book of 1755 reveals the evolution of the calculus during these 20 years (to a great extent due to Euler himself) and the modification of his orientation: while the manuscript reveals his approach to the infinitesimals as a pupil of Johann Bernoulli, in the book of 1755 he founded the calculus on his own 'calculus of zeros' . "The exposition, which is very succinct, comprises two Parts, each with its own sequence of numbered chapters and articles. Despite the diversity of the topics and the impressive size, it is a complete, well-organized treatise. Many of the results are Euler's own. The first Part is devoted to the differential calculus and its foundations, and the second Part contains applications of the differential calculus related to analysis and algebra. At the end of the first Part and in the last chapters of the second Part he states his intention to write a third Part, devoted to the geometrical applications of the differential calculus; but he never realizes it . "In the extended introduction Euler explains the purpose of calculus, including, in particular, his famous 'expanded' conception of a mathematical function: 'if some quantities depend on others in such a way as to undergo variation when the latter are varied, then the former are called functions of the latter'. This formulation has an extensive character; it embraces all the ways by which one quantity can be determined by means of others, and anticipates the definitions of later mathematicians such as N. I. Lobachevsky and J. P. G. Dirichlet. However, in his book Euler's conception is not utilized in practice: functions are mainly considered as analytical expressions, including infinite series. His introduction also includes a very concise and schematic historical essay, a criticism of the foundation of the calculus on the infinitesimals, and a very brief survey of the book's contents" (Demidov, p. 192). The work is divided- $13,500

- $13,500

## De magnete, magneticisque corporibus, et de mango magnete tellure; Physiologia nova, plurimis & argumentis, & experimentis demonstrate

GILBERT, William First edition, an exceptionally fine copy, the nicest we have seen, of the first work of experimental physics published in England. Gilbert was chiefly concerned with magnetism; but as a digression he discusses in his second book the attractive effect of amber (electrum), and thus may be regarded as the founder of electrical science. He coined the terms 'electricity,' 'electric force' and 'electric attraction.' His 'versorium', a short needle balanced on a sharp point to enable it to move freely, is the first instrument designed for the study of electrical phenomena, serving both as an electroscope and electrometer. He contended that the earth was one great magnet; he distinguished magnetic mass from weight; and he worked on the application of terrestrial magnetism to navigation. Gilbert's book influenced Kepler, Bacon, Boyle, Newton and, in particular, Galileo, who used his theories [in the Dialogo] to support his own proof of the correctness of the findings of Copernicus in cosmology" (PMM). "Gilbert provided the only fully developed theory . and the first comprehensive discussion of magnetism since the thirteenth century Letter on the Magnet of Peter Peregrinus" (DSB). Although this book does appear with some regularity on the market, copies such as ours in fine condition and in untouched contemporary bindings are rare. Provenance: presentation inscription on front free endleaf dated 1622 to the Bibliotheca Academiae Juliae Carolinae, Helmstedt: 'In bibliotheca illustris et inclutae academiae Juliae, quae Helmosteti est, nutrici meritissimae et aeternum venerandae, donarium hoc exiguum dedicavit Bartholdus Nihusius anno MDCXXII'; the donor, the German Catholic Bishop Barthold Nihus (1590-1657) was a correspondent of Athanasius Kircher; old stamp 'Ex bibliotheca Academiae Iuliae Carolinae Helmstadt' on verso of title, with deaccession stamp across it; Herbert McLean Evans (1882-1971) with his bookplate (all of the Evans books I have seen have been outstanding copies). 'Herbert McLean Evans . made a monumental contribution to the field of endocrinology through his studies of the physiology of reproduction. . Four of his lines of research and discovery were often mentioned as deserving of the Nobel Prize: (1) development of the vascular system, (2) elucidation of the estrous cycle in the rat, and the role of pituitary gonadotropin in reproduction, (3) discovery of growth hormone, and (4) discovery of and isolation of vitamin E. The first of these was entirely Evans' own work. The other three were collaborative efforts, but Evans' contribution to each was crucial.' (A History of UCSF; People). Evans was also a historian of science and medicine, pioneering collector, and author of the outstanding Epochal Achievements in the History of Science (Berkeley, University of California Press, 1934), the first such compilation of its kind, and precursor of Dibner and Horblit. "During the fifteenth century the widespread interest in navigation had focused much attention on the compass. Since at that time the orientation of the magnetic needle was explained by an alignment of the magnetic poles with the poles of the celestial sphere, the diverse areas of geography, astronomy, and phenomena concerning the lodestone overlapped and were often intermingled. Navigators had noted the variation from the meridian and the dip of the magnetic needle and had suggested ways of accounting for and using these as aids in navigation. The connection between magnetic studies and astronomy was less definite; but so long as the orientation of the compass was associated with the celestial poles, the two studies were interdependent . "Gilbert divided his De magnete into six books. The first deals with the history of magnetism from the earliest legends about the lodestone to the facts and theories known to Gilbert's contemporaries . In the last chapter of book I, Gilbert introduced his new basic idea which was to explain all terrestrial magnetic phenomena: his postulate that the earth is a giant lodestone and thus has magnetic properties . The remaining five books of the De magnete are concerned with the five magnetic movements: coition, direction, variation, declination and revolution. Before he began his discussion of coition, however, Gilbert carefully distinguished the attraction due to the amber effect from that caused by the lodestone. This section, chapter 2 of book II, established the study of the amber effect as a discipline separate from that of magnetic phenomena, introduced the vocabulary of electrics, and is the basis for Gilbert's place in the history of electricity . "Having distinguished the magnetic and amber effects, Gilbert presented a list of many substances other than amber which, when rubbed, exhibit the same effect. These he called electrics. All other solids were nonelectrics. To determine whether a substance was an electric, Gilbert devised a testing instrument, the versorium. This was a small, metallic needle so balanced that it easily turned about a vertical axis. The rubbed substance was brought near the versorium. If the needle turned, the substance was an electric; if the needle did not turn, the substance was a nonelectric. "After disposing of the amber effect, Gilbert returned to his study of the magnetic phenomena. In discussing these, Gilbert relied for his explanations on several assumptions: (1) the earth is a giant lodestone and has the magnetic property; (2) the magnetic property is due to the form of the substance; (3) every magnet is surrounded by an invisible orb of virtue which extends in all directions from it; (4) pieces of iron or other magnetic materials within this orb of virtue will be affected by and will affect the magnet within the orb of virtue; and (5) a small, spherical magnet resembles the earth and what can be demonstrated with it is applicable to the earth. This small spherical magnet he called a terrella . "In discussing coition Gilbert was careful to distinguish ma- $75,000

- $75,000

## A Treatise on Electricity and Magnetism

MAXWELL, James Clerk PMM 355 - LIGHT AS A FORM OF ELECTRICITY. First edition of Maxwell's presentation of his theory of electromagnetism, advancing ideas that would become essential for modern physics, including the landmark "hypothesis that light and electricity are the same in their ultimate nature" (Grolier/Horblit). "This treatise did for electromagnetism what Newton's Principia had done from classical mechanics. It not only provided the mathematical tools for the investigation and representation of the whole electromagnetic theory, but it altered the very framework of both theoretical and experimental physics. It was this work that finally displaced action-at-a-distance physics and substituted the physics of the field" (Historical Encyclopedia of Natural and Mathematical Sciences, p. 2539). "From a long view of the history of mankind - seen from, say, ten thousand years from now - there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics" (R. P. Feynman, in The Feynman Lectures on Physics II (1964), p. 1-6). "[Maxwell] may well be judged the greatest theoretical physicist of the 19th century . Einstein's work on relativity was founded directly upon Maxwell's electromagnetic theory; it was this that led him to equate Faraday with Galileo and Maxwell with Newton" (PMM). "Einstein summed up Maxwell's achievement in 1931 on the occasion of the centenary of Maxwell's birth: 'We may say that, before Maxwell, Physical Reality, in so far as it was to represent the process of nature, was thought of as consisting in material particles, whose variations consist only in movements governed by [ordinary] differential equations. Since Maxwell's time, Physical Reality has been thought of as represented by continuous fields, governed by partial differential equations, and not capable of any mechanical interpretation. This change in the conception of Reality is the most profound and the most fruitful that physics has experienced since the time of Newton'" (Longair). Issues: The Treatise is found in various forms and publisher's bindings. We know of two different cloth bindings, both certainly official publisher's bindings: one with the arms of Clarendon Press blind stamped to the boards; another slightly brighter cloth without the arms (as the offered copy). The copies in the first type of binding (with arms to the boards) seem always to have advertisements for the Clarendon Press bound in the end of volume 2. These adds can be found in two different forms: one with 'just published' at the entry for Maxwell's Treatise itself, and one not mentioning 'just published'. A copy with the just-published-adds seems always to have the short errata slips in volume 1 and 2. Copies with the adds not mentioning 'just published' seems always to have the extended errata leaves, with further corrections than the errata slips. A set in the blind stamped bindings with just-published-adds and short errata slips are usually said to be first issue and a set with longer errata leaves and adds not mentioning 'just published' are usually called third issue. Sets in the brighter publisher's bindings (i.e., without the arms of the Clarendon Press blind stamped to the boards), which in our experience are rarer than the darker blind stamped form, seem always to be without the advertisements for the Clarendon Press in the end of volume 2. These sets can however be found with the shorter errata slips or with the extended errata leaves (as the offered copy). We have so far been unable to determine the exact chronological order in which these various forms were issued. Hence there seems so far to be two first issues (with short errata slips), two second issues (with extended errata leaves), and one third issue (with adds not mentioning 'just-published)'. "Maxwell's great paper of 1865 established his dynamical theory of the electromagnetic field. The origins of the paper lay in his earlier papers of 1856, in which he began the mathematical elaboration of Faraday's researches into electromagnetism, and of 1861-1862, in which the displacement current was introduced. These earlier works were based upon mechanical analogies. In the paper of 1865, the focus shifts to the role of the fields themselves as a description of electromagnetic phenomena. The somewhat artificial mechanical models by which he had arrived at his field equations a few years earlier were stripped away. Maxwell's introduction of the concept of fields to explain physical phenomena provided the essential link between the mechanical world of Newtonian physics and the theory of fields, as elaborated by Einstein and others, which lies at the heart of twentieth and twenty-first century physics" (Longair). The 1865 paper "provided a new theoretical framework for the subject, based on experiment and a few general dynamical principles, from which the propagation of electromagnetic waves through space followed without any special assumptions . In the Treatise Maxwell extended the dynamical formalism by a more thoroughgoing application of Lagrange's equations than he had attempted in 1865. His doing so coincided with a general movement among British and European mathematicians about then toward wider use of the methods of analytical dynamics in physical problems . Using arguments extraordinarily modern in flavor about the symmetry and vector structure of the terms, he expressed the Lagrangian for an electromagnetic system in its most general form. [George] Green and others had developed similar arguments in studying the dynamics of the luminiferous ether, but the use Maxwell made of Lagrangian techniques was new to the point of being almost a new approach to physical theory-though many years were to pass before other physicists fully exploited the ground he had broken . "In 1865, and again in the Treatise, Maxwell's next step after completing the dynamical analogy was to develop a group of eight equations descr- $16,000

- $16,000

Recherches sur les mouvements de la planète Herschel: https://rarebookinsider.com/rare-books/recherches-sur-les-mouvements-de-la-planete-herschel/