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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
book (2)

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
De magnete

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
book (2)

Selenotopographische Fragmente zur genaueren Kenntnis der Mondflache, ihrer erlittenen Veranderungen und Atmosphare, sammt den dazu gehorigen Specialcharten und Zeichnungen

SCHRÖTER, Johann Hieronymus A PIONEERING WORK OF THE SCIENCE OF SELENOGRAPHY. First edition, extremely rare when complete, of this important early study of the topography of the Moon. "Schröter was the first to observe the surface of the moon and the planets systematically over a long period. He made hundreds of drawings of lunar mountains and other features, and discovered and named the lunar rilles" (DSB). His observations were published in the present work, together with a second volume that appeared in 1802. The visual lunar albedo scale developed in this work was later popularised by the British astronomer Thomas Gwyn Elger (1836-97) and now bears his name. "Schröter studied law at Gottingen but also attended lectures in mathematics, physics, and astronomy, the last under Kästner. Upon completing his law studies he was appointed junior barrister in Hannover. Through his appreciation of music he met the Herschel family, who revived his interest in astronomy. In 1781 he became chief magistrate at Lilienthal, a post that left him free time to devote to astronomy. With the aid of the optician J. G. Schrader he built and equipped an observatory that subsequently became world-famous for the excellence of the instruments. Some were made in his own workshop; others he bought from Herschel, the latter including a reflector with a twenty-seven-foot focal length, the largest on the Continent . Lilienthal was occupied during the Napoleonic Wars by the French, who looted and partly destroyed the observatory, although most of the instruments were saved. In the ensuing fire Schröter lost all copies of his own works, which he had published himself. He returned to Erfurt and built a new observatory, but his health failed and he did little observing. He died soon afterward" (DSB). A second volume, with a further 32 plates, was published in 1802. "The 75 engraved plates published in the two volumes include anything from whole-page drawings of larger areas to groups of twelve or more sketches of specific small details. Examination shows that while a few drawings appear quite amateurish . others are reasonably accurate in their portrayal. Schröter consistently gives the rims of craters the appearance of an overhead view of a ring of closely spaced trees . even though many of those craters display sharp rims as viewed in the telescope. Nevertheless, comparing the many drawings with modern photos shows that they include virtually all of the more important details of each region except in only one or two rare cases where he apparently became confused by what he observed. Whatever criticisms may be leveled against Schröter's work. it can fairly be said that he pioneered the science of detailed and comprehensive selenography which, with Mayer's pioneering attention to positional accuracy, laid the ground for an unprecedented burst of lunar observation and cartography in Germany" (Whitaker, pp.107-9). No complete copy on RBH since 1939. The decisive event in Schröter's life occurred in March 1781, when he was told of William Herschel's discovery of the Georgium Sidus (Uranus). "The effect was electrifying. In the spirit of emulation, the young bureaucrat resigned his position in Hanover, and applied for, and received, the position of magistrate of the small, somewhat secluded village of Lilienthal, the 'Vale of the Lilies,' which is located on the edge of the moor near Bremen. It was a dramatic move, almost headstrong some might say, but Schroeter knew well what he was about. Lilienthal was lonely and isolated, the population relatively small in numbers. Official duties would be minimal, allowing him ample leisure time to devote to astronomy. Thus, in anticipation of starlit nights, he took possession of the Amthaus, his official residence, in May 1782. "His enthusiasm afire he cast around for an instrument to match his great ambition. Through his relationship with the Herschel family he purchased from William in England, for what was then a very large sum, two reflecting telescopes, one of 4.75 inches (12.01 cm) and the other of 6.5 inches (16.51 cm). According to the convention of the day there were known by their focal lengths, thus the 4-foot (1.22 m) and 7-foot (2.13 m) reflectors. "'Activated solely by irresistible impulse to observe,' as he once wrote, Schroeter immediately embarked upon his voyages of discovery and exploration with unflagging zeal. Initially he studied the markings of Jupiter and the phenomena of the Sun accessible to his telescope, viz., the faculae and spots . "His attention abruptly turned moonwards in April 1787, when William Herschel announced his sighting of what he believed were three active volcanoes on the dark side of the moon. As we now know, Herschel had made one of his rare mistakes; he was only seeing the bright rayed craters Aristarchus, Copernicus and Kepler illuminated by earthshine. Nevertheless, the observation had a magical effect on Schroeter, and that winter he announced his intention to draw a new map of the moon. The best available map was that of Tobias Mayer, published posthumously in 1775. It was skilfully made and based on accurate measures, but measured only 7.5 inches to the moon's diameter. "Schroeter soon changed his plans, and instead of a complete map, decided to sketch as many individual formations as possible as they appeared under varying conditions of illumination. These 'fragments,' as he called them, were published in his Selenotopographische Fragmente in 1791. This is typical of Schroeter's publications. It is a big thick book of 680 pages and 43 copperplates. The title is characteristic; the text rambling and difficult to read, being full of undigested details. Yet it has keen insights; emerging as a vast preliminary sketch, more suggestive that definitive, a rough first clearing away of the brush to create a path into a wilderness. "Never had such a powerful telescope or so keen an eye been trained so systematically and indefatigably on the moon. Using a crude micromete
  • $18,500
  • $18,500
book (2)

Diophanti redivivi pars prior [- posterior], in qua, non casu, ut putatum est, sed certissimâ methodo, & analysi subtiliore, innumera enodantur problemata, quae triangulum rectangulum spectant

BILLY, Jacques de DIOPHANTINE PROBLEMS SOLVED USING FERMAT'S METHODS. First edition, rare, of this early treatise on number theory, explicating and extending the indeterminate problems in the Arithmetica of Diophantus (fl. 3rd century AD). It represents an important testament to the early development of this branch of mathematics. Some of the methods used by Billy (1602-79) derived from Pierre de Fermat (1601-65), the inventor of modern number theory, with whom Billy corresponded starting in 1659. Billy's purpose in the present work was to develop some general methods of solution of such Diophantine problems (Fermat undoubtedly had such methods but did not publish them). "This mathematician, pronounced by M. Charles 'géomètre d'un grand merite', was highly esteemed by Fermat and Bachet de Meziriac. All his writings are rare. This work contains many of the discoveries on the theory of numbers made by Fermat, who was in frequent communication with Billy. It is a curious fact that Father Billy, without any mention of the name of Fermat, gives here, as his own, the resolution of some equations, which, in the Diophantus published with Fermat's annotations in the same year, he [Billy] acknowledges to have found in the letters of Fermat to himself" (Libri Catalogue, lot 1037). The first edition of the Greek text of the Arithmetica was first published by Claude-Gaspard Bachet de Méziriac, of whom Billy was a pupil, in 1621. One of the annotations in Fermat's own copy of this edition was a statement of his famous "last theorem". Fermat's son published a reprint of Bachet's edition in 1670, including his father's annotations. This edition also included a treatise by Billy, the Doctrinae Analyticae Inventum Novum, in which Billy gives an account of some of Fermat's methods of proof. The present work can be seen as an extension of the Doctrinae Analyticae, giving further applications of Fermat's methods. The problems treated in the first volume of the work typically ask whether there exist right-angled triangles whose sides are positive rational numbers (fractions) satisfying certain additional conditions. For example, if we require that each side of the triangle is the square of an integer (whole number) we have the question of whether there are positive whole numbers x,y, z such that x4 + y4 = z4. That no such numbers exist is one case of Fermat's last theorem (actually the first case to be proved). The second volume contains problems of a more arithmetic nature, such as (generalizations of) the problem of finding squares in arithmetic progression (for example, 1, 25, 49) - this is related to the first part, since if x2, y2, z2 is an arithmetic progression, then y is the hypotenuse of a right-angled triangle of which x is the difference and z the sum of the other two sides. Billy also considers the problem of determining when a given cubic or quartic with numerical coefficients can be equal to a square (Dickson, p. 569). RBH lists four copies since Honeyman, with only the Macclesfield copy being in comparable condition to ours. Almost all copies (including Macclesfield and Honeyman) lack some of the blank leaves A1 and T8 in part I and l7-8 in part II (almost all copies lack the blank A1) - all these blanks are present in our copy. OCLC lists Brown, Cincinnati, Harvard, and Huntington in US. Provenance: Old collectors stamp with the initials F.T. to front pastedown. "Jacques de Billy entered the Jesuit order and studied theology at the Colleges of the Order. He was ordained a Jesuit. The Jesuit Order had been created about sixty years before de Billy was born and, from the very beginning, education and scholarship became the principal work of the Order. By the time Billy entered the Order it contained around 15,000 men. "Billy taught mathematics and theology at Jesuit colleges all his life, in particular those colleges which were in the administrative region of Champagne, a region which covered the present-day northeastern French districts of Marne and parts of Ardennes, Meuse, Haute-Marne, Aube, Yonne, Seine-et-Marne, and Aisne. From 1629 to 1630 he taught mathematics at the Jesuit College at Pont à Mousson, during this time he was still studying theology. "From 1631 to 1633 Billy taught mathematics at the Jesuit college at Rheims. He became a close friend of Bachet. After this Billy taught in Grenoble and then was rector of a number of Jesuit Colleges in Chalons, Langres and in Sens. From 1665 to 1668 he was professor of mathematics at the College of Dijon" (MacTutor). There, "one of his students was Jacques Ozanam, whom he taught privately because there was no chair of mathematics at the college, and in whom he instilled a profound love for calculus. Finally, a professorship having been created in mathematics, he taught his favourite subject from 1665 to 1668" (DSB). Ozanam composed a 1200-page manuscript on Diophantine problems, entitled The Six Books of Diophantus' Arithmetic, which was only rediscovered in the twentieth century. This manuscript establishes the correctness of the methods used by Billy, to be described below. "In 1670 the Jesuit Father Jacques de Billy published his work Diophanti redivivi where he treats a very large number of diophantine problems [algebraic equations the solutions of which are required to be integers (whole numbers) or rational numbers (fractions)]. In the first of the two volumes which constitute the work, the author treats many problems on rational right triangles.Willingness to give general methods for certain classes of problems is obvious.The originality of the methods used provides elements new to Diophantine analysis.The treatment of "double equations" of the second degree and the "triple equations" of the first degree, necessary for the resolution of the aforementioned problems, is an important part of this new contribution. "In several places in the work, father Billy refers to Jacques Ozanam, whom he considers very competent on diophantine problems (see pp. 8-9 & 26
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  • $12,500
book (2)

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
book (2)

Recherches sur les mouvements de la planète Herschel

LE VERRIER, Urbain Jean Joseph 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
  • $3,500
  • $3,500
book (2)

De Humani Corporis Fabrica librorum Epitome

VESALIUS, Andreas [Andries van Wezel] First edition, extremely rare, of the Epitome, an illustrated summary of Dehumani corporis fabrica. "The Epitome is without doubt one of the great contributions to the medical sciences, but it is a great deal more, being an exquisite piece of creative art with a perfect blend of format, typography and illustration" (Maley). "The work of Andreas Vesalius (1514-1564) of Brussels constitutes one of the greatest treasures of Western civilization and culture . [The] author has come to be ranked with Hippocrates, Galen, Harvey and Lister among the great physicians and discoverers in the history of medicine" (Saunders and O'Malley, p. 9). "De humani corporis fabrica may be the only masterwork in the history of medicine and science that was published simultaneously with a synopsis prepared by the author. Vesalius designed his Epitome to serve as a more affordable outline key to the encyclopedic and expensive Fabrica. In its dedication Vesalius stated: 'I have made [the Epitome] to be as it were a footpath beside the larger book, and as an index of what is set forth in it.' However, unlike the Fabrica, which begins with the skeletal system and works outward, the Epitome's approach to anatomy is topographical: that is, the muscles are first discussed, followed by a combined study of the vessels, nervous system, and viscera. The various parts of the anatomy are illustrated in nine woodcuts, divided into two skeletal, four muscular, and two circulatory charts, plus a neurological chart. The skeletal, muscular, and one of the circulatory plates are similar, but not identical, to plates found in the Fabrica: the Epitome's plates are some sixty millimeters taller, the figures are in slightly different attitudes, and less space is devoted to background scenery (sheet K duplicates the Fabrica's thinking skeleton, but the inscription on the pedestal has been changed). The remaining circulatory plate and the neurological plate are reproduced, with different texts, on the two folding plates found in the Fabrica . In addition to these nine anatomical plates, the Epitome includes two woodcuts of a nude male and female figure, accompanied by long descriptions of the surface regions of the body; nothing like them appears in the Fabrica. The Epitome's title-page woodcut and portrait of Vesalius are from the same blocks used in the Fabrica. Published in larger format than the Fabrica, in the form of separate sheets to be used for wall charts, and not necessarily bound, the Epitome is considerably rarer than the Fabrica today. Many copies of the Epitome are incomplete, and the last two, unsigned sheets ([N] and [O]), printed with individual parts of the body to be cut out and used as overlays for other figures, are especially rare" (Grolier Medicine). Both of these sheets are present in our copy. "Written in language which does not merely repeat that of the Fabrica, the Epitome is a book in its own right, independent in treatment, point of view, and purpose. The book embodies the principles of his educational method in a more striking fashion than does the Fabrica . Seldom has so large an amount of scientific knowledge been so skillfully compressed into the narrow limits of a few pages" (Lind, pp. xxiv-xxv). Because of the Epitome's clearer, succinct, and more populist approach to the material, it has been argued that "it was not actually the Fabrica itself but the Epitome . . . which had the bigger influence on generations of future anatomists, physicians, and surgeons" (MacLean). Joffe and Buchanan's 2015 world census locates 95 copies of the Epitome, of which only 4 are in private hands (this copy unknown to the census). They estimate that "over the last 470 years since it was published, nearly half of the 1543 edition of the Epitome have survived." Provenance: Pierre II Mariette (1634-1716) (ink signature on title 'P.[ierre] Mariette 1684'), for whom the book was probably bound. He was a "print dealer and publisher, the greatest [print] publisher of the century; son of Pierre Mariette I; married Madeleine, the widow of François Langlois, in 1655 and managed the Langlois business at the 'Colonnes d'Hercules'. In 1657 settled at his father's address (Rue St Jacques à l'Espérance) of which he owned a quarter, before buying all the remaining shares in 1663. In 1658, bought the 'Colonnes d'Hercules', and for a while rented it to a hat-maker then to a bookseller before passing it to his son Jean in 1691 (/collection/term/BIOG61698); ink signature on front flyleaf [H. Ashledos (?)]; eighteenth century American private collection. "Vesalius's Fabrica and Epitome are arguably the most important and influential books in the history of anatomy and possibly in medicine as well. Vesalius reformed the study of human anatomy and decisively broke away from centuries of Galenic tradition, by applying the powers of direct observation and the use of detailed illustration of human anatomy to provide an entirely new standard for the presentation of scientific information. This novel approach would gradually be applied to works of physiology, pathology, and all of the medical sciences. The influence of the book was far reaching - lasting centuries and influencing all anatomical illustration to come. Although not without his own errors, Vesalius denounced the doctrines of incorrect Galenic anatomy and emphasized the importance of human dissection and direct observation for the description of human anatomy. "The book achieved its universal recognition for two reasons. It is the first complete modern medical textbook describing the whole of human anatomy based on its author's own dissection. Vesalius introduced completely new and unique pedagogical techniques. Secondly, in the art of printing and production of scientific works, the marriage of artistically superb illustrations and layout with the descriptive text is unsurpassed. The Fabrica is a large folio and was intended to serve as a reference work for established physicians, surg
  • $250,000
  • $250,000
book (2)

Ars de statica medicina aphorismorum sectionibus septem comprehensa

SANTORIO, Santorio GALILEAN PHYSIOLOGY. First edition, exceptionally rare, of the work that introduced quantitative experimentation into biological science and founded the science of metabolism. "Through most of the 17th and 18th centuries Santorio's name was linked with that of Harvey as the greatest figure in physiology and experimental medicine because of his introduction of precision instruments for quantitative studies. He was also the founder of modern metabolic research" (Garrison and Morton 572.1). "In 1614 he published De statica medicina, a short work on the variation in weight experienced by the human body as a result of ingestion and excretion. The latter work made him famous. Filled with incisive and elliptic aphorisms, De statica medicina dazzled his contemporaries . On 9 February 1615 Santorio sent a copy of De statica medicina to Galileo. In an accompanying letter he explained that his work was based on two principles: first, Hippocrates' view that medicine is essentially the addition of what is lacking and the removal of what is superfluous; and second, experimentation. The origin of 'static medicine' was, in fact, the Hippocratic conception that health consists in the harmony of the humors . To verify this supposition, Santorio turned to quantitative experimentation. With the aid of a chair scale, he systematically observed the daily variations in the weight of his body and showed that a large part of excretion takes place invisibly through the skin and lungs (perspiration insensibilis). Moreover, he sought to determine the magnitude of this invisible excretion; its relationship to visible excretion, and its dependence on various factors, including the state of the atmosphere, diet, sleep, exercise, sexual activity, and age. Thus he invented instruments to measure ambient humidity and temperature. From this research he concluded (1) that perspiratio insensibilis, which had been known since Erasistratus but which was considered imponderable, could be determined by systematic weighing; (2) that it is, in itself, greater than all forms of sensible body excretions combined; and (3) that it is not constant but varies considerably as a function of several internal and external factors; for example, cold and sleep lessen it and fever increases it . Throughout the seventeenth century and the first half of the eighteenth, physicians sympathetic with the doctrines of iatrophysics praised Santorio as one of the greatest innovators in physiology and practical medicine. Many scientists agreed with Baglivi that the new medicine was based on two pillars: Santorio's statics and Harvey's discovery of the circulation of the blood" (DSB). "Santorio's book changed European science. It had more than 84 editions in around 100 years, with translations into almost every European language, it laid the foundation for the experiments of Antoine Lavoisier and Armand Séguin" (Bigotii, 'The forgotten father of chemistry,' Chemistry World online, 14 October 2017). Santorio was a professor at Padua, and a member of Galileo's circle in Venice, which included Giovanni Francesco Sagredo and Paolo Sarpi. The only copy of this work to appear at auction in the last 50 years was the Norman copy (Christie's NY, 16 June 1998, lot 771, $63,000). Provenance: Library of M.D. Johannes Büttner, Germany. "Santorio Santorio was born March 29, 1561, in Capodistria, a pleasant little town on an island in the Adriatic, 17 miles distant from Trieste. At the time, it was the capital city of the district of Istria, hence its name. His father was Chief of Ordnance in the district and his family well to do. He was taken to Venice for his schooling and, at 14, entered the University of Padua where he studied philosophy and then medicine. He received his medical degree at 21 years of age. "Maximilian, King of Poland, wrote to the faculty of Padua in 1587 asking that they recommend to him an excellent physician. The vicar wrote back 'We have a very excellent man, name and surname, Santorio, native of Justinopolis (the Latin name for Capodistria). His learning, fidelity, and industry is most highly esteemed by all of us, it is possible he can easily be induced to take this journey.' Santorio went to Poland where he remained for 14 years and where he was known as a skillful physician and was consulted throughout Eastern Europe. It was while in Poland that Santorio wrote his first book, Methodus Vitandorum Errorum Omnium qui in Arte Medica Contingent (Method of combating all errors that occur in the art of Medicine) published in Venice in 1602. It was, in the main, a work on differential diagnosis drawing mainly from Hippocrates, Galen, and Avicenna. A favourable response to the book led to his appointment as professor of medicine at Padua in 1611 . "One year later Santorio published his Commentary on the Medicine of Galen. In the second edition of this book is the first clear description of the use of the thermometer . It is believed that Santorio became aware of the thermometer through his friendship with Galileo. He realized its potential clinical utility and explored this in some detail in his Commentaria in Primum Fen Primi Libri Canonis Avicenna (Commentaries on the first part of the first book of the Canon of Avicenna). "Santorio's greatest achievement, however, was the discovery of insensible water loss. This was accomplished by the simple means of living for days at a time on a balance. His weight, all that he consumed, and all that he excreted were carefully measured and revealed that there was an insensible loss of water that could not be accounted for even by perspiration. Santorio concluded that there was abundant water in exhaled air, as revealed by a cold mirror. These findings were reported in his next book, Ars Sanctorii Sanctorii de Statica Medicina. This book, published in 1614, passed through 28 Latin editions and was translated into Italian, English, and German. The sensation it created in the medical world was due to its innova
  • $70,000
  • $70,000
Chilias logarithmorum ad totidem numerous rotundos

Chilias logarithmorum ad totidem numerous rotundos, praemissa demonstration legitima ortus logarithmorum eorumque usus . [with:] Supplementum chiliadis logarithmorum, continens praecepta de eorum usu

KEPLER, Johannes the first theoretical work on the construction of logarithms. First edition, the Macclesfield copy, of Kepler's logarithmic tables, constructed by means of his own original method. Of the greatest rarity, especially when complete with the correction leaf and the second part, which gives examples of the application of logarithms and details of their construction. It was through the use of these tables that Kepler was able to complete his monumental Tabulae Rudolphinae (1627), the superiority of which "constituted a strong endorsement of the Copernican system, and insured the tables' dominance in the field of astronomy throughout the seventeenth century" (Norman). Kepler indicated the importance of logarithms allegorically on the frontispiece to the Tabulae Rudolphinae. On the top of the temple stand six goddesses. The third from the left represents logarithms: in her hands she holds rods of the ratio of one to two, and the number around her head shows the Keplerian natural logarithm of 1/2: 0.6931472. But logarithms played another important role in Kepler's astronomical work, since without them he may never have discovered his third law of planetary motion. Kepler discovered this law early in 1618, at the same time that he first had access to tables of logarithms (see below). Moreover, his initial formulation of the third law was (to use modern terminology) in terms of a log-log plot, rather than the more familiar terms of squared periods and cubed distances: "The proportion between the periodic times of any two planets is precisely one and a half times the proportion of the mean distances" (Werke VI, 302). "In a sense, logarithms played a role in Kepler's formulation of the Third Law analogous to the role of Apollonius' conics in his discovery of the First Law, and with the role that tensor analysis and Riemannian geometry played in Einstein's development of the field equations of general relativity. In each of these cases we could ask whether the mathematical structure provided the tool with which the scientist was able to describe some particular phenomenon, or whether the mathematical structure effectively selected an aspect of the phenomena for the scientist to discern" (Brown, p. 555). Provenance: The Earls of Macclesfield, Shirburn Castle, with engraved bookplate, shelf-mark on front pastedown, and blind-stamped Macclesfield crest on blank margins of first three leaves. After painstakingly extracting from the observational data of Tycho Brahe his first two laws of planetary motion around 1605 (first published in Astronomia nova, 1609), there followed a period of more than twelve years during which Kepler searched for further patterns or regularities in the data."Then, as Kepler later recalled, on the 8th of March in the year 1618, something marvelous 'appeared in my head'. He suddenly realized that The proportion between the periodic times of any two planets is precisely one and a half times the proportion of the mean distances. why, after twelve years of struggle, [did] this way of viewing the data suddenly 'appear in his head' early in 1618? . It seems as if a purely mathematical invention, namely logarithms, whose intent was simply to ease the burden of manual arithmetical computations, may have led directly to the discovery/formulation of an important physical law, i.e., Kepler's third law of planetary motion . Kepler announced his Third Law in Harmonices Mundi, published in 1619, and also included it in his Ephemerides of 1620. The latter was actually dedicated to Napier, who had died in 1617. The cover illustration showed one of Galileo's telescopes, the figure of an elliptical orbit, and an allegorical female (Nature?) crowned with a wreath consisting of the Napierian logarithm of half the radius of a circle. It has usually been supposed that this work was dedicated to Napier in gratitude for the 'shortening of the calculations', but Kepler obviously recognized that it went deeper than this, i.e., that the Third Law is purely a logarithmic harmony" (Brown, p. 555). Kepler further illustrated the importance he attached to logarithms in the famous frontispiece to Tabulae Rudolphinae (which he designed himself): one of the muses standing on the temple is 'Logarithmica', and in her halo shines the number 69314.72 (100,000 times the natural logarithm of the number 2). "Kepler first saw Napier's tables [Mifirici logarithmorum canonis descriptio, 1614] in the spring of 1617, but he examined them only superficially at that time. Not until 1619 did Kepler have a copy of Napier's tables, but by then he was more familiar with the logarithms in a book of 1618 by Benjamin Ursinus [Trigonometria logarithmica], his former assistant at Prague and Linz, who had adapted Napier's logarithms, abbreviating the tabular data to two places. The value and significance of the new tables now became clear to Kepler" (Belyi, p. 655). "However, he was not content simply to accept the new mechanical aid as he found it. Napier, in his work, had simply presented the tables of numbers without stating how his logarithms were to be computed. So in the first instance his "wonderful canon" must have operated like a magic trick. In fact, in the beginning, mathematicians as serious as Maestlin mistrusted the new aid to calculation. Was it permissible for a rigorous mathematician to utilize numerical tables about whose construction he knew nothing? Was there not danger that employing them might lead to false conclusions, even if the calculation was proved to agree in many cases? When Kepler, during his visit to Württemberg in 1621, discussed these questions with Maestlin, the latter even ventured so far as to observe "it is not seemly for a professor of mathematics to be childishly pleased about any shortening of the calculations." Kepler differed. He wanted to prove and interpret the new aid to calculation by solid methods and subsequently calculate logarithms himself. "In the winter of 1621-1622 he carried out hi
  • $75,000
  • $75,000
De plantis libri XVI

De plantis libri XVI

CESALPINO, Andrea the first true textbook of botany (PMM 97). First edition, and an exceptionally fine copy, of "the first true textbook of botany' (DSB): the introduction of Cesalpino's classification system, which anticipated Linnaeus' system of binomial nomenclature. "Whereas other sixteenth-century botanists were content simply to compile vast haphazard catalogues of plants, Cesalpino was the first to devise a rational classification system based upon plant morphology, the principles of which he set forth in the first book of De plantis" (Norman). "With Andreas Caesalpinus a new era begins . His book 'On Plants' was the first attempt to classify plants in a systematic manner based on a comparative study of forms . The traditional division into trees, shrubs, half-shrubs and herbs is retained, but they are now subdivided into different categories according to their seed, fruit and flower. The first section contains the general system, while the other fifteen sections describe 1,520 plants in fifteen classes. Caesalpinus's philosophy is Aristotelian: plants have a vegetable soul which is responsible for nutrition and for the reproduction of organisms. Nutrition was believed to come from the roots in the soil and to be carried up the stems to produce the fruit. Hence, the roots, stems and fruit are the main characteristics selected by Caesalpinus as the basis for his classification. His descriptive terminology was finally based on the fruits of plants. Lower plants such as lichens and mushrooms, having no reproductive organs, were believed to arise by spontaneous generation from decaying matter. They were placed at the lower end of the hierarchy of plants, providing the link between plants and inorganic nature. Sex in plants had not yet been discovered; and leaves were considered simply as a protection for the seed. Imperfect as it was, Cesalpinus's was the first rational system of plant classification by which their ever-growing number (six thousand were known in 1600, but nearly twenty thousand by the beginning of the eighteenth century) could be described. The discovery of sex on plants by Camerarius further supported Caesalpinus's method, as reproductive organs could now be used as classifying elements in greater detail. His influence on his contemporaries was not at first very great; they continued to use empirical descriptions. His chief follower was J. Jung (1587-1657). Within one hundred years, however, the need for a system based on comparative morphology was clearly recognized, culminating in the work of Linné who was greatly indebted to this book as well as to Bauhinus. A modern basis for classification of plants was eventually provided by the theory of organic evolution" (PMM). Greene, however, believes that Cesalpino's classification system quickly gained adherents, noting that "only three years later, in 1586, the Arabic physician QÄsim ibn-Muhammad al-WazÄ«r al GhassÄnÄ« wrote his á ¤adÄ«quat al-azhÄr fÄ«, sará ¥ mÄhÄ«yat al-'ushb wa al-'aq qÄr [Garden of flowers, or explanation of the characters of herbs and drugs], which contained the first Arabic classification of plants" (p. 808). Provenance: from the library of the Königliches Joachimsthalsches Gymnasium (their stamp used before 1911 on the verso of titlepage), a Brandenburg princely school (founded in 1607, dissolved in 1953), one of the largest School libraries owned in German-speaking countries. Front board of the binding with initials and date 1585 in blindstamp. "Cesalpino's principal contribution to science lies in botany. Whereas such contemporary botanists as Brunfels, Bock, Leonhart Fuchs, Mattioli, and Tabernaemontanus merely described and illustrated a great number of plants in their Krättterbücher. Cesalpino wrote the first true textbook of botany. The first book of this text is of outstanding historical importance. Here, in thirty pages of admirably clear Latin, Cesalpino presented the principles of botany, grouping a wealth of careful observations under broad categories, on the model of Aristotle and Theophrastus. "Cesalpino considered the portion of the plant between the roots and the shoots -which he called the 'heart' (cor) - to be the seat of its 'soul' (anima), although he added that the soul is present throughout the plant. The task of the roots is to draw nourishment from the ground, and that of the shoots is to bear seeds. The leaves protect the shoots and the fruit from sunlight; they fall off in autumn, when the fruit is ripe and the shoots are developed Cesalpino's description of the tendrils on the shoots and leaves, the climbing petioles of the Clematis, the anchoring roots of the Hedera, the secretion of the nectar from the blossoms, and many other phenomena testify to extraordinary skill in observation. "The parts of the plant, Cesalpino asserted, exist either 'for a purpose' (alicuius gratia) or 'out of (inner) necessity' (ex necessitate); with this distinction he anticipated the concepts of adaptive characteristics and organizational characteristics. Cesalpino considered the fruit to be the most important part of the plant and, accordingly, made it the basis of his system of the plant kingdom. In this system the perianth and the stamens serve only to protect the young fruit; for in his opinion plants do not possess sexuality. He called the outer covering of the fruit the pericarpium. Among fruits he distinguished 'racema' (Vitis), 'juba' (Milium), 'panicula' (Panicum), and 'umbella' (Ferula). "Like Aristotle, Cesalpino divided plants into four 'genera': Arbores (trees), Frutices (shrubs), Suffrutices (shrubby herbs), and Herbae (herbs). Trees possess a single stem, whereas shrubs have many thin stems. Shrubby herbs live for many years and often bear fruit, but herbs die after formation of the seeds. The distinction among species should be made, he held, only according to similarity and dissimilarity of forms; 'unessential features' (accidentia), such as medicinal use, practical application, and habi
  • $48,000
  • $48,000