GÖDEL, Kurt, VON NEUMANN, John (& others)
VERY RARE COMPLETE SET OF THE VIENNA ERGEBNISSE - GÖDEL ON LOGIC AND THE FOUNDATIONS OF MATHEMATICS VON NEUMANN ON MATHEMATICAL ECONOMICS. First editions, a very rare complete set in the original printed wrappers, of all eight issues of these proceedings to which Gödel contributed thirteen important papers and remarks on the foundations of logic and mathematics. The last three issues are particularly rare, and are important for containing several seminal papers on mathematical economics, notably von Neumann's "A model of general economic equilibrium" in Heft 8, which "E. Roy Weintraub, current President of the History of Economics Society, described as 'the greatest paper in mathematical economics that was ever written'" (Cabral, p. 126). "In stark contrast to the short eight years of its existence, the colloquium that met in Vienna from 1928 to 1936 had a long lasting influence on economic theory" (Debreu - winner of the 1983 Nobel Prize in Economics). The most important of the Gödel papers are perhaps 'Über Vollständigkeit und Widerspruchsfreiheit' ('On completeness and consistency') in Heft 3 and 'Zur intuitionistischen Arithmetik und Zahlentheorie' ('On intuitionist arithmetic and number theory') in Heft 4. Based on the lecture at the Colloquium required for his Habilitation, in the first paper Gödel presented a different approach to his epochal incompleteness theorem, published just a few months earlier in Monatshefte für Mathematik: instead of Russell's theory of types, in the present version he used Peano's axioms for the natural numbers; this soon became the standard approach. In the second paper, Gödel proved that intuitionist mathematics is no more certain, or more consistent, than ordinary mathematics. "By invitation, in October 1929 Gödel began attending Menger's mathematics colloquium, which was modelled on the Vienna Circle. There in May 1930 he presented his dissertation results, which he had discussed with Alfred Tarski three months earlier, during the latter's visit to Vienna. From 1932 to 1936 he published numerous short articles in the proceedings of that colloquium (including his only collaborative work) and was co-editor of seven of its volumes. Gödel attended the colloquium quite regularly and participated actively in many discussions, confining his comments to brief remarks that were always stated with the greatest precision" (DSB XVII: 350). Von Neumann also attended the colloquium in the early years. Although subsets of this collection occasionally appear on the market, complete sets of all eight issues are extremely difficult to find. Working under Hans Hahn, Karl Menger (1902-85) received his PhD from the University of Vienna in 1924 and accepted a professorship there three years later. "During the academic year 1928/29, several students asked Menger to direct a Mathematical Colloquium, somewhat analogous to the philosophically motivated Vienna Circle . This Colloquium, which met on alternate Tuesdays during semester time, had a flexible agenda including lectures by members or invited guests, reports on recent publications and discussion of unsolved problems. Menger kept a record of these meetings, which he published, regularly in November of the following year, under the title 'Ergebnisse eines mathematischen Kolloquiums' . "Gödel had entered the university in 1924, and Menger first met him as the youngest and most silent member of the Vienna Circle. In 1928, Gödel started working on Hilbert's program for the foundation of mathematics, and in 1929 he succeeded in solving the first of four problems of Hilbert, proving in his PhD thesis (under Hans Hahn) that first order logic is complete: Any valid formula could be derived from the axioms. "At that time Menger, who was greatly impressed by the Warsaw mathematicians, had invited Alfred Tarski to deliver three lectures at the Colloquium. Gödel, who had asked Menger to arrange a meeting with Tarski, soon took a hand in running the Colloquium and editing its Ergebnisse. "Menger was visiting the USA [in 1931] when Gödel discovered the incompleteness theorem and used it to refute the remaining three of Hilbert's conjectures. He learned by letter that Gödel had lectured in the Colloquium 'On Completeness and Consistency'. This was the lecture required for Gödel's habilitation. The paper required for the same procedure, 'On the undecidability of certain propositions in the Principia Mathematica,' had been published in Hahn's 'Monatshefte'. In his Colloquium lecture, Gödel presented a simpler approach. Instead of Russell's theory of types, he used Peano's axioms for the natural numbers. This soon became the standard approach . "Menger was particularly fond of Gödel's results on intuitionism. These vindicated his own tolerance principle. Specifically, Gödel proved that intuitionist mathematics is no more certain, or more consistent, than ordinary mathematics ('Zur intuitionistischen Arithmetik und Zahlentheorie', Heft 4) . Menger brought Oswald Veblen to the Colloquium when Gödel lectured on this result. Veblen, who had been primed by John von Neumann, was tremendously impressed by the talk and invited Gödel to the Institute for Advanced Study during its first full year of operation: A signal honour that proved a blessing in Gödel's later years" (Karl Sigmund in Selecta Mathematica, pp. 14). The Gödel papers contained in these five volumes are as follows, with summaries based on the Annotated Bibliography of Gödel by John Dawson: 'Ein Spezialfall des Entscheidungsproblems der theoretischen Logik,' Heft 2, pp. 27-28. This undated contribution was not presented to a regular meeting of the colloquium, but appeared among the Gesammelte Mitteilungen for 1929/30. In the context of the first-order predicate calculus without equality, Gödel describes an effective procedure for deciding whether or not a certain formula is satisfiable; the procedure is related to the method used in [his dissertation Die Vollstandigkeit der Axiome
WIGNER, Eugene Paul
PARITY AND TIME-REVERSAL IN QUANTUM MECHANICS. First edition, very rare offprints, of these two fundamental papers in quantum mechanics, the "invention of spatial parity as a quantum mechanical conserved quantity [I] [and the] introduction of the time inversion transformation in quantum mechanics [II]" (). "Wigner was invited to Göttingen in 1927 to become Hilbert's assistant. Hilbert, already interested in quantum mechanics, felt that he needed a physicist as an assistant to complement his own expertise. This was an important time for Wigner who produced papers of great depth and significance, introducing in his paper 'On the conservation laws of quantum mechanics' (1927) [I] the new concept of parity" (). "Wigner performed pioneering work by studying such symmetries in the laws of motion for the electrons and had made important discoveries by investigating e.g., those symmetries which express the fact that the laws mentioned make no difference between left and right and that backward in time according to them is equivalent to forward in time. These investigations were extended by Wigner to the atomic nuclei at the end of the 1930s and he explored then also the newly discovered symmetry property of the force between two nucleons to be the same whether either of the nucleons is a proton or a neutron. This work by Wigner and his other investigations of the symmetry principles in physics are important far beyond nuclear physics proper. His methods and results have become an indispensable guide for the interpretation of the rich and complicated picture which has emerged from recent years' experimental research on elementary particles" Presentation speech for Wigner's Nobel Prize). "Wigner was a member of the race of giants that reformulated the laws of nature after the quantum mechanics revolution of 1924-25. In a series of papers on atomic and molecular structure, written between 1926 and 1928, Wigner laid the foundations for both the application of group theory to quantum mechanics and for the role of symmetry in quantum mechanics" (David J. Gross, 'Symmetry in Physics: Wigner's legacy,' Physics Today, December 1995, pp. 46-50). Wigner was awarded the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles." "Nearly a decade after he was awarded the Nobel Prize, Wigner's early group theory research was described as so farsighted that it was not immediately recognized for its importance as a pioneering advance in mathematical physics . The parity law states that particles emitted during a physical process should emanate from the left and right in equal numbers or equivalently that a nuclear process should be indistinguishable from its mirror image. The parity concept was not challenged until 1956 when it was disproved in certain so-called 'weak decay' interactions in experiments by Tsung-Dao Lee of Columbia and Chen-Ning Yang of Princeton. Lee and Yang were awarded the Nobel Prize in 1957 for their empirical refutation of Wigner's parity theory in this special case. The theory however remained substantially intact and along with other of Wigner's discoveries useful as a further guide in nuclear research" (DSB). "It is scarcely possible to overemphasize the role played by symmetry principles in quantum mechanics" (C. N. Yang, Nobel Lecture, p. 394). No copies on OCLC or RBH. Provenance: I. Felix Bloch (1905-83), Swiss-American physicist who shared the 1952 Nobel Prize for Physics with Edward Purcell for "their development of new ways and methods for nuclear magnetic precision measurements" ('Bloch' written in ink on front wrapper). II. Ralph Kronig (1904-95), German physicist who first put forward the concept of electron spin ('Kronig' written in pencil on front wrapper). The concept of parity refers to the behavior of classical and quantum systems under the 'inversion' operation, which takes a point in three dimensions with Cartesian coordinates x, y, z to the point with coordinates -x, -y, -z (more generally, this can be any 'linear transformation' that is not a rotation, for example the 'mirror reflection' that takes x, y, z to -x, y, z). Symmetry under inversion, or reflection, was used in classical physics, but was not of any great practical importance there. One reason for this derives from the fact that right-left symmetry is a discrete symmetry, unlike rotational symmetry which is continuous. In a famous paper in 1918, Emmy Noether showed that continuous symmetries always lead to conservation laws in classical physics - but a discrete symmetry does not. With the introduction of quantum mechanics, however, this difference between discrete and continuous symmetries disappears. Wigner was led to his study of parity by work of Otto Laporte in 1924. Laporte studied the structure of the spectrum of iron and found that there are two kinds of energy levels, which he called 'stroked' ('gestrichene') and 'unstroked' ('ungestrichene'). He discovered a selection rule (later called Laporte's rule) that the transitions occurred always from stroked to unstroked levels or vice versa, and never between stroked or between unstroked levels. A few months later similar observations on the spectrum of titanium were made by Henry Norris Russell. No convincing explanation of the existence of two types of levels was found within the framework of the old quantum theory. In 1927, Wigner analysed Laporte's finding and showed that the two types of levels and the selection rule followed from the invariance of the electromagnetic forces in the atom under the operation of inversion of coordinates. This led him quickly to the idea of parity conservation in quantum mechanics. He wrote, 'But that was very easy. I knew the spectroscopic rules, and Laporte's rule was similar to the theory of inversion'. Wigner introduced the parity operator, and parity conservation, forma
BOERHAAVE, Herman
UNCUT LARGE PAPER COPY. First edition, very rare uncut large paper copy, and a very early printing of this great work (see below). "The first and best edition, and rare" (Duveen). "[Boerhaave] introduced exact quantitative methods into chemistry by measuring temperature and using the best available balances made by Fahrenheit; indeed he may be considered the founder of physical chemistry as well as a contributor to pneumatic chemistry and biochemistry . When a spurious edition of his chemical lecture notes was published in 1724 . he felt impelled to publish a textbook on chemistry, the Elementa chemiae, which was later translated into English and French and remained the authoritative chemical manual for decades" (DSB). In the preface, Boerhaave pointedly disowned the unauthorised 1724 publication, railing that "The false Notions, Absurdities, and Barbarisms, that are imputed to me in every page of that Work, are so abominable, that they will not bear mentioning" (quoted in Powers, Inventing Chemistry, p. 144). To distinguish the present authorised edition from that published in 1724, Boerhaave signed all copies on the verso of the title page. This copy is printed on thick paper - the text block of this copy is about one-third thicker than that of a normal copy - and is entirely uncut. The only other uncut large paper copy we have located is that in the British Library; the only other large paper having appeared in commerce was the Macclesfield copy (although it was not so described in the Macclesfield catalogue). This copy is 2 cm taller and 1 cm wider than the Macclesfield copy. "To some historians of science the great event of the 18th century is the rise of modern chemistry. This is commonly associated with the names of men like Black, Cavendish, Scheele, Priestley or Lavoisier, whose careers, distinguished by brilliant discoveries, fell mainly in the later part of the century. But if we are to judge history not only in terms of individual men's accomplishments, but also of the influence which guided them, the name of Herman Boerhaave and the title of his great work, Elementa chemiae, stand out among all the others. Boerhaave gathered up the chemistry of the centuries before him, extracted what was factually sound, eliminated what was theoretically irrelevant, and re-presented it in a form congenial to a century which was to seek above all things a dignified enlightenment. Boerhaave assimilated to a chemistry which was a practical art a chemistry which was a material philosophy, and he expounded the product as a science unified as best he knew . "Like all chemists of his time and even after him, he had to come to terms with the traditions of alchemy. He did so experimentally, finding that he could repeat some of the alchemists' experiments, while others he could not. To some extent he retained a theory of the composition of metals similar to that of the alchemists but experiment was for him the deciding factor in his choice, not tradition. "His chemical lectures were enormously successful and suffered a common fate. They were recorded, transcribed, and published by students, without his consent. They appeared in 1724 as Institutiones et experimenta chemiae, followed by other editions and in 1727 an English translation. Anyone may be expected to be angry at unauthorised publications. Boerhaave was doubly angry to see his books being brought into his own lectures. He could rectify the position only by producing his own textbook. It appeared in 1732, each copy bearing a signed declaration as a guarantee of authenticity . "The leading characteristic of this great work is its realism. Stahl defined chemistry succinctly as the art of resolving compound bodies into their principles and of recombining them again. By comparison Boerhaave's definition is ponderous: Chemistry is "an art which teaches the manner of performing certain physical operations, whereby bodies cognizable to the sense, capable of being rendered cognizable, and of being contained in vessels, are so changed by means of proper instruments, as to produce certain determinate effects, and at the same time discover the causes thereof, for the service of various arts." Yet while Stahl's writings are complicated, argumentative and self-opinionated, Boerhaave's are clear and purposeful, superior in their discipline to the author's definition of the subject. Perhaps the biggest difference between these two influential men was that Stahl denied the relevance of chemistry to medicine, whereas Boerhaave saw the relevance of chemistry to every art including medicine" (Greenaway, pp. 102-4). "Boerhaave was firmly convinced of the usefulness of chemistry in medicine and the "mechanical arts", among which he mentioned in particular painting, enamelling, staining glass, manufacturing glass, dyeing, metallurgy, the art of war, natural magic, cookery, the art of winemaking, brewing, and alchemy. In the "practical part" of his textbook he presented a collection of 227 "processes" which were, apart from dozens of experiments devoted unambiguously to chemical analysis, recipe-like descriptions of "the actual operations of chemistry" - that is, familiar operations performed in pharmaceutical and chemical laboratories all over Europe, both for the acquisition of knowledge and for the manufacture of useful goods. Much of the fame of Boerhaave's Elementa chemiae depended on this second, practical part of the book" (Klein & Lefèvre, Materials in 18th century Science: A Historical Ontology (2007), p. 29). "Boerhaave's [Elementa chemiae] is dedicated to his brother Jacobus (James), 'in memory of the many days and nights we have spent together in the chemical examination of natural bodies, at the time when your chief view was to Medicine and mine to Theology.' It begins in Part I with a good history of Chemistry; Part II is on the Theory of Chemistry (metals, salts, the universal acid, sulphur, bitumens, stones, earths, semi-metals, vegetables, and anim
NEWTON, Sir Isaac
NEWTON'S FIRST EXPOSITION OF HIS FLUXIONAL CALCULUS. First edition of Newton's first exposition of his fluxional calculus. Originally written in 1671, in Latin, this was Newton's first comprehensive presentation of his method of fluxions which, according to Hall 'might have effected a mathematical revolution in its own day' (Philosophers at War, pp. 65-6). It should properly be placed first in the great trilogy of Newton's major works: Fluxions, Principia (1687) and Opticks (1704). Newton's Methodus fluxionum was originally prepared in 1671, but remained unpublished until this English translation by John Colson. In it he presents a method of determining the magnitudes of finite quantities by the velocities of their generating motions. At its time of preparation, it was Newton's fullest exposition of the fundamental problem of the calculus, in which he presented his successful general method. Newton prepared this treatise just before his death and entrusted the Latin manuscript to Henry Pemberton, who never published it. In the preface, Colson writes "I thought it highly injurious to the memory and reputation of our own nation, that so curious and useful a piece should be any longer suppressed." The engraved plate demonstrates the concept of fluxions in the shooting of two birds at once. The method of fluxions was not published in its original Latin until 1779, in Samuel Horsley's Opera omnia. Newton wrote three accounts of the calculus. The composition of the first, a tract entitled 'De analysi per aequationes numero terminorum infinitas,' resulted from Newton's reception from Isaac Barrow, in the early months of 1669, of a copy of Mercator's Logarithmotechnia, a work which contained the series for log(1 + x). The work, in which Newton demonstrated his much more general methods of infinite series, was not published until 1711, when William Jones included it, along with a number of other tracts, in his Analysis per quantitatum series. In 'De analysi,' however, Newton "did not explicitly make use of the fluxionary notation or idea. Instead, he used the infinitely small, both geometrically and analytically, in a manner similar to that found in Barrow and Fermat, and extended its applicability by the use of the binomial theorem. . It will be noticed that although the work of Newton contains the essential procedures of the calculus, the justification of these is not clear from the explanation he gave. Newton did not point out by what right the terms involving powers of o were to be dropped out of the calculation, any more than Fermat or Barrow . His contribution was that of facilitating the operations, rather than of clarifying the conceptions. As Newton himself admitted in this work, his method is 'shortly explained rather than accurately demonstrated'" (Boyer, The Concept of Calculus, p.191). It was first in 'Methodus fluxionum' that "Newton introduced his characteristic notation and conceptions. Here he regarded his variable quantities as generated by the continuous motion of points, lines, and planes, rather than as aggregates of infinitesimal elements, the view which had appeared in 'De analysi'. . In the 'Methodus fluxionum' Newton stated clearly the fundamental problem of the calculus: the relation of quantities being given, to find the relation of the fluxions of these; and conversely" (ibid., pp. 192-3). In Newton's third exposition, De quadratura, which was composed some twenty years after 'Methodus fluxionum' and published as an appendix to the Opticks, "Newton sought to remove all traces of the infinitely small" (ibid.). "It was often lamented that the world had had to wait so many years to see Newton's masterpiece on fluxions. It is astonishing to realize that publication sixty years beforehand would have changed the history of the calculus and would have avoided for Newton any controversy over priority. In 1736 all the results contained in Newton's treatise were well known to mathematicians. However, it was too concise for a beginner, and Colson added almost 200 pages of explanatory notes. His commentary contributed to the establishment of a kinematical approach to the problem of foundations. In his explanatory notes Colson presents the 'geometrical and Mechanical Elements of Fluxions'. He writes: 'The foregoing Principles of the Doctrine of Fluxions being chiefly abstracted and Analytical. I shall here endeavour, after a general manner, to shew something analogous to them in Geometry and Mechanicks: by which they may become not only the object of the Understanding, and of the Imagination, (which will only prove their possible existence) but even of Sense too, by making them actually to exist in a visible and sensible form' (p. 266). "Colson was convinced that by using moving diagrams it is possible to exhibit 'Fluxions and Fluents Geometrically and Mechanically . so as to make them the objects of Sense and ocular Demonstration' (p. 270). The motivation for using the geometrical and mechanical elements of fluxions is clearly that of guaranteeing an ontological basis to the calculus; in fact: 'Fluents, Fluxions, and their rectilinear Measures, will be sensibly and mechanically exhibited, and therefore must be allowed to have a place in rerum natura' (p. 271). "Colson's approach to the calculus is representative of a whole generation of British mathematicians: his 'sensibly exhibited rectilinear measures' of fluxions are a naive anticipation of Maclaurin's kinematic definitions of the basic concepts of the calculus" (Guicciardini, The Development of Newtonian Calculus in Britain 1700-1800, pp. 56-57). "In his preface [to the present work] ., Colson noted: 'The chief Principle, upon which the Method of Fluxions is here built, is. taken from the Rational Mechanicks; which is, That Mathematical Quantity, particularly Extension, may be conceived as generated by continued local Motion; and that all Quantities may be conceived as generated after a like manner. Consequently there must be
LONDON, Fritz & LONDON, Heinz
THE FIRST THEORY OF SUPERCONDUCTIVTY: THE LONDON EQUATIONS. First edition, very rare offprints, of the first successful macroscopic theory of superconductivity, the vanishing of electrical resistance in some materials at very low temperatures. This is embodied in the 'London equations', the analogue for a superconductor of Ohm's law for a normal conductor. 'In 1933 shortly before Heinz London joined his brother at Oxford, W. Meissner and R. Ochsenfeld made a startling discovery. It was well known that currents in superconductors flow in such a way as to shield points inside the material from changes in the external magnetic field . But a superconductor does more. Whereas a zero resistance medium only counteracts changes in the field, it actually tends to expel the field present in its interior before cooling" (DSB). "In 1935, the brothers Fritz London and Heinz London developed the first phenomenological theory of superconductivity [II]. The London equations provide a theoretical description of the electrodynamics of superconductors, including the Meissner effect. In a thin surface layer, just inside the superconductor, screening currents flow without resistance, which cancel the applied magnetic field in the interior of the superconductor. The thickness of this layer, known as the 'London penetration depth', is a characteristic of the superconductor in question. In addition, London recognized that superconductivity is an example of a macroscopic quantum phenomenon. The behavior of a superconductor is governed by the laws of quantum mechanics like that of a single atom, but on a macroscopic scale" ('A brief history of superconductivity,' in: Discovering Superconductivity: An Investigative Approach (Ireson, ed.), 2012). "In 1934 two brothers, Fritz and Heinz London, both refugees from Nazi Germany, were working in an upstairs room in a rented house in Oxford. There they solved what was then one of the biggest problems in superconductivity, a phenomenon discovered 23 years earlier. The moment of discovery seems to have been sudden: Fritz shouted down to his wife 'Edith, Edith come, we have it! Come up, we have it!' She later recalled, "I left everything, ran up and then the door was opened into my face. On my forehead I had a bruise for a week.' As Edith recovered from her knock, Fritz told her with delight 'The equations are established - we have the solution. We can explain it' . In formulating their theory, the London brothers made the most significant progress in our understanding of superconductors in the first half of the 20th century . John Bardeen, who won his second Nobel prize in 1972 for co-developing the Bardeen-Cooper-Schrieffer (BCS) theory that provided a coherent framework for understanding superconductivity, regarded the achievement of the London brothers as pivotal. 'By far the most important step towards understanding the phenomena', Bardeen once wrote, 'was the recognition by Fritz London that both superconductors and superfluid helium are macroscopic quantum systems.' Before then, quantum theory had only been thought to account for the properties of atoms and molecules at the microscopic level. As Bardeen explained, 'It was Fritz London who first recognized that superconductivity and superfluidity result from manifestations of quantum phenomena on the scale of large objects'" (Blundell, 'The forgotten brothers,' Physics World, April 2011, pp. 26-29). "Fritz London was born in 1900 in the German city of Breslau (now Wroclaw, Poland) and nearly became a philosopher. However, he switched to physics and became immersed in the heady intellectual atmosphere of the 1920s that surrounded the new quantum theory. London's early career saw him travelling around Germany, taking positions with some of the great quantum pioneers of the time: Max Born in Göttingen; Arnold Sommerfeld in Munich; and Paul Ewald in Stuttgart. London worked on matrix mechanics and studied how the newly discovered operators of quantum mechanics behave under certain mathematical transformations, but he really made his name after moving again to Zurich in 1927. The lure of Zurich had been to work with Erwin Schrödinger, but almost immediately Schrödinger moved to Berlin and London teamed up with Walter Heitler instead. Together they produced the Heitler-London theory of molecular hydrogen - a bold and innovative step that essentially founded the discipline of quantum chemistry. "The following year London moved to Berlin, where he worked on intermolecular attraction and originated the concept of what are now known as London dispersion forces. He also succumbed to the interpersonal attraction of Edith Caspary, whom he married in 1929. By now the name 'Fritz London' was becoming well known - he was fast gaining a reputation as a creative and productive theorist. However, with Hitler becoming German chancellor in 1933, the Nazis began a process of eliminating the many Jewish intellectuals from the country's academic system, putting both London and his younger brother Heinz at risk. Born in Bonn in 1907, Heinz had followed in his older brother's footsteps, studying physics, but became an experimentalist instead, obtaining his PhD under the famous low-temperature physicist Franz Simon. "A possible way out from the Nazi threat was provided by an unlikely source. Frederick Lindemann, later to become Winston Churchill's wartime chief scientific adviser and to finish his days as Viscount Cherwell, was then the head of the Clarendon Laboratory. Lindemann was half-German and had received his PhD in Berlin, so was well aware of the political situation in Germany. He decided to do what he could to provide a safe haven in Oxford for refugee scientists. His motives were not entirely altruistic, however: Oxford's physics department was then a bit of an intellectual backwater and this strategy would effect an instantaneous invigoration of its academic firepower in both theoretical and experimental terms. Later that year Linde
WATSON, J. D. & CRICK, F. H. C.; WILKINS, M. H. F., STOKES, A. R. & WILSON, H. R.; FRANKLIN, R. E. & GOSLING, R. G.
DISCOVERY OF THE STRUCTURE OF DNA. SIGNED BY ALL BUT ONE OF THE AUTHORS. First edition, offprint, signed by Watson, Crick, Wilkins, Gosling, Stokes & Wilson, i.e. six of the seven authors. We know of no copy signed by Franklin, and strongly doubt that any such copy exists. Furthermore this copy is, what we believe to be, just one of three copies signed by six authors. One of the most important scientific papers of the twentieth century, which "records the discovery of the molecular structure of deoxyribonucleic acid (DNA), the main component of chromosomes and the material that transfers genetic characteristics in all life forms. Publication of this paper initiated the science of molecular biology. Forty years after Watson and Crick's discovery, so much of the basic understanding of medicine and disease has advanced to the molecular level that their paper may be considered the most significant single contribution to biology and medicine in the twentieth century" (One Hundred Books Famous in Medicine, p. 362). "The discovery in 1953 of the double helix, the twisted-ladder structure of deoxyribonucleic acid (DNA), by James Watson and Francis Crick marked a milestone in the history of science and gave rise to modern molecular biology, which is largely concerned with understanding how genes control the chemical processes within cells. In short order, their discovery yielded ground-breaking insights into the genetic code and protein synthesis. During the 1970s and 1980s, it helped to produce new and powerful scientific techniques, specifically recombinant DNA research, genetic engineering, rapid gene sequencing, and monoclonal antibodies, techniques on which today's multi-billion dollar biotechnology industry is founded. Major current advances in science, namely genetic fingerprinting and modern forensics, the mapping of the human genome, and the promise, yet unfulfilled, of gene therapy, all have their origins in Watson and Crick's inspired work. The double helix has not only reshaped biology, it has become a cultural icon, represented in sculpture, visual art, jewelry, and toys" (Francis Crick Papers, National Library of Medicine, profiles./SC/Views/Exhibit/narrative/). In 1962, Watson, Crick, and Wilkins shared the Nobel Prize in Physiology or Medicine "for their discoveries concerning the molecular structure of nucleic acids and its significance for information transfer in living material." This copy is signed by all the authors except Rosalind Franklin (1920 -1958) - we have never seen or heard of a copy signed by her. In 1869, the Swiss physiological chemist Friedrich Miescher (1844-95) first identified what he called 'nuclein' inside the nuclei of human white blood cells. (The term 'nuclein' was later changed to 'nucleic acid' and eventually to 'deoxyribonucleic acid,' or 'DNA.') Miescher's plan was to isolate and characterize not the nuclein (which nobody at that time realized existed) but instead the protein components of leukocytes (white blood cells). Miescher thus made arrangements for a local surgical clinic to send him used, pus-coated patient bandages; once he received the bandages, he planned to wash them, filter out the leukocytes, and extract and identify the various proteins within the white blood cells. But when he came across a substance from the cell nuclei that had chemical properties unlike any protein, including a much higher phosphorous content and resistance to proteolysis (protein digestion), Miescher realized that he had discovered a new substance. Sensing the importance of his findings, Miescher wrote, "It seems probable to me that a whole family of such slightly varying phosphorous-containing substances will appear, as a group of nucleins, equivalent to proteins". But Miescher's discovery of nucleic acids was not appreciated by the scientific community, and his name had fallen into obscurity by the 20th century. "Researchers working on DNA in the early 1950s used the term 'gene' to mean the smallest unit of genetic information, but they did not know what a gene actually looked like structurally and chemically, or how it was copied, with very few errors, generation after generation. In 1944, Oswald Avery had shown that DNA was the 'transforming principle,' the carrier of hereditary information, in pneumococcal bacteria. Nevertheless, many scientists continued to believe that DNA had a structure too uniform and simple to store genetic information for making complex living organisms. The genetic material, they reasoned, must consist of proteins, much more diverse and intricate molecules known to perform a multitude of biological functions in the cell. "Crick and Watson recognized, at an early stage in their careers, that gaining a detailed knowledge of the three-dimensional configuration of the gene was the central problem in molecular biology. Without such knowledge, heredity and reproduction could not be understood. They seized on this problem during their very first encounter, in the summer of 1951, and pursued it with single-minded focus over the course of the next eighteen months. This meant taking on the arduous intellectual task of immersing themselves in all the fields of science involved: genetics, biochemistry, chemistry, physical chemistry, and X-ray crystallography. Drawing on the experimental results of others (they conducted no DNA experiments of their own), taking advantage of their complementary scientific backgrounds in physics and X-ray crystallography (Crick) and viral and bacterial genetics (Watson), and relying on their brilliant intuition, persistence, and luck, the two showed that DNA had a structure sufficiently complex and yet elegantly simple enough to be the master molecule of life. "Other researchers had made important but seemingly unconnected findings about the composition of DNA; it fell to Watson and Crick to unify these disparate findings into a coherent theory of genetic transfer. The organic chemist Alexander Todd had determined t
FRANK, Ilya & TAMM, Igor
CHERENKOV RADIATION EXPLAINED - NOBEL PRIZE 1958. First edition, very rare offprint, of the explanation of Cherenkov radiation, for which Frank and Tamm shared (with Cherenkov) the Nobel Prize in Physics 1958. "In certain media the speed of light is lower than in a vacuum and particles can travel faster than light. One result of this was discovered in 1934 by Pavel Cherenkov, when he saw a bluish light around a radioactive preparation placed in water. Ilya Frank and Igor Tamm explained the phenomenon in 1937. On their way through a medium, charged particles disturb electrons in the medium. When these resume their position, they emit light. Normally this does not produce any light that can be observed, but if the particle moves faster than light, a kind of backwash of light appears" (). "Cherenkov radiation derives its name from Pavel Cherenkov,who as a young PhD student at Moscow's Lebedev Institute in the early 1930s,was assigned by Sergei Vavilov the task of investigating what happens to the radiation from a piece of radium when it is immersed in a fluid. Such radioactive materials give off an eerie blue light,such as that seen in a 'swimming pool' nuclear reactor. Initially,this was thought to be fluorescence,similar to that seen when X-rays strike a screen,but Vavilov and Cherenkov were not convinced. After heroic investigations,where Cherenkov would typically prepare for a working day by staying in a totally dark room for one hour,he found that the radiation was produced by electrons and was essentially independent of the liquid used,thereby ruling out fluorescence. The explanation for theeffect came in 1937 from Ilya Frank andIgor Tamm,who explained that theradiation is a shock wave resulting from a charged particle moving through a material faster than thevelocity of light in thematerial - theoptical equivalent of thesonic boom produced by an aircraft as it accelerates beyond thespeed of sound. The 'Cherenkov' radiation propagates as a cone whose opening angle depends on the particle velocity. When this cone hits a flat surface,a characteristic ring is seen" ('More light on the Cherenkov effect,' CERN Courier, 26 November 1998). Not on OCLC. No copies in auction records. "In 1888, [Oliver] Heaviside published a paper in The Electrician, in which he explored the electromagnetic effects of a charge moving through a dielectric. "If the speed of the motion exceeds that of light, the disturbances are wholly left behind the charge, and are confined within a cone," he wrote. Unfortunately, nobody paid much attention to Heaviside's work in this area-he was an eccentric recluse later in life. His contribution wasn't uncovered until 1974, revealed in a one-page letter to Nature by physicist Tom Kaiser. "A 1904 paper by Arnold Sommerfeld theoretically predicting Cherenkov radiation also failed to gain traction within the scientific community. And in 1910, Marie Curie notably referenced an observation of a strange blue light during her research into a highly concentrated radium solution. 'Nor was this the end of the wonders of radium,' she wrote. 'It also gave phosphorescence to a large number of bodies incapable of emitting light by their own means.' Neither Marie nor her husband Pierre followed up on the observation, but their French colleague, Leon Mallett, began studying the phenomenon in earnest in 1922. "Enter Cherenkov. Born in July 1904 in a small village called Novaya Chigla, he graduated from Voronezh State University in 1928 and became a senior research in the Lebedev Physical Institute. In 1934, Cherenkov began conducting his own experiments on this strange form of radiation, working with his institute colleague Sergei Vavilov. (In fact, it was termed 'Vavilov-Cherenkov radiation' in the Soviet Union.) He noted that same emission of blue light when bombarding a bottle of water with radiation" ('December 1934: Discovery of Cherenkov radiation,' APS News, Vol. 29, No. 11, December 2020). "Ilya Frank (1908-90) was born in St. Petersburg, Russia, to Mikhail Lyudvigovich Frank, a talented mathematician descended from a Jewish family, and Yelizaveta Mikhailovna Gratsianova, a Russian Orthodox physician. His father participated in the student revolutionary movement, and as a result was expelled from Moscow University. After the October Revolution, he was reinstated and appointed professor. Ilya Frank studied mathematics and theoretical physics at Moscow State University. From his second year he worked in the laboratory of Sergey Ivanovich Vavilov, whom he regarded as his mentor. After graduating in 1930, on the recommendation of Vavilov, he started working at the State Optical Institute in Leningrad. There he wrote his first publication - about luminescence -with Vavilov. The work he did there would form the basis of his doctoral dissertation in 1935" (). Igor Tamm (1895-1971) "was born in Vladivostok on July 8, 1895, as the son of Evgenij Tamm, an engineer, and Olga Davydova. He graduated from Moscow State University in 1918, specializing in physics, and immediately commenced an academic career in institutes of higher learning. He was progressively assistant, instructor, lecturer, and professor in charge of chairs, and he has taught in the Crimean and Moscow State Universities, in Polytechnical and Engineering-Physical Institutes, and in the J.M. Sverdlov Communist University. Tamm was awarded the degree of Doctor of Physico-Mathematical Sciences, and he has attained the academic rank of Professor. Since 1934, he has been in charge of the theoretical division of the P.N. Lebedev Institute of Physics of the U.S.S.R. Academy of Sciences" (). "In 1934, Frank moved to the Institute of Physics and Mathematics of the USSR Academy of Sciences, were he started working on nuclear physics, a new field for him. He became interested in the effect discovered by Pavel Cherenkov that charged particles moving through water at high speeds emit light. In 1937, working with his colleague Igor Y. Tamm, Fra
DARWIN, Charles
PRESENTATION COPY OF DARWIN'S GREATEST WORK. First edition, presentation copy, of "the most influential scientific work of the nineteenth century" (Horblit), "the most important biological work ever written" (Freeman), and "a turning point, not only in the history of science, but in the history of ideas in general" (DSB). "Darwin not only drew an entirely new picture of the workings of organic nature; he revolutionized our methods of thinking and our outlook on the natural order of things. The recognition that constant change is the order of the universe had been finally established and a vast step forward in the uniformity of nature had been taken" (PMM). Bern Dibner's Heralds of Science describes On the Origin of Species as "the most important single work in science." When the first edition was published on 24 November 1859, in a print run of 1,250 copies, it created an immediate sensation. Fifty-eight were distributed by Murray for review, promotion, and presentation, and Darwin reported that the balance was sold out on the first day of publication. Five further editions, each variously corrected and revised, appeared in Darwin's lifetime, as did eleven translations. The Origin was actually an 'abstract' of a larger work, tentatively titled Natural Selection, that Darwin never completed, although he salvaged much of the first part of the manuscript for The Variation of Animals and Plants under Domestication, published in 1868. The presentation copies likely number less than 30, allhaving secretarial inscriptions and were sent by the publisherat Darwin's request. "There are no known author's presentation copies of the first edition inscribed in Darwin's hand" (Norman). Provenance: Inscribed in a secretarial hand 'Dr. Buist / Bombay / from the author' (as described in the list of presentation copies of the Origin in Vol 8, Appendix III, p 556 and further note on p 559). Dr. George Buist (1805-60) was a founding member of the Literary and Philosophical Society of St. Andres, of which Darwin was an 'Honorable Member'. After taking degrees at St. Andrews and the University of Edinburgh, Buist left Scotland for a journalistic posting in India, where his scientific interests led him to serve as Secretary to the Bombay Geographical Society, the same role Darwin played for the London Geographical Society. Both men were fellows of the Royal Society. "England became quieter and more prosperous in the 1850s, and by mid-decade the professionals were taking over, instituting exams and establishing a meritocracy. The changing social composition of science-typified by the rise of the freethinking biologist Thomas Henry Huxley-promised a better reception for Darwin. Huxley, the philosopher Herbert Spencer, and other outsiders were opting for a secular nature in the rationalist Westminster Review and deriding the influence of "parsondom." Darwin had himself lost the last shreds of his belief in Christianity with the tragic death of his oldest daughter, Annie, from typhoid in 1851 . "After speaking to Huxley and Hooker at Downe in April 1856, Darwin began writing a triple-volume book, tentatively called Natural Selection, which was designed to crush the opposition with a welter of facts. Darwin now had immense scientific and social authority, and his place in the parish was assured when he was sworn in as a justice of the peace in 1857. Encouraged by Lyell, Darwin continued writing through the birth of his 10th and last child, Charles Waring Darwin (born in 1856, when Emma was 48), who was developmentally disabled. Whereas in the 1830s Darwin had thought that species remained perfectly adapted until the environment changed, he now believed that every new variation was imperfect, and that perpetual struggle was the rule. He also explained the evolution of sterile worker bees in 1857. Those could not be selected because they did not breed, so he opted for "family" selection (kin selection, as it is known today): the whole colony benefited from their retention. "Darwin had finished a quarter of a million words by June 18, 1858. That day he received a letter from Alfred Russel Wallace, an English socialist and specimen collector working in the Malay Archipelago, sketching a similar-looking theory. Darwin, fearing loss of priority, accepted Lyell's and Hooker's solution: they read joint extracts from Darwin's and Wallace's works at the Linnean Society on July 1, 1858. Darwin was away, sick, grieving for his tiny son who had died from scarlet fever, and thus he missed the first public presentation of the theory of natural selection. It was an absenteeism that would mark his later years. "Darwin hastily began an "abstract" of Natural Selection, which grew into a more-accessible book, On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life. Suffering from a terrible bout of nausea, Darwin, now 50, was secreted away at a spa on the desolate Yorkshire moors when the book was sold to the trade on November 22, 1859. He still feared the worst and sent copies to the experts with self-effacing letters ("how you will long to crucify me alive"). It was like "living in Hell," he said about those months. "The book did distress his Cambridge patrons, but they were marginal to science now. However, radical Dissenters were sympathetic, as were the rising London biologists and geologists, even if few actually adopted Darwin's cost-benefit approach to nature. The newspapers drew the one conclusion that Darwin had specifically avoided: that humans had evolved from apes, and that Darwin was denying mankind's immortality. A sensitive "Darwin, making no personal appearances, let Huxley, by now a good friend, manage that part of the debate. The pugnacious Huxley, who loved public argument as much as Darwin loathed it, had his own reasons for taking up the cause, and did so with enthusiasm. He wrote three reviews of Origin of Species, defended human evolution at the Oxfo
BENESE, Richard
LAND AS PRIVATE PROPERTY - A NEW ERA OF CAPITALISM. First edition of "the first English textbook on geometrical land-measurement and surveying" (Buisseret, p. 39), an outstanding copy in its original binding, and extremely rare thus. Benese's Maner of Measurynge All Maner of Lande marks an epoch, the widespread idea of land as private property."If there is a single date when the idea of land as private property can be said to have taken hold, it is 1538. In that year a tiny volume was published with a long title that began, This boke sheweth the maner of measurynge of all maner of lande.In it, the author, Sir Richard Benese, described for the first time in English how to calculate the area of a field or an entire estate . [T]his interest in exact measurement was also new. Until then, what mattered was how much land would yield, not its size . Accurate measurement became important in 1538 because beginning in that year a gigantic swath of England--almost half a million acres--was suddenly put on sale for cash. The greatest real-estate sale in England's history occurred after king Henry VIII dissolved a total of almost 400 monasteries, which had been acquiring land for centuries . Upon the monasteries' dissolution, all their land, including some of the best soil in England, automatically reverted to their feudal overlord, the king [who needed money to defend England against the French]. The sale of so much land for cash was a watershed . [U]p to that point the fundamental value of land remained in the number of people it supported. From then on the balance shifted increasingly to a new way of thinking . The emphasis in Benese's book on exact measurement reflected the change in outlook. Once land was exchanged for cash, its ability to support people became less important than how much rent it could produce. And to compare the value of rent produced by different estates, it was essential to know their exact size. The units could no longer vary; the method of surveying had to be reliable. The surveyor ceased to be a servant and became an agent of change from a system grounded in medieval practice to one that generated money" (Linklater, pp. 10-12). Richard Benese (d. 1546) was a canon of the Augustine priory of Merton in Surrey. "He supplicated for the degree of Bachelor of Common Law at Oxford, 6 July 1519, and signed the surrender of the Augustine Priory of Merton to Henry VIII on 16 April 1538. Before this he was a surveyor to Henry VIII and it was during this period that he wrote his treatise on surveying. This is a remarkable survival, not only because this copy was extensively used by practitioners (as evidenced by extensive arithmetical calculations on the free endpaper), but also because it is extremely unusual in general to find early 16th century English books in original state. Following the fashion prevalent in the 19th century, most such books were trimmed, often washed, and rebound. Indeed, of the four complete copies listed on RBH in the last century, three were in 19th or 20th century bindings (and one was disbound). ESTC lists a total of 10 copies - 6 in the UK and 4 in the US (Harvard (2 copies? - only one is listed on Hollis), Huntington and Madison-Wisconsin). The title page is undated; a publication date of 1537 is conjectured by STC, although some authorities give 1538. Provenance: John Grande (signature on title, crossed out); at least one other early signature on title, faded and undecipherable; early annotations and calculations on free endpaper and front cover; Sotheby, Wilkinson & Hodge, November 4, 1918, lot 64 ('Extremely rare in this genuine state"). "Modern English land surveying had its origins in the sixteenth century, partly brought about by the beginning of enclosing. In simplest form enclosing was the process of combining the strips of the open fields into larger fields and then enclosing these larger fields with fences, hedges, or other boundaries. Later, meadows, parts of the commons, and reclaimed lands were brought into the enclosed system. This system of cultivation began in the late fifteenth century, gained momentum in the sixteenth century, and continued for many years thereafter. Combining and reorganising the land of the open field system to the enclosed form caused many complaints over titles, rights, and quantities of land involved, and often led to a state of such complete confusion that the true issues were obscured before the courts. This confusion brought about the realisation that a more exact determination of the quantities of land and a definite location of the boundaries were needed. Appeals were made to the surveyor for a correction of these faults" (Richeson, pp. 29-30). Following the dissolution of the monasteries greatly increased the importance of the surveyor. "Prominent among the purchasers of church property were land-hungry owners like the duke of Northumberland, who had been enclosing common pastures, but far more common were the landlords who had done well from the rise in the market value of wool and corn, and chose to invest in monastery estates . The new owners and their surveyors realised that the monasteries' widely separated rigs and shares of common land would become more valuable once they were consolidated into fields. Their predecessors, the old abbots and priors, had understood land ownership to be part of a feudal exchange of rights for services. But those who had bought their land knew that ownership depended on money passing hands, and that the old ways had to change if they were to maximize the return on their investment . What the new class of landowners required of their surveyors above all was exactness" (Linklater, pp. 11-12). A further stimulus to the development of surveying at this time was the increasing importance of geometry in practical matters. "John Dee, in his introduction to the first English translation of Euclid in 1570 echoed a change that was already making itself felt. How many were the error
HEISENBERG, Werner
HEISENBERG'S S-MATRIX PROGRAMME. First edition, extremely rare offprints, of Heisenberg's S-matrix approach to the study of elementary particles. "Heisenberg's prewar researches in quantum field theory, undertaken in part with Pauli, had led him to the study of cosmic rays, the highest energy particles then available for research. When an extremely high-energy cosmic ray strikes the earth's atmosphere, it induces a shower of newly created particles and photons. This effect was to be explained on the basis of quantum field theory. Heisenberg's researches had previously convinced him and others of the inadequacy of field theories for this task. Infinities and divergences plagued all three of the available theories - quantum electrodynamics, Fermi's theory of beta decay (relating to what is now the weak force), and Yukawa's meson theory (relating to what is now the strong, or nuclear, force). The small size of elementary particles and the close approach of the particles to each other in a cosmic ray collision - which triggered the particle shower - indicated to Heisenberg during the 1930s that the difficulties in quantum field theory could be resolved only if a universal minimum length, a new fundamental constant, were introduced into the theory. according to Heisenberg, quantum mechanics itself broke down when applied to events occurring within regions smaller than the size of an elementary particle . Pauli had already suggested that Heisenberg, as he did when formulating the 1925 breakthrough in quantum mechanics, should focus only on observable quantities and attempt to exclude all unobservable variables from the theory. Heisenberg now attempted to do so, at the height of the World War. His effort led to what became after the war his widely studied new theory of elementary particles, the so-called S-matrix theory. In his new approach, Heisenberg used this hypothetical fundamental length to define the allowed changes in the momentum and energy of two colliding high-speed elementary particles. This limitation would help identify the properties of the collision that were observable in present theories. Those at smaller distances were unobservable. For two colliding particles, this yielded four sets of observable quantities with which to work: two of these were the properties of the two particles as seen in the laboratory long before they collide with each other; and two were their properties long after the collision. During the collision they approach within a distance of less than the fundamental length and are thus unobservable. These four sets of observable properties could be arranged in a table, or in this type of work, a matrix, which Heisenberg called the scattering or S-matrix. Although Heisenberg could not actually specify the four elements of the S-matrix, he demonstrated that it must contain in principle all of the information about the collision. In his second paper, completed in October 1942, Heisenberg further showed that the S-matrix for several simple examples of scattering of particles yielded the observed probabilities for scattering. It also gave the possibility for his favorite phenomenon - the appearance of cosmic-ray explosion showers" (Beyond Uncertainty, pp. 347-9). "In a series of papers during the period 1943-1946 Heisenberg proposed as an alternative to quantum field theory a program whose central entity was a matrix he denoted by S and termed the 'characteristic matrix' of the scattering problem . Heisenberg wanted to avoid any reference to a Hamiltonian or to an equation of motion and base his theory only on observable quantities. This emphasis on observables was a return to an idea which had proven useful in his earlier successful formulation of matrix mechanics. Heisenberg's stated purpose in his seminal paper [I.], 'The 'Observable Quantities' in the Theory of Elementary Particles', was to abstract as many general, model-independent features of S as possible. In the abstract and introduction to that paper we read (p. 513): 'The known divergence problems in the theory of elementary particles indicates that the future theory will contain in its foundation a universal constant of the dimension of a length, which in the existing form of the theory cannot be built in in any obvious manner without a contradiction. In consideration of such a later modification of the theory, the present work attempts to extract from the foundation of quantum field theory those concepts which are not likely to be discarded from that future, improved theory and which, therefore, will be contained in such a future theory.' 'In recent years, the difficulty, which still stands in the way of a theory of elementary particles, has been pointed up in many ways. This difficulty manifests itself surprisingly in the appearancr of divergences (infinite self energy of the electron, infinite polarization of the vacuum, and the like), which hinders the development of a mathematically consistent theory and must probably be perceived as an expression of the fact that, in one manner of speaking, a new universal constant of the dimension of a length plays a decisive role, which has not been considered in the existing theory.' "This paper is remarkable for the number of new ideas it introduces, many of which would be put on a firm mathematical basis only years later. Using a momentum-space representation, he defined the S-matrix as the coefficient of the outgoing waves in the scattering state . This paper contains (in an often symbolic and certainly non-rigorous fashion) the essential elements of formal time-dependent scattering theory, which would later be further developed, for example, by Lippmann and Schwinger (1950), by Gell-Mann and Goldberger (1953) and by Brenig and Haag (1959) . Heisenberg certainly brought the concept of the S-matrix to the attention of theoretical physicists. It has remained one of the central tools of modern physics . "The Hermitian phase matrix Î [related to the S-matrix by
FERMI, Enrico & SZILARD, Leo
THE BIRTH OF PRACTICAL NUCLEAR ENERGY. First edition, incredibly rare, of this "historic patent [2,708,656], covering the first nuclear reactor" (New York Times, May 19, 1955). "No published reference article behind the present Patent exists. Some partial results may be found in several papers of [Fermi], but here very many technical data and some information of historic interest (mainly on the experiments performed in order to obtain the data reported) are given" (Esposito & Pisanti, pp. 218-9). This patent "is the first one on this topic issued by the U.S. Patent Office, and served as a reference for the subsequent Patents on the same subject. In this long Patent, the theory, experimental data and principles of construction and operation of 'any' type of nuclear reactor known at that time are discussed in an extremely detailed way" (ibid., p. 217). The second patent is a variant of the first, with a different arrangement of the uranium within the reactor. Fermi emigrated from Italy to the US in January 1939, and immediately accepted a position at Columbia University, New York. "Within weeks of [Fermi's] arrival, news that uranium could fission astounded the physics community . The implications were both exciting and ominous, and they were recognized widely. When uranium fissioned, some mass was converted to energy, according to Albert Einstein's famous formula E = mc2. Uranium also emitted a few neutrons in addition to the larger fragments. If these neutrons could be slowed to maximize their efficiency, they could participate in a controlled chain reaction to produce energy; that is, a nuclear reactor could be built. The same neutrons traveling at their initial high speed could also participate in an uncontrolled chain reaction, liberating an enormous amount of energy through many generations of fission events, all within a fraction of a second; that is, an atomic bomb could be built . Fermi had built a series of 'piles,' as he called them, at Columbia. Now he moved to the University of Chicago, where he continued to construct piles in a space under the stands of the football field. The final structure, a flattened sphere about 7.5 metres (25 feet) in diameter, contained 380 tons of graphite blocks as the moderator and 6 tons of uranium metal and 40 tons of uranium oxide as the fuel, distributed in a careful pattern. The pile went 'critical' on Dec. 2, 1942, proving that a nuclear reaction could be initiated, controlled, and stopped" (Britannica). "On December 2, 1942, man first initiated a self-sustaining nuclear chain reaction, and controlled it. Beneath the West Stands of Stagg Field, Chicago, late in the afternoon of that day, a small group of scientists witnessed the advent of a new era in science. History was made in what had been a squash-rackets court. Precisely at 3:25 p.m., Chicago time, scientist George Weil withdrew the cadmium-plated control rod and by his action man unleashed and controlled the energy of the atom. As those who witnessed the experiment became aware of what had happened, smiles spread over their faces and a quiet ripple of applause could be heard. It was a tribute to Enrico Fermi, Nobel Prize winner, to whom, more than to any other person, the success of the experiment was due" (The First Reactor, US Department of Energy, December 1982). Fermi "was the only physicist in the twentieth century who excelled in both theory and experiment, and he was one of the most versatile" (DSB). OCLC lists just one copy of the first patent worldwide (Argonne National Laboratory), and none of the second. There is a copy of both patents in the Enrico Fermi Collection at the University of Chicago (/e/scrc/findingaids/?eadid=ICU.SPCL.FERMI). We are not aware of any other copy of either patent having appeared in commerce. Fermi has described the construction of the Chicago Pile, and the events leading up to it, in his autobiography Fermi's Own Story (in The First Reactor, op. cit.): "The year was 1939. A world war was about to start. The new possibilities appeared likely to be important, not only for peace, but also for war.A group of physicists in the United States-including Leo Szilard, Walter Zinn, now director of Argonne National Laboratory, Herbert Anderson, and myself-agreed privately to delay further publications of findings in this field. "We were afraid these findings might help the Nazis. Our action, of course, represented a break with scientific tradition and was not taken lightly. Subsequently, when the government became interested in the atom bomb project, secrecy became compulsory.Here it may be well to define what is meant by the 'chain reaction,' which was to constitute our next objective in the search for a method of utilizing atomic energy. "An atomic chain reaction may be compared to the burning of a rubbish pile from spontaneous combustion. In such a fire, minute parts of the pile start to burn, and in turn ignite other tiny fragments. When sufficient numbers of these fractional parts are heated to the kindling points, the entire heap bursts into flames.A similar process takes place in an atomic pile, such as was constructed under the West Stands of Stagg Field at the University of Chicago in 1942. "The pile itself was constructed of uranium, a material that is embedded in a matrix of graphite. With sufficient uranium in the pile, the few neutrons emitted in a single fission that may accidentally occur strike neighboring atoms, which in turn undergo fission and produce more neutrons.These bombard other atoms and so on at an increasing rate until the atomic 'fire' is going full blast.The atomic pile is controlled and prevented from burning itself to complete destruction by cadmium rods, which absorb neutrons and stop the bombardment process. The same effect might be achieved by running a pipe of cold water through a rubbish heap; by keeping the temperature low, the pipe would prevent the spontaneous burning. "The first atomic chain reaction experiment was desi
DIRAC, Paul Adrien Maurice
THE BIRTH OF QUANTUM ELECTRODYNAMICS. First edition, extremely rare offprint, of Dirac's quantum theory of the electromagnetic field, which for the first time reconciled the wave and particle nature of light. "This paper marks the birth of quantum electrodynamics. In his 'Introduction and Summary,' Dirac noted that the new quantum theory, based on non-commuting dynamical variables, was by then sufficiently developed to form a 'fairly complete theory of any 'dynamical system' composed of a number of particles with instantaneous forces acting between them, provided it is describable by a Hamiltonian function.' But hardly anything had been done 'up to the present on quantum electrodynamics.' 'The questions of the correct treatment of a system in which the forces are propagated with the velocity of light instead of instantaneously, of the production of an electromagnetic field by a moving electron, and of the reaction of this field on the electron, have not yet been touched. In addition there is a serious difficulty in making the theory satisfy all the requirements or the restricted principle of relativity' . Gregor Wentzel, who contributed significantly to the development of quantum electrodynamics during the 1920s, commented in 1959: 'Today the novelty and boldness of Dirac's approach to the radiation problem may be hard to appreciate . there had been no possibility within the correspondence principle framework to understand the process of spontaneous emission or the disappearance of a photon. Dirac's explanation . came as a revelation' . In his paper, Dirac dealt with the problem of an atom interacting with the radiation field in two distinct ways that can be characterized as the 'corpuscular' and the 'wave' approaches. In the corpuscular approach, the light quanta are described as an assembly of 'non-interactive particles moving with the speed of light and satisfying the Einstein-Bose statistics' . In the last brief section of his paper, Dirac turned to the interaction of an atom with the electromagnetic field as described from the wave point of view . In a lecture on the origin of quantum field theory in 1982, Dirac characterized the two approaches as follows: 'Instead of working with a picture of the photons as particles one can use instead the components of the electromagnetic field. One thus gets a complete harmonizing of the wave and corpuscular theories of light. One can treat light as composed of electromagnetic waves, each wave to be treated like an oscillator; alternatively, one can treat light as composed of photons, the photons being bosons and each photon state corresponding to one of the oscillators of the electromagnetic field. One then has the reconciliation of the wave and corpuscular theories of light. They are just two mathematical descriptions of the same physical reality" (Schweber, pp. 23-31). "Dirac's approach was instantly welcomed as the first consistent quantum theory of radiation and accepted as the paradigm in a whole series of subsequent studies" (Kojevnikov, p. 232). "Salam and Wigner, in their preface to the Festschrift that honored Dirac on his seventieth birthday and commemorated his contributions to quantum mechanics, succinctly assessed the man. 'Dirac is one of the chief creators of quantum mechanics . Posterity will rate Dirac as one of the greatest physicists of all time . He is a legend in his own lifetime and rightly so'" (ibid., pp. 11-12). Not on OCLC, no copies in auction records. Provenance: Bertha Swirles (1903-99) (signature on front wrapper, marginal pencil annotations including an equation in the lower margin of p. 261). As an undergraduate at Cambridge Swirles attended lectures by J. J. Thomson and Rutherford. She remained at Cambridge in 1925 to undertake research in mathematical astronomy under the supervision of Ralph Fowler; another of Fowler's research students, a couple of years ahead of Swirles, was Paul Dirac. After periods at Bristol, Imperial College, London, and Manchester, Swirles took up a lectureship in mathematics at Girton College, Cambridge in 1938, where she remained for the rest of her career. Before Dirac's work, the understanding of the emission and absorption of radiation was founded on that set out by Einstein in 1917. Einstein admitted the existence of three kinds of processes involving the interaction of radiation with matter: spontaneous emission, absorption, and stimulated emission. Einstein denoted the probability per unit time of these processes A, ÏB, and ÏB', where Ï is the intensity of the incident radiation in the cases of absorption and stimulated emission. Einstein showed that, in order to satisfy Planck's radiation law, one must have B = B', so that the processes were determined by two coefficients, A and B. The new process of stimulated emission, in which an atom is 'persuaded' to undergo a quantum jump between two quantum states when radiation of the correct frequency is incident upon it, is the process involved in the operation of the laser. Dirac's first study of radiation theory was the subject of the last section of the important paper 'On the Theory of Quantum Mechanics'. The first part of this paper is best known for establishing the connection between Bose-Einstein statistics and symmetric wave functions, on the one hand, and what became known as Fermi-Dirac statistics and anti-symmetric wave functions, on the other. In the second part of this paper, "Dirac considered a system of atoms subjected to an external perturbation that could vary arbitrarily with the time. Of course, the particular perturbation he had in mind was an incident electromagnetic field, but, characteristically, he stated the problem in the most general way possible . [Dirac obtained results] 'in agreement with the ordinary Einstein theory,' that is, with the quantum mechanical derivation of the B coefficients that occurred in Einstein's theory of 1917. Since he made use of a classical description of the electromagnetic fiel
KEPLER, Johannes
KEPLER ANTICIPATES THE INTEGRAL CALCULUS. First edition, the fine Huet-Honeyman-Tomash copy, of Kepler's contribution to the mathematics of integration techniques, an important precursor to the calculus. This is one of very few copies with the errata leaf. This copy is also printed on superior paper stock, quite white and crisp, whereas most copies are on a poor quality paper and often browned. The Nova Stereometria is "generally regarded as one of the significant works in the prehistory of the calculus" (DSB). Kepler "made wide application of an old but neglected idea, that of infinitely great and infinitely small quantities. Greek mathematicians usually shunned this notion, but with it modern mathematicians completely revolutionized the science" (Cajori). Kepler "employs primitive integration techniques in attempting to find volumes of bodies with curved surfaces, his researches in this area having been spurred by comparison of the current methods used to find the volume of wine casks with the work of Archimedes on volume measurement. Kepler views solids as composed of infinitesimal pieces and proceeds to determine volumes of various solids of revolution, some not considered by Archimedes" (Parkinson, Breakthroughs). "Desiring to outfit his new household with the produce of a particularly good wine harvest, Kepler installed some casks in his house. When he discovered that the wine merchant measured only the diagonal length of the barrels, ignoring their shape, Kepler set about computing their actual volumes. Abandoning the classical Archimedean procedures, he adopted a less rigorous but productive scheme in which he considered that the figures were composed of an infinite number of thin circular laminae or other cross sections. Captivated by the task, he extended it to other shapes, including the torus" (DSB). "Kepler opens his work on curvilinear mensuration with the simple problem of determining the area of a circle. In this he abandoned the classical Archimedean procedures. He did not substitute for these the limiting consideration proposed by Stevin and Valerio, but had recourse instead to the less rigorous but more suggestive approach of Nicholas of Cusa. Like Stifel and Viète, he regarded the circle as a regular polygon with an infinite number of sides, and its area he therefore looked upon as made up of infinitesimal triangles of which the sides of the polygon were the bases and the center of the circle the vertex. The totality of these was then given by half the product of the perimeter and the apothem (or radius). Kepler did not limit himself to the simple proposition above, but with skill and imagination applied this same method to a wide variety of problems" (Boyer, The History of the Calculus and its Conceptual Development). Boyer also examines the influence of this work on Fermat, Cavalieri, Guldin, and finally Leibniz and Newton: "It is Kepler's mode of expression which appeared in the work of Fermat. Although the Scholastic views on variation played a significant role in the anticipations of the calculus, the static approach of Kepler predominated. Increments and decrements, rather than rates of change, were the fundamental elements in the work leading to that of Leibniz, and played a larger part in the calculus of Newton than is generally recognized". Provenance: Pierre Daniel Huet (1630-1721), bishop of Avranches, with printed shelfmark label 'XLVII.C' on front pastedown; living gift of his library to the Jesuit order of Paris in 1692, with manuscript inscription of gift on title and the Jesuits printed label 'Ne extra hanc Bibliothecam efferatur. Ex obedienta' on foot of title, with manuscript shelfmark on front flyleaf; Honeyman sale, Sotheby's 12 May 1980, lot 1791 (with Honeyman ex libris on front pastedown); Bernard Quaritch collation note dated May 1981 on rear pastedown. Huet, 'un des hommes les plus savants de France' (NBG), was an accomplished mathematician and celebrated scholar and author. He studied mathematics and wrote a critique of Cartesian philosophy. 'His great library and manuscripts, after being bequeathed to the Jesuits, were bought by the King for the Royal Library' (Encyclopaedia Britannica 11th edn.); Erwin Tomash (bookplate on front pastedown); his sale, Sotheby's 18 September 2018, lot 311. Kepler (1571-1630) became interested in stereometry as a result of a serendipitous event that took place in November 1613 in Linz, where Kepler was then living. Kepler purchased some barrels to lay in a supply of wine for his family and had them delivered to his house. When the wine dealer came to the house to measure the volume of wine the barrels contained, he used the standard gauger's technique which in effect meant approximating the barrel by a cylinder of the same height as the barrel but with cross-sectional area equal to the average of the area of the ends of the barrel and that of its middle bulge. Thus, the approximate formula for the volume of the barrel was V = ½ x height x (end-diameter2 + bulge-diameter2) V0, where V0 was the known volume of a cylinder of unit height and diameter. To simplify the calculation a gauging rod was used. This was a rod marked with a quadratic scale (i.e., 1 at the first mark, 4 at the second, 9 at the third, etc.); by laying it across the end of the barrel, then inserting it through the bung hole in the middle of the bulge, and reading off the numbers on the scale, the gauger could then calculate an approximation to the volume of wine in the barrel by using the above formula. Kepler was more than sceptical about the accuracy of this method of volume determination, especially how it could work for barrels of any shape and size, and he immediately decided to try to find a better mathematical method, and one that would also deal with the case of partly empty barrels, for which the gauger had no solution. By December 17, 1613 Kepler believed that he had reached his goal. He had composed a short six-page manuscript with
BUNYAKOVSKY (or BUNIAKOVSKY), Viktor Yakovlevich
THE FIRST RUSSIAN WORK ON PROBABILITY. First edition, very rare, of the first Russian work on probability. "The prime impetus for the initial development in the 1820s of probability theory in the Russian Empire (putting aside the eighteenth-century contributions of Leonhard Euler and Daniel Bernoulli) was the need for a proper basis for actuarial and demographic work, and for the statistical treatment of observations generally. Pierre Simon Laplace's classic work on probability (Théorie analytique des probabilités, 1812), which initiated the Paris school of probabilistic investigations, not only laid foundations for the subject, but also contained applications to real-world situations. Its ideology was brought to the Russian Empire, partly in response to the statistical needs mentioned above, by Viktor Yakovlevich Bunyakovsky (1804-89) . Bunyakovsky's prime achievement was the first treatise on probability in the Russian language [the offered work]. Its aim was the simplification and classification of existing theory; its lasting achievement was the creation of a Russian probabilistic terminology" (Seneta, Russian probability and statistics before Kolmogorov, Section 10.6 in: Companion Encyclopedia of the History and philosophy of the Mathematical Sciences, pp. 1325-26). Bunyakovsky sought to adapt Laplace's Théorie analytique des probabilités (1812) for Russian mathematicians and statisticians. He applied Laplace's theory to applied mathematics and statistics, and in particular to the statistical control of quality. His work also discussed the analysis of election results and legal decisions, demographics, population increase, compiling mortality tables, and much else. Bunyakovsky studied in Paris where he attended lectures by Laplace. In 1825 he received his doctorate under Cauchy's supervision. Upon his return to St. Petersburg he devoted the rest of his life to research and teaching. He was elected vice-president of the St. Petersburg Academy of Sciences and held the post for 25 years. Among his numerous outstanding pupils was Pafnuty Lvovich Chebychev (1821-1894), one of Russia's greatest mathematicians. The present copy of Bunyakovsky's book is bound up with Chebyshev's fundamental work on approximation theory and orthogonal polynomials, Sur l'interpolation dans le cas d'un grand nombre de données fournies par les observations (St Petersburg: Imperial Academy of Sciences, 1859), in which he introduced the famous 'Chebyshev polynomials'. No other copy of either work located in auction records. "Buniakovsky's book [the offered work] is his main contribution to the theory of probability. Here (p. ii) he stated that, while following Laplace, he had sought to simplify its exposition. Buniakovsky also expressed a justified hope that he succeeded in making easier the study of the Théorie analytique, a classic which 'is intelligible [only] to very few readers' . "In the Introduction (p. 3), Buniakovsky indicated that some events were more likely than others and called probability the measure of likelihood . Following Laplace (p. 176), he maintained that 'the analysis of probabilities considers and quantitatively estimates even such phenomena . which, due to our ignorance, are not subject to any suppositions' . "If factor x in the expression for the expectation of a continuous random variable X is replaced by log x, the new quantity will be the 'moral expectation' of X. Daniel Bernoulli made use of moral expectation, if not the term itself, in order to study the Petersburg paradox, an imaginary game of chance whose investigation by means of mathematical expectation patently contradicted common sense. He also noted that an equal distribution of a given cargo on two ships increases the moral expectation of the freight owner's capital as compared with the transportation of the cargo on a single ship. Buniakovsky (pp. 103-122) described Bernoulli's reasoning and proved the validity of his remark . "Following Buffon and Laplace, Bunia
CASSINI, Giovanni Domenico
THE SUN'S MOTION, THE 1664-5 COMETS, JUPITER'S MOONS AND THE DISCOVERY OF ITS GREAT RED SPOT, AND THE FIRST DETAILED ILLUSTRATIONS OF MARS. An extraordinary sammelband containing the first editions of seven exceptionally rare works documenting Cassini's very accurate observations of the motion of the Sun relative to the Earth, which enabled him to confirm Kepler's second law, of the comets of 1664-5, of Jupiter's spots, including his discovery of the Great Red Spot, and the first detailed illustrations of Mars, which enabled him to determine the rotation periods of these two planets - all made possible by his new collaboration with the lens makers Eustachio Divini and, most importantly, Giuseppe Campani. The first work records numerous observations made by Cassini using a new 'meridian' he had constructed (essentially a large sundial). These include measurements of the obliquity of the ecliptic, and the exact position of the solstices and the equinoxes, and, most importantly, of the speed of the sun's apparent motion and the variation of its diameter. These latter measurements enabled Cassini to confirm the validity of Kepler's second law of motion, thus disproving one of the main statements of the geocentric model, namely that of uniform motion along circular orbits. The next two works document Cassini's observations of the comets of 1664-5, which were observed by many astronomers, including Auzout, Borelli, Fabri, Hooke, Hevelius, Petit, and Newton as a student. The Theoriae motus "is very important because it is the first that reports a precise sequence of observations and the entire path of a comet, also supported by mathematical calculations" (Bernardi, p. 47). Cassini observed the comets "in the presence of Queen Christina [to whom the first work is dedicated] and formulated on this occasion a new theory (in agreement with the Tychonian system) in which the orbit of the comet is a great circle whose center is situated in the direction of Sirius and whose perigee is beyond the orbit of Saturn" (DSB). The large engraved plate depicts the course of the comet in the southern celestial hemisphere from December 13, 1664 through the middle of January 1665; it also shows the appearance and direction of the comet's tail. Cassini's detailed observations were made with a powerful new telescope made by Giuseppe Campani, which he describes in the preface to the first work. "Through his friendship with the famous Roman lens-makers Giuseppe Campani and Eustachio Divini, Cassini, beginning in 1664, was able to obtain from them powerful celestial telescopes of great focal length. He used these instruments-very delicate and extremely accurate for the time- with great skill, and made within several years a remarkable series of observations." (ibid). The third work, addressed to the archaeologist Falconieri, presents further observations on the comet, and Cassini's remarks about the observations made by Auzout and Hevelius. "In July 1664 [Cassini] detected the shadow of certain satellites on Jupiter's surface and was thus able to study the revolution of the satellites" (ibid.). These observations are reported in the fourth work in our sammelband. "A controversy about the results of these observations started quite soon. First, someone from Rome observed one dark shadow and another less dark one. Cassini clarified that the latter was not the shadow of a satellite but rather a physical spot on the planet. To prove his statement . he observed that it did not follow the movement of any orbiting body, and that it appeared every 9 hours 56 min, which the astronomer attributed to the rotation period of the planet . In support of the statement of the Italian scientist, Abbot Ottavio Falconieri published the letters between Cassini and himself as proof of his past observations, and Cassini made public his predictions on the return of the spot on Jupiter, to dispel any doubts" (Bernardi, p. 53). This was the discovery of the Great Red Spot (although
DALTON, John
THE ATOMIC THEORY OF MATTER (PMM 261). First edition, untouched in uniform original publisher's bindings with original printed spine labels, of Dalton's classic work on the atomic theory of matter. "Dalton reconstructed Newton's speculations on the structure of matter, and, applying them in a new form to chemistry, gave Lavoisier's reformation of that science a deeper significance" (PMM). "Dalton's chemical atomic theory was the first to give significance to the relative weights of the ultimate particles of all known compounds, and to provide a quantitative explanation of the phenomena of chemical reaction. Dalton believed that all matter was composed of indestructible and indivisible atoms of various weights, each weight corresponding to one of the chemical elements, and that these atoms remained unchanged during chemical processes. Dalton's work with relative atomic weights prompted him to construct the first periodic table of the elements (in Vol. I, pt. 1), to formulate laws concerning their combination and to provide schematic representations of various possible combinations of atoms. His equation of the concepts "atom" and "chemical element" was of fundamental importance, as it provided the chemist with a new and enormously fruitful model of reality" (Norman). "He developed a system of chemical symbols and a table [plate 4 in part 1] showing the relative weights of the atoms of a list of elements. From his principles he deduced the law of definite proportions and the law of multiple proportions" (Dibner). This, and pp. 546-548 along with the 4 plates in part 2, in effect describe the first periodic table, which Mendeleev was to refine later. "In 1808 John Dalton published A New System of Chemical Philosophy, which described principles such as the uniqueness of atoms of the same element, relative atomic masses, and the rules of chemical combination, which taken together comprise the tablets of modern chemistry. The adoption of molecular formulas based on the laws of definite and multiple proportions, and the assignment of relative atomic masses, placed the science on a new quantitative footing" (Grossman, p. 339). This set is complete with the two parts of Vol. I and Vol. II, Part I (no further parts were published). Only one complete copy in uniform publisher's bindings has appeared since Norman, but that copy was made up with varying provenances, one part being ex-library. The Norman copy itself was in non-uniform bindings without the printed paper spine labels. Dalton (1766-1844) was born of a Quaker family at Eaglesfield, a small village in the English Lake District. As a young boy, he worked in the fields with his older brother, and helped his father in the shop where they wove cloth. In 1776, when only ten years old, he entered the service of Elihu Robinson, a wealthy Quaker, who taught him mathematics. In 1781, after a brief period of teaching in the village school, he joined his brother who was a master at a school in Kendal. In 1793 he moved to Manchester and, in the same year, published Meteorological Observations in which he suggested that the processes of evaporation and condensation were not chemical changes of state but rather changes in the physical form of water. These ideas laid the foundations for his theory that all matter is composed of discrete 'atoms'. At first after he moved to Manchester he taught mathematics and natural philosophy at New College, and began observing the behavior of gases, but after six years he resigned. Thereafter he devoted his life to research, which he financed by giving private tuition. By 1800, Dalton had become the secretary of the Manchester Literary and Philosophical Society (LPS), and in 1805 he presented a series of papers to the society outlining key points about the behaviour of gases in his series of essays, "Experimental Essays on the Constitution of Mixed Gases". He proposed that particles of an elastic fluid or gas were in fact elastic only with particles of their
DESARGUES, Girard
DESARGUES ON PERSPECTIVE - ONLY TWO OTHER COPIES KNOWN. First and only edition, incredibly rare, of the last (surviving) contribution published by the brilliant French mathematician Girard Desargues in the notorious 'perspective wars' - Desargues was "the greatest perspectivist and projective geometer of his generation" (Kemp, The Science of Art, p. 120). Desargues published his works in very small editions, mostly for his friends and scientific colleagues. Today more than half of them are lost, and the survivors are of the greatest rarity, most known in just one or two copies. Desargues' bio-bibliographer Poudra believed the Six erreurs to be lost, but two other copies are known today, both in the Bibliothèque nationale de France. It is likely that our copy of Six erreurs is the only work published by Desargues now in private hands. We know of no copy of any original work of Desargues having appeared on the market for at least a century. In 1636 Desargues (1591-1661), published Exemple de l'une des manières universelles . . . touchant la pratique de la perspective, describing a 'universal technique' which, he claimed, subsumed all previous methods of perspective drawing. Although this work appears not to have excited a great deal of interest among practitioners, "Descartes and Fermat, to whom Mersenne had communicated it, were able to discern Desargues's ability" (DSB). "Through his own efforts as a polemicist and with the conspicuous assistance of Abraham Bosse in the [Académie Royale de Peinture et de Sculpture], the Manière became the centre of a noisily prominent controversy . The immediate cause was the publication of Perspective pratique . by a 'Jesuit of Paris' (actually Jean Dubreuil). This was a substantial, effective, and not overly technical introduction for artists, which imprudently contained a bowdlerised version of Desargues' Manière. The mathematician's response was immediate. He issued two hand bills [both now lost] accusing the anonymous author of 'incredible error' and 'enormous mistakes and falsehoods.' Dubreuil's answer, in a pamphlet entitled Diverses méthodes universelles ., was to accuse Desargues of having plagiarized the ideas of Vaulezard and Aleaume (which does not appear to have been the case). The Jesuit's publishers also issued a collected edition of anti-Desargues pamphlets under the ironic title Avis charitables sur les diverses oeuvres et feuilles volantes du Sieur Girard Desargues. Desargues replied with pamphlets devoted to Six errors in Pages 87, 118, 124, 128, 132, and 134 in the Book Entitled the Perspective Pratique . [the offered work] and a Response to the Sources and Means of Opposition . [the latter now lost]. Such terms as 'imbecility' and 'mediocrity' were used with undisguised venom by both parties" (Kemp, pp. 120 & 122). The dispute continued until 1679, drawing in other mathematicians and practitioners, notably Desargues' supporter Bosse and his opponents Jean Beaugrand and Jacques Curabelle. It cannot be said that Desargues prevailed, at least initially. Dubreuil's 'practical perspective' was popular until the 18th century; in England his book became known as the 'Jesuit perspective'. Desargues was far ahead of his time and it was not until the 19th century that the importance of his work was fully understood. Our copy of the Six erreurs is bound after the first edition of the first volume of Dubreuil's La perspective practique, which includes the Diverses méthodes universelles and Advis charitables. This is accompanied by the third edition of the second and third volumes (despite the 'seconde édition' on their titles - another edition appeared in 1663). Provenance: François du Verdus (1621-75) (signature on title of Dubreuil, 'Du Verdus'). Du Verdus was a student of Gilles Personne de Roberval (1602-75). Based upon Roberval's lectures, in 1643 Du Verdus wrote Observations sur la composition des mouvemens, et sur le moyen de trouver les touchantes des lignes courbes (first pub
ROSÉN VON ROSENSTEIN, Nils
A seminal treatise on paediatrics. First edition in book form, rare, of this seminal treatise on paediatrics. "Sir Frederic Still considered this work 'the most progressive which had yet been written;' it gave an impetus to research which influenced the future course of paediatrics. Rosen was particularly interested in infant feeding. The Underrattelser were originally published in the calendars of the Academy and were later collected and issued in book form in 1764" (Garrison-Morton). "In 1764 a very important work on the diseases of children and their treatment was published in Stockholm by a physician who had already become famous" (Still). The book contained chapters on such topics as smallpox and smallpox inoculation, teething, and measles. Also included were suggestions on the frequency of breastfeeding and information on how breastfeeding affects an infant's health. He was ahead of his time when he recommended feeding young children with diluted cow's milk by means of a bottle for sucking. He also advised that children's foods be covered to avoid contact with insects, along with other hygienic precautions. He accurately described and prescribed care for scarlet fever, whooping cough, diarrhoea, and other illnesses. "Nils Rosén lived and worked in a time when Sweden was a poor country with a low average life span and a child mortality rate exceeding fifty per cent . In 1753, when the Gregorian calendar was introduced and Sweden got a new chronology, Nils Rosén started to publish articles in small almanacs published by the Royal Academy of Sciences. The articles dealt with children Ìs diseases, breast-feeding, nursing and preventive medical treatment, e.g., what then constituted fresh and new results of his empirical research work. Later, the articles were collected, re-edited and published in a book, Underrättelser om Barn-Sjukdomar och deras Bote-Medel (1764). It was the first veritable textbook of paediatrics. In 1771 it appeared in a new, improved and enlarged edition. The book was soon translated into many other European languages and became the Swedish textbook - all categories - that has been the most spread throughout the world. It was published in twenty-six editions and in ten different languages within the eighteen and nineteenth centuries. One of Linné's 'apostles', Anders Sparrman, translated it into English during a round-the-world sailing tour with the legendary captain James Cook on board The Resolution (1772-75). This book, The Diseases of Children and their Remedies, was printed in London in 1776" (Sjögren). RBH lists three copies. OCLC lists, in the US: Yale, New York Academy of Medicine, NLM, Minnesota, Indiana, Austin, Harvard. "Nils Rosen was born in Westgothland in 1706. In his youth he studied theology at Lund, but later deserted this subject for medicine. He was a pupil of Stobaeus at Upsala, and later of Friedrich Hoffmann at Halle. After a short period of study in Paris he returned to Sweden and took his M.D. at Harderwijk in I73I. For a time he taught anatomy and practical medicine at Upsala, and published a Compendium Anatomicum (Stockholm, 1738). He was early marked out for distinction, for in 1735, at the age of twenty-nine years, he became physician to the King of Sweden. The Swedish Academy of Sciences was founded in 1739 and Rosen became one of its original members. In 1740 he was appointed Professor of Natural History at Upsala, and Carl von Linné was Professor of Medicine. To the good fortune of posterity these two agreed to exchange appointments, so that the great naturalist and botanist occupied his proper position whilst Rosen became Professor of Medicine. With two such distinguished occupants of chairs, the University of Upsala became renowned as a seat of learning. Honours were poured upon Rosen. He was appointed 'Archiater' - Physician-in-Chief - at Upsala, and in 1762 was ennobled under the title of Rosen von Rosenstein. Upon his death in 1773 the Swedish Academy of Sciences had
GUNTER, Edmund
"THE MOST IMPORTANT WORK ON THE SCIENCE OF NAVIGATION TO BE PUBLISHED IN THE SEVENTEENTH CENTURY". First edition, extremely rare complete as here, of Gunter's book on the sector and other mathematical instruments, "one of the most influential scientific works on navigation" (Waters, p. 359), the work which introduced logarithms into the science of navigation and led to the development of the slide-rule. "This book must be reckoned, by every standard, to be the most important work on the science of navigation to be published in the seventeenth century. It opened the whole subject of mathematical application to navigation and nautical astronomy to every mariner who was sufficiently interested in devoting time to the perfecting of his art. The sector described by Gunter consisted basically of two hinged arms (like a carpenter's ruler) on which were engraved several scales . Gunter's book was given in two main parts. In the first he concentrated his attention on the sector; and in the second on the cross-staff. In the first part he gave solutions, not only to nautical astronomical problems but also to plane and Mercator sailing. He also provided a novel traverse table, this being the first of its kind and of the type that is now commonly used by navigators. In the second part of his book Gunter described a novel form of cross-staff, the most useful feature of which was the several scales engraved on the staff. These were logarithmic scales by means of which, using a pair of dividers, problems of multiplication and division could be solved easily and quickly" (Cotter, pp. 363-4). Gunter's sector "allowed calculations involving square and cubic proportions, and carried various trigonometrical scales. Moreover, it had a scale for use with Mercator's new projection of the sphere, making this projection more manageable for navigators who were only partially mathematically literate. The sector was sold as a navigational instrument throughout the seventeenth century and survived in cases of drawing instruments for nearly three hundred years. The most striking feature of the cross-staff, distancing it from other forms of this instrument, was the inclusion of logarithmic scales. This was the first version of a logarithmic rule, and it was from Gunter's work that logarithmic slide rules were developed, instruments that remained in use until the late twentieth century" (ODNB). This book is justly renowned as a contribution to navigation, but it seems not to be widely known that it also contains (p. 60 of the second part) the first printed observation of the temporal variation of magnetic declination, the discovery of which is normally ascribed to Henry Gellibrand who published it 12 years later. "In 1622 Gunter's investigations at Limehouse, Deptford, of the magnetic variation of the compass needle produced results differing from William Borough's, obtained more than forty years earlier. He assumed an error in Borough's measurements, but this was in fact the first observation of temporal change in magnetic variation, a contribution acknowledged by his successor, Henry Gellibrand" (ODNB). All of Gunter's instruments are shown in use on the engraved title page. This particular engraving was used for many of the reprints of Gunter's work, the central title being changed and various inscriptions being added to the shield at the base (blank in this first edition). The present copy of Gunter's De sectore is here bound with the second edition of his Canon triangulorum (first, 1620), the first published table of logarithmic sines and tangents. This edition includes the first table of base-ten logarithms, first published by Henry Briggs in 1617 (this is not present in the first edition of the Canon). Our copy of De sectoreis complete with the full text, the engraved and letterpress titles (sometimes omitted), and the volvelle present but not assembled. Only a handful of copies of the first edition of De sectore have appeared at auction since 1957, no
"AN IMPORTANT MILESTONE IN GEOLOGY" (ODNB) . First edition, and a fine copy, complete with the very rare hand-coloured engraved folding three-sheet geological map. This work is considered to be Murchison's masterpiece, placing him among the founders of modern geology. "An important milestone in geology, for it established the oldest fossil-bearing classification then known" (ODNB). "The publication of this splendid monograph forms a notable epoch in the history of modern geology, and well entitles its author to be enrolled among the founders of the science. For the first time, the succession of fossiliferous formations below the Old Red Sandstone was shown in detail. Their fossils were enumerated, described and figured. It was now possible to carry the vision across a vast series of ages, of which hitherto no definite knowledge existed, to mark the succession of their organisms, and thus to trace backward, far farther than had ever before been possible, the history of organised existence on this globe . The Silurian system was found to be developed in all parts of the world and Murchison's work furnished the key to its interpretation" (Geikie, pp. 420-21). The Silurian is a geologic period and system that extends from the end of the Ordovician Period, about 443 million years ago, to the beginning of the Devonian Period, about 416 years ago. The base of the Silurian is set at a major extinction event when 60% of marine species were wiped out. "The culmination of twenty years of geological research, Murchison's stratigraphical studies, begun in the Welsh Borderland and continued in South Wales, created a new epoch in earth history from what had hitherto been a confused, poorly understood complex of so-called 'Transition' rocks, so named because of their position between the unfossiliferous Primary and the highly fossiliferous Secondary strata. Murchison was the first to establish a uniform sequence of Transition strata, to which he gave the name 'Silurian' after an ancient British tribe; these strata constituted a major system with uniform fossil remains, displaying an abundance of invertebrates and a complete lack (except in the youngest strata) of the remains of vertebrates or land plants. By the time Murchison published his Silurian system, Silurian fossils had been discovered throughout both hemispheres and the system's validity had been accepted by most geologists. Murchison's work was primarily responsible for undermining Lyell's 'steady-state' uniformitarianism: the uniformity of the Silurian fauna demonstrated the greater uniformity of the global climate in Silurian times, and the temporal sequence of fossil faunas and floras over all stratigraphical systems supported a directional interpretation of the history of life" (Norman). "Although the map is a rarity today, every copy of the text was published with a map" (Thackray, p. 69) - Thackray consulted 25 institutional examples of the work, with only 11 containing the map. Murchison's great work is here accompanied by an ALS from him to the eminent French invertebrate geologist Henri Milne-Edwards (1800-85), who studied under Georges Cuvier. Murchison requests a description he had been promised of a "Serpuline formed shelly body", and which is necessary for him to complete the description of the Ludlow rocks in the present work; the fossil in question is described on p. 608. Murchison (1792-1871) was born into a long-established family of Highland landowners. With the advantages of a private income, he was able to devote himself entirely to science. He joined the Geological Society of London in 1825 and in the following five years explored Scotland, France, and the Alps and collaborated alternately with the British geologists Adam Sedgwick and Charles Lyell. In 1831 he was elected president of the Geological Society, after serving as secretary for five years. "Taking as a model the stratigraphical handbook of W. D. Conybeare and W. Phillips (1822), Murchison began the long series of geological studies which brought him worldwide fame and recognition. Almost every summer, for over twenty years, he undertook long and often arduous journeys in search of new successions of strata which would help to bring order to the reconstruction of the history of the earth. He entered geology during the first great period of stratigraphical research, and stratigraphy remained his chief area of interest. He was not a theoretician and generally delegated the paleontological parts of his work to others, but he was an excellent observer with a flair for grasping the major features of an area from a few rapid traverses . "At this time the major features of the stratigraphical succession had been clarified down to the Old Red Sandstone underlying the Carboniferous rocks, but below that was what Murchison called 'interminable grauwacke'-rocks containing few fossils, in which no uniform sequence had been detected. It was widely doubted whether the method of correlation by fossils would even be applicable to these ancient Transition strata, yet in them-if anywhere-lay the possibility of finding evidence for the origin of life itself. Acting on a hint of Buckland's, Murchison was fortunate to find in the Welsh borderland an area in which there was a conformable sequence downward from the Old Red Sandstone into Transition strata with abundant fossils. He gave a preliminary report of his work at the first meeting (1831) of the British Association for the Advancement of Science; and in 1835, after further fieldwork, he named the strata Silurian after the Silures, a Romano-British tribe that had lived in the region. "The Silurian constituted a major system of strata with a highly distinctive fauna, notable for an abundance of invertebrates and for the complete absence, except in the youngest strata, of any remains of vertebrates or land plants. It thus seemed to Murchison to mark a major period in the progressive history of life on earth. Even before he had comp
ARCHIVE ON THE WORLD'S FIRST COMMERCIAL COMPUTER - THE UNIVAC. An extensive and unique archive revealing the inner workings of UNIVAC, the world's first commercial computer. J. Presper Eckert, together with his partner John Mauchly, invented and constructed the first general-purpose digital computer (the ENIAC) during World War II. After the war he and Mauchly founded the first commercial computer company in the United States, the Electronic Control Co., soon renamed the Eckert-Mauchly Computer Corporation (EMCC). This company first developed the BINAC for Northrop Aviation, and later designed the UNIVAC, initially for the Bureau of the Census, which paid for much of its development. But the production of the BINAC essentially bankrupted the EMCC, and in 1949 it was sold to Remington Rand. "J. Presper Eckert and John Mauchly, almost alone in the early years, sought to build and sell a more elegant follow-on to the ENIAC for commercial applications. The ENIAC was conceived, built, and used for scientific and military applications. The UNIVAC, the commercial computer, was conceived and marked as a general-purpose computer suitable for any application that one could program it for. Hence the name: an acronym for 'universal automatic computer'" (Ceruzzi, p. 51). "The first UNIVAC was delivered to the Census Bureau on 31 March 1951, and the remaining two were shipped within the next 18 months. The UNIVAC thus became the second electronic computer to be produced under contract for a commercial customer, only being beaten by Ferranti's delivery of the Mark I to Manchester University about a month earlier. A further 43 UNIVACs were produced for sale to both government and industry; these established Remington-Rand as the world's first large-scale computer company" (Williams, pp. 364-5). These unique documents provide an important historical look into Eckert's work on early computers and his involvement with the project from its inception through the 1970s. Provenance: from the collection of G. Richard Adams, who worked as an assistant to Eckert and was responsible for overseeing paperwork and filing for projects. "After leaving the Moore School of Electrical Engineering at the University of Pennsylvania, J. Presper Eckert, Jr., and John Mauchly, who had worked on the engineering design of the ENIAC computer for the United States during World War II, struggled to obtain capital to build their latest design, a computer they called the Universal Automatic Computer, or UNIVAC. (In the meantime, they contracted with the Northrop Corporation to build the Binary Automatic Computer, or BINAC, which, when completed in 1949, became the first American stored-program computer.) The partners delivered the first UNIVAC to the U.S. Bureau of the Census in March 1951, although their company, their patents, and their talents had been acquired by Remington Rand, Inc., in 1950. [In 1955 Remington Rand merged with Sperry Corporation to become Sperry Rand.] Although it owed something to experience with ENIAC, UNIVAC was built from the start as a stored-program computer, so it was very different architecturally. It used an operator keyboard and console typewriter for simple, or limited, input and magnetic tape for all other input and output. Printed output was recorded on tape and then printed by a separate tape printer. "The UNIVAC I was designed as a commercial data-processing computer, intended to replace the punched-card accounting machines of the day. It could read 7,200 decimal digits per second (it did not use binary numbers), making it by far the fastest business machine yet built. Its use of Eckert's mercury delay lines greatly reduced the number of vacuum tubes needed (to 5,000), thus enabling the main processor to occupy a 'mere' 14.5 by 7.5 by 9 feet (approximately 4.4 by 2.3 by 2.7 metres) of space. It was a true business machine, signaling the convergence of academic computational research with the office automation trend of the late 19th and early 20th centuries. As such, it ushered in the era of 'Big Iron' - large, mass-produced computing equipment" (Britannica). The UNIVAC I remained in production until 1957 when Remington-Rand replaced it with the more sophisticated UNIVAC II. The improvements included magnetic (non-mercury) core memory of 2000 to 10000words, UNISERVOII tape drives, which could use either the old UNIVACI metal tapes or the new PET film tapes, and some circuits that were transistorized (although it was still a vacuum-tube computer). It was fully compatible with existing UNIVACI programs for both code and data. The UNIVACII also added some instructions to the UNIVACI's instruction set. Sperry Rand began shipment of UNIVAC III in 1962, and produced 96 UNIVACIII systems. Unlike the UNIVACI and UNIVACII, it was a binary machine as well as maintaining support for all UNIVACI and UNIVACII decimal and alphanumeric data formats for backward compatibility. This was the last of the original UNIVAC machines. "One of the most dramatic events in the early days of computer usage took place on the evening of the 1952 presidential election. Several months earlier the CBS network had arranged to have a UNIVAC machine attempt to predict the outcome of the election based on a sample of the early returns . At 8.30 that evening, after only a very few results were available, the UNIVAC predicted a landslide victory for Eisenhower over Stevenson. Quick conferences between the computer people, election officials and CBS resulted in the decision that something must be wrong and the risk of publishing this result was not worth taking . In fact, Eisenhower won by almost exactly the landslide first predicted by UNIVAC, and many television and computer people went to bed that night feeling very sorry they had not taken advantage of the publicity they could have had for the developing computer industry" (Williams, pp. 366-7). This unique archive is divided into three major sections: Large 'UNIVAC Uniservo 12 for
THE METHOD OF INDIVISIBLES. Second edition (first, 1635) of Cavalieri's text containing the discovery of the 'method of indivisibles', one of the most important forerunners of the integral calculus. Book II of the work includes the statement of 'Cavalieri's principle' for the determination of areas and volumes, which considers an area as made up of an indefinite number of equidistant parallel line segments ('omnes lineae'), and a solid as made up of an indefinite number of parallel plane areas. It states that, if two planar figures are contained between a pair of parallel lines, and if the lengths of the two segments cut by them from any line parallel to the including lines are always in a given ratio, then the areas of the two planar pieces are also in this ratio (there is an analogous principle for the determination of volumes). Cavalieri's principle provided a simple and effective alternative to the Archimedean method of exhaustion, and was used by Kepler, Galileo, Cavalieri's pupil Torricelli, Wallis, Pascal, and others. The first edition of the Geometria is a notorious rarity, ABPC/RBH listing only the Macclesfield copy in the last 80 years. This second edition is not as rare, but is still very difficult to find in such fine condition as in our copy. "For Cavalieri a surface consists of an indefinite number of equidistant parallel straight lines and a solid of a set of equidistant parallel planes. These constitute the line and surface indivisibles respectively. For plane figures (or solids) a regula, that is, a line (or plane) drawn through the vertex, is the starting point. The regula moves parallel to itself until it comes into coincidence with a second line (or plane) termed the base or tangens opposita. The intercepts (lines or plane sections) of the regula with the original plane (or solid) figure are the elements or indivisibles making up the totality of lines (or planes) of the figure. "In the techniques developed by Cavalieri the indivisibles of two or more configurations are associated together in the form of ratios and from these ratios the relations between the areas (or volumes) of the figures themselves are derived. In moving from a relation between the sums of the indivisibles and thus to a relation between the spaces the infinite is employed, but purely in an auxiliary role. "Cavalieri's defence of indivisible methods was based primarily on the idea of a device or artificium which works rather than on any definite or dogmatic views as to the nature of indivisibles and the spaces which they occupy. Nevertheless the classic problem of the nature of the continuum imposed itself upon him and, from the outset, he felt himself obliged to try to meet some of the arguments which he felt might be directed against his methods. He admits that some might well doubt the possibility of comparing an indefinite number of lines, or planes (indefinitae numero lineae, vel plana). When such lines (or planes) are compared, he says, it is not the numbers of such lines which are considered but the spaces which they occupy. Since each space is enclosed it is bounded and one can add to it or take away from it without knowing the actual number of lines or planes. Whether indeed the continuum consists of indivisibles or of something else neither the space nor the continuum is directly measurable. The totalities, or sums, of the indivisibles making up such spaces are, however, always comparable. To establish a relation between the areas of plane figures, or the volumes of solid bodies, it is therefore sufficient to compare the sums of the lines, or planes, developed by any regula. "The foundations for Cavalieri's indivisible techniques rest upon two distinct and complementary approaches which he designates by the terms collective and distributive respectively. In the first, the collective sums, Σ l1 and Σ l2, of the line (or surface) indivisibles for two figures P1 and P2 are obtained separately and then used to establish the ratio of the areas (or volumes) of the figures themselves. If, for example, Σ l1 / Σ l2 = α/Π, then P1/P2 = α/Π. This approach was given the most extensive application by Cavalieri and he exploited it with skill and ingenuity to obtain a fascinating collection of new results which he exhibited in the Exercitationes [Geometriae Sex, 1647]. The distributive theory, on the other hand, was developed primarily in order to meet the philosophic objections which Cavalieri felt might be raised against the comparison of indefinite numbers of lines and planes. Fundamental here is Cavalieri's Theorem: the spaces (areas or volumes) of two enclosed figures (plane or solid) are equal provided that any system of parallel lines (or planes) cuts off equal intercepts on each. In brief, if for every pair of corresponding intercepts l1 and l2, l1 = l2, then P1 = P2. An immediate extension follows: if l1/ l2 = α/Π, then P1/P2 = α/Π. Cavalieri himself only made use of this method in a limited number of cases where α/Πis constant for all such pairs of intercepts. This technique, however, in the hands of Gregoire de Saint-Vincent and others in the seventeenth century, became a valuable means of integration by geometric transformation. Ultimately, whichever of the two methods was applied, Cavalieri was prepared to concede that absolute rigour required in each case an Archimedean proof with completion by reductio ad absurdum" (Baron, The Origins of the Infinitesimal Calculus, 1969, pp. 124-6). "The concept of indivisibles does sometimes show up fleetingly in the history of human thought: for example, in a passage by the eleventh-century Hebrew philosopher and mathematician Abraham bar Hiyya (Savasorda); in occasional speculations - more philosophical than mathematical - by the medieval Scholastics; in a passage by Leonardo da Vinci; in Kepler's Nova stereometria doliorum . [and in] Galileo . "In Cavalieri we come to a rational systematization of the method of indivisibles, a method that
ONE OF THE MOST IMPORTANT PRECURSORS OF VIÈTE IN THE USE OF ALGEBRAIC SYMBOLISM. First edition of this very rare and celebrated treatise on algebra, the superb de Thou copy bound in early seventeenth-century French citron morocco with his arms - scientific books in de Thou bindings very rarely appear on the market. "Considered the greatest of Portuguese mathematicians, Nuñez reveals in his discoveries, theories, and publications that he was a first-rate geographer, physicist, cosmologist, geometer and algebraist" (DSB). Nuñez's work is distinguished from other algebra textbooks of the time by its greater level of abstraction and its use of letters rather than numbers. Indeed, it is the first modern work to use algebraic symbolism in something like the way it is used today. This marks Nuñez as one of the most important precursors of François Viète. "We notice first of all a generality in the demonstrations, an abstraction in the statements of the exercises, which is very exceptional for the time and which gives the Libro de algebra an already quite modern character. Thus, the 110 problems of algebra, which are the object of chapter 5 of the third part, are not drawn, as in the texts of other algebraists of the time, from commerce, industry, or other situations in real life; these are problems about numbers. When the author borrows from Pacioli or someone else a question in which players share their winnings, for example, he is careful to reduce the problem to one about numbers . This same quality of abstraction is also noticed in the 77 exercises on the application of algebra to geometry which form the subject of the last chapter of the third part" (translated from Bosmans (1907-8), pp. 157-158). The first part of the Libro de Algebra treats the solution of equations of the first and second degree. The second part is divided into three subsections: the first treats the addition, subtraction, multiplication, and division of polynomials; the second the same manipulations of radicals (square and higher roots); and the third the theory of proportion, treated algebraically rather than in the geometric language used by his predecessors. The third and longest part is devoted to the solution of polynomial equations (including one chapter on systems of linear equations). The work concludes with a chapter on the application of algebra to geometry. It was valued highly by most of the leading seventeenth century mathematicians, in England, France and Germany, as well as in Spain and Portugal, especially by John Wallis, Jacques Peletier, Elias Vinet, and Guillaume Gosselin. "Stevin was acquainted with it and credited Nuñez with leading him to apply Euclid's algorithm to polynomials" (Malet, p. 193). Until the appearance of Christoph Clavius's Algebra in 1608, the Libro de algebra was one of the most widely used algebra texts in the Jesuit colleges, and it was highly praised by Clavius himself. The manuscript of this work was prepared in Portuguese some thirty years before Nuñez published this Spanish translation (the preface is in Portuguese), but he added to the work substantially in the intervening years (for example, reference is made to Peletier's edition of Euclid's Elements, published in 1557). ABPC/RBH lists only three other copies since 1935: the Honeyman/Streeter copy (Christie's NY 2007 & Sotheby's 1978); Macclesfield (Sotheby's 2005); and Hartung 2005 (a copy in a late 19th-century binding with paper repairs). The Macclesfield copy, in a similar seventeenth-century morocco binding to the present copy, realized a little over $17,000. OCLC lists only Folger and Michigan in the US. Provenance: The Peeters-Fontainas copy (the sale of his library, Sotheby's London, May 23, 1978, lot 382), with the combined arms of J. A. de Thou and those of his second wife, Gasparde de La Chastre, on the covers. Pedro Nuñez Salaciense (1502-78) was born in Alcácer do Sol, Portugal and studied at Salamanca, Spain, and in 1524 or 1525 at Lisbon. He held a professorship in Lisbon, which was moved to Coimbra in 1537. He taught Clavius, Nicolaus Coelho de Amaral, Manuel de Figueredo and Joao de Castro, one of the greatest Portuguese navigators. "Both as Royal Cosmographer under King John III (the Pious) of Portugal and as professor of mathematics at the University of Coimbra, Nunes gave instruction in the art of navigation to those associated with Portugal's merchant and naval fleets. His Libro de algebra provided the mathematical underpinnings of that instruction - and much more - adopting Luca Pacioli's abbreviated notational style and treating the solution not only of linear and quadratic equations but also that of a cubic equation of the type x3 + cx = d following the spectacular mid-sixteenth-century work of the Italians Niccolò Tartaglia and Girolamo Cardano" (Katz & Parshall, Taming the Unknown, p. 205). "By 1533, Nunes had already translated most of the scientific works of Aristotle, Euclid and Ptolemy, and mathematical treatises by Arabic and Italian authors, and he had been appointed as the first Royal Cosmographer. It seems highly probable that his theories in geometry and algebra were by then well thought out, already sufficiently advanced for him to have a far better understanding of the workings of the globe, of cartography and of the differing shadows, as can be seen in his Tratado da Sphera, published in 1537, and his Crepusculis, published in 1542. Only four years later he was also well able to refute solutions to apparently insoluble problems for the Ancient Greeks, as propounded by France's leading mathematician, Oronce Finé (De erratis Orontii Finaei, 1546). The major addition from his thirty years of research and teaching mathematics at the University of Coimbra was the collection of problems (187 in all), in Part 3 of his Spanish Algebra . "When Nunes dedicated his magnum opus on algebra to Cardinal Henry, he dated it 1564, and located it not in Coimbra, but in Lisbon. It seems quite likely that
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