KEPLER, Johannes
KEPLER'S GEOMETRICAL COSMOS. Second, enlarged, edition of the Mysterium cosmographicum (first, 1596), Kepler's first scientific book, "the first unabashedly Copernican treatise since De revolutionibus itself" (Gingerich in DSB), which laid "the foundation of his vast later astronomical work [and] immediately made him famous in scientific circles, and got him into contact with Galileo and Tycho Brahe" (Caspar). "Kepler maintained the basic ideas of the work of his youth throughout his life. In the dedication to the present edition he proudly points out his early achievement: 'As if an oracle from the heavens had been dictated to me,' he writes in fond memory. He realises that 'almost all astronomical books which I have published since that time relate to one of the main chapters in this little book, representing an expansion, or an improvement upon it.' Thus the present edition is especially suited to introduce Kepler's thought: it offers the promising beginnings and the perfection - the beginnings as in the original text written by the young Magister, the perfection in the extensive annotations" (ibid.). In the Prodromus Kepler proposes his famous model of the planetary system according to which the celestial spheres carrying the orbits of the six known planets should circumscribe and inscribe a nested set of the five Platonic regular solids (cube, tetrahedron, octahedron, icosahedron and dodecahedron), which is spectacularly illustrated on the engraved plate. This system not only explained why there were exactly six known planets, it also predicted the relative diameters of their orbits; and of course it only made sense of the spheres carrying the orbits had a common center, in other words for a heliocentric universe. Although the model is erroneous, Kepler's values for the relative diameters of the orbits are, in fact, within 5% of the true values. This edition presents the text of the first edition, which also included an Appendix containing a reprint of Rheticus' Narratio prima (1540), the first publication of Copernicus' heliocentric theory - the version here includes Kepler's additional notes reflecting the development of his thinking in the intervening 25 years and references to his own works published during that period - and Kepler's teacher Michael Maestlin's account of Copernican planetary theory, De dimensionibus orbium et sphaerarum coelestium iuxta Tabulas Prutenicas, ex sententis Nicolai Copernici. The volume concludes with the first publication of Kepler's Pro suo Opere Harmonices Mundi Apologia (with separate title page), a reply to Robert Fludd, the Oxford Rosicrucian, who had attacked Kepler's theories on musical harmony. Kepler's first cosmological work was published shortly after his arrival in Graz. "Kepler's fertile imagination hit upon what he believed to be the secret key to the universe. His own account, here greatly abridged, appears in the introduction to the resulting work, the Mysterium cosmographicum of 1596. 'When I was studying under the distinguished Michael Maestlin at Tübingen six years ago, seeing the many inconveniences of the commonly accepted theory of the universe, I became so delighted with Copernicus, whom Maestlin often mentioned in his lectures, that I often defended his opinions in the students' debates about physics. I even wrote a painstaking disputation about the first motion, maintaining that it happens because of the rotation of the earth. I have by degrees-partly out of hearing Maestlin, partly by myself-collected all the advantages that Copernicus has over Ptolemy. At last in the year 1595 in Graz when I had an intermission in my lectures, I pondered on this subject with the whole energy of my mind. And there were three things above all for which I sought the causes as to why it was this way and not another-the number, the dimensions, and the motions of the orbs.' "After describing several false attempts, Kepler continues: 'Almost the whole summer was lost with this agonizing labor. At last on a quite trifling occasion I came near the truth. I believe Divine Providence intervened so that by chance I found what I could never obtain by my own efforts. I believe this all the more because I have constantly prayed to God that I might succeed if what Copernicus had said was true. Thus it happened 19 July 1595, as I was showing in my class how the great conjunctions [of Saturn and Jupiter] occur successively eight zodiacal signs later, and how they gradually pass from one trine to another, that I inscribed within a circle many triangles, or quasi-triangles such that the end of one was the beginning of the next. In this manner a smaller circle was outlined by the points where the line of the triangles crossed each other.' "The proportion between the circles struck Kepler's eye as almost identical with that between Saturn and Jupiter, and he immediately initiated a vain search for similar geometrical relations. 'And then again it struck me: why have plane figures among three-dimensional orbits? Behold, reader, the invention and whole substance of this little book! In memory of the event, I am writing down for you the sentence in the words from that moment of conception: The earth's orbit is the measure of all things; circumscribe around it a dodecahedron, and the circle containing this will be Mars; circumscribe around Mars a tetrahedron, and the circle containing this will be Jupiter; circumscribe around Jupiter a cube, and the circle containing this will be Saturn. Now inscribe within the earth an icosahedron, and the circle contained in it will be Venus; inscribe within Venus an octahedron, and the circle contained in it will be Mercury. You now have the reason for the number of planets." "Kepler of course based his argument on the fact that there are five and only five regular polyhedrons. 'This was the occasion and success of my labors. And how intense was my pleasure from this discovery can never be expressed in words. I no longer regrett
SIMPSON, James Young
THE DISCOVERY OF CHLOROFORM ANAESTHESIA - PRESENTATION COPY OF THE EARLIEST OBTAINABLE PUBLICATION . Second edition, extremely rare first issue, inscribed presentation copy, of the first use of chloroform as an anaesthetic. This is the earliest obtainable version of Simpson's discovery - the first edition, published two or three days earlier, is known in only two copies, both in institutional collections. "While searching for an anaesthetic less irritating than ether, Simpson discovered the advantages of chloroform, and was the first to apply it as a painkiller during labor and childbirth. Simpson first used chloroform in an obstetrical case on 8 November 1847, when he administered it to a woman with a previous history of difficult labor; the baby was born without complications about twenty-five minutes after the first inhalation. Simpson reported his success in an address delivered at the Medico-Chirurgical Society of Edinburgh on 10 November, and immediately afterwards published the address in this pamphlet, with a postscript describing surgical cases. In spite of Simpson's success with chloroform, he encountered a great deal of opposition from conservative doctors and clergyman who considered labor pains a God-given punishment for Eve's sins, and he embarked on a long publishing campaign to convert the opposition. His most famous non-scientific argument was that God Himself had been the first anaesthetist when he 'caused a deep sleep to fall upon Adam before bringing forth Eve from his rib' (Genesis II:21). Simpson's efforts were finally accepted by the medical establishment when Queen Victoria chose to take chloroform for the birth of Prince Leopold in 1853" (Norman). "Chloroform and ether have not been used as human anesthetics since the 1950s; in the past few decades synthetic gases with fewer side effects have replaced the older agents. Yet Simpson's work a century and a half ago legitimized the use of medical interventions to relieve the pain of labor. Millions of women around the world whose labor pains have been eased by various types of anesthesia have benefited from Simpson's ground-breaking efforts" (Science and Its Times: Understanding the Social Significance of Scientific Discovery). ABPC/RBH list no copy of the first edition and only this copy (the Norman copy) of the first issue of the second edition (the second and later issues are notably less rare). Provenance: 1. Presentation copy, inscribed on the title: 'Dr. Smith/from J.Y.S.' Simpson apparently mailed the pamphlet to Smith without an envelope, addressing it on the blank verso of the last leaf to: 'Dr. Smith/Editor of Boston Med: & Surgical/Journal/Boston/United States.' This page also bears two postmarks, one dated 19 November 1847 at Edinburgh, and the other dated 21 November 1847 at Liverpool. The Boston Medical and Surgical Journal, edited by J. V. C. Smith, first mentioned Simpson's discovery in its issue of 29 December 1847, and acknowledged receipt of Simpson's pamphlet in its issue of 5 January 1848. 2. Warren G. Atwood. 3. Haskell F. Norman. Until the end of the 18th century, surgeons were unable to offer patients much more than opium, alcohol or a bullet to bite on to deal with the agonizing pain of surgery. Based upon his 'Researches, Chemical and Philosophical: Chiefly Concerning Nitrous Oxide' (1799), the English chemist Humphry Davy suggested inhalation of nitrous oxide during surgical operations, but this was not acted upon. In 1813, Davy was joined at the Royal Institution by his assistant Michael Faraday, who studied the inhalation of ether. He published his findings, which included soporific and analgesic effects, in 1818, but again these findings were not followed up, possibly because of the difficulty of quantifying and controlling the effects of ether (one subject had taken over 24 hours to recover full consciousness). The focus of developments now moved to the United States. In 1845, Boston dentists William T.G. Morton and Horace Wells experimented with nitrous oxide, but in an infamous demonstration at Harvard Medical School, the two dentists failed to deaden the pain of a subject having a tooth pulled. Morton persisted, however, and on October 16, 1846, he used sulphuric ether to anaesthetize a man who needed surgery to remove a vascular tumour from his neck; Morton had attended lectures in 1844 by the Harvard chemist Charles Jackson who demonstrated that sulphuric ether could render a person unconscious or even insensate. News of Morton's discovery did not reach Britain until December 1846 (it was first formally announced in the Lancet in July 1847). Dr. Francis Boott, an expatriate American, learning of Morton's success through a letter from Boston, arranged for a Miss Lonsdale to have a tooth removed by James Robinson before a group which included Robert Liston. Liston, then London's leading surgeon, was so impressed that he arranged to perform an amputation under ether on December 21at University College Hospital, the first public demonstration in Britain. This happened to be the time of the annual visit to London of James 'Young' Simpson, Professor of Midwifery in Edinburgh. James Simpson was born in Bathgate, Scotland on 7th June 1811. He qualified in medicine in 1830 at the age of nineteen and went on to specialize in obstetrics. He was appointed Professor of Midwifery in Edinburgh at the age of thirty, an extremely prestigious appointment for one so young. It is rumoured that he added 'Young' to his name at this time although there is no conclusive evidence to support this. Simpson was quick to recognize the significance of ether anaesthesia. He had always been concerned with the issue of surgical pain and began experimenting with potential solutions. On 19 January 1847, Simpson introduced ether anaesthesia into obstetrics. He initially used ether for pain relief when surgically intervening during childbirth, but eventually employed it for normal labour as well. After some time using
![Zur allgemeinen Relativitätstheorie [with:] Zur allgemeinen Relativitätstheorie (Nachtrag). Offprint from Sitzungsberichte der Preussischen Akademie der Wissenschaften XLIV](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
EINSTEIN, Albert
EINSTEIN'S COMPLETION OF THE GENERAL THEORY OF RELATIVITY. First editions, very rare offprint, of the first two of the papers published in November 1915 that document Einstein's final version of the general theory of relativity. "In the half century and more of Einstein's work in science, one discovery stands above all as his greatest achievement. It is his general theory of relativity" (Norton). "There was difficulty reconciling the Newtonian theory of gravitation with its instantaneous propagation of forces with the requirements of special relativity; and Einstein working on this difficulty was led to a generalization of relativity - which was probably the greatest scientific discovery that was ever made" (Dirac, quoted in Chandrasekhar, p. 3). Einstein's special theory of relativity (1905) showed that the laws of physics are the same in all inertial (i.e., non-accelerating) frames of reference. It was then natural to ask whether it was possible to extend this principle of relativity to the more general case of frames of reference in arbitrary states of motion. This problem became linked to a theory of gravitation with Einstein's 'equivalence principle' of 1907, according to which the effects of gravity are locally equivalent to those of accelerated motion. Einstein's first steps towards a geometrical theory of gravitation were taken in August 1912, when his friend Marcel Grossmann provided the necessary mathematical tools. "Some time between August 10 and August 16, it became clear to Einstein that Riemannian geometry is the correct mathematical tool for what we now call general relativity theory. The impact of this abrupt realization was to change his outlook on physics and physical theory for the rest of his life" (Pais, p. 210). The resulting 'Entwurf' theory (1913) had much in common with the final theory of 1915, but based on a fallacious argument Einstein abandoned the requirement that the theory should be 'generally-covariant', i.e., that arbitrary frames of reference should be allowed. "After three years of fruitless peregrinations, the revelation came to Einstein that he had been constantly on the wrong track, although in 1913 he had been so near to the right solution" (Lanczos, p. 211). On November 4, 1915 he presented to a plenary session of the Prussian Academy a new version of general relativity, 'Zur allgemeinen Relativitätstheorie,' "based on the postulate of covariance with respect to transformations with determinant 1", and stated that he had "completely lost confidence" in the 'Entwurf' equations. On November 18, he published his calculation of the precession of the perihelion of Mercury based on the new theory: its agreement with observation confirmed that the theory was correct (the Entwurf theory predicted half the observed value of the precession). "In June 1905, while still a patent examiner in Bern, Einstein submitted his famous work on the electrodynamics of moving bodies to the Annalen der Physik. This work contained his special theory of relativity, in which he asserted the equivalence of all inertial frames of reference as a fundamental postulate of physics. The question which then naturally arose was whether it was possible to extend this principle of relativity to the more general case of frames of reference in arbitrary states of motion. But he could find no workable basis for such an extension, until he tried to incorporate gravitation into his new special theory of relativity for a review article in 1907 ['Uber das Relativitätsprinzip und die ausdemselben gezogenen Folgerungen,' Jahrbuch der Radioaktivitat und Elektronik 4 (1907), 411-62]. The difficulties of this task led him to a new principle, later to be called the 'principle of equivalence.' "On the basis of the fact that all bodies fall alike in a gravitational field, Einstein postulated the complete physical equivalence of a homogeneous gravitational field and a uniform acceleration of the frame of reference. This extended the principle of relativity to the case of uniform acceleration. It also foreshadowed the problem whose complete solution would lead him to his general theory of relativity: the construction of a relativistically acceptable theory of gravitation, based on the principle of equivalence" (Norton, p. 258). One application of the equivalence principle proved crucial to the subsequent development of his ideas on general relativity. Einstein considered an observer standing on a rotating disc - a non-inertial (accelerating) reference frame. According to special relativity, measuring rods aligned with the circumference of the disc will contract due to their motion, whereas measuring rods positioned along the radius of the disc will not. Hence the ratio of the circumference of the disc to its diameter will be less than Ï. "The spatial geometry for the rotating observer is therefore non-euclidean. Invoking the equivalence principle, Einstein concluded that this will be true for an observer in a gravitational field as well. This then is what first suggested to Einstein that gravity should be represented by curved space-time. "To describe curved space-time Einstein turned to Gauss's theory of curved surfaces, a subject he vaguely remembered from his student days at the ETH in Zürich. He had learned it from the notes of his classmate Marcel Grossmann. Upon his return to his alma mater as a full professor of physics in 1912, Einstein learned from Grossmann, now a colleague in the mathematics department of the ETH, about the extension of Gauss's theory to spaces of higher dimension by Riemann and others. Riemann's theory provided Einstein with the mathematical object with which he could unify the effects of gravity and acceleration: the metric field" (Janssen, p. 65). The first product of this collaboration was the Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation, published before the end of June 1913, which contained many of the essential features of the
FRAUNHOFER, Joseph
THE FOUNDING WORK OF ASTROPHYSICS THE FIRST ILLUSTRATION OF THE SOLAR SPECTRUM . First edition, journal issue, of the founding work of astrophysics, the discovery of the absorption lines in the solar spectrum; the second plate, which reproduces Fraunhofer's drawing of these lines (etched by Fraunhofer himself), is the first illustration of the solar spectrum. "In 1802, when describing his new process for measuring the refraction of light, W. H. Wollaston reported the occurrence of dark lines in the solar spectrum but regarded them as simply natural dividing lines between the colours. Fraunhofer, originally not a scientist, but a practising optician, concentrated on these dark lines, and the title of his paper describes the method and purpose of his investigations: 'Definition of the Capacity of Refraction and Colour-diffusion of various kinds of Glass' . His achievements justify describing him as the founder of astrophysics. He charted several hundred lines, which have been known as 'Fraunhofer lines' ever since" (PMM). "These observations stimulated considerable interest for the next half-century among natural philosophers, whose speculations culminated in the classical explanation of absorption and emission spectra made by Kirchoff and Bunsen in 1859" (DSB). "Fraunhofer's discovery represented the beginning of what later came to be called chemical spectral analysis, the development of which was associated with the names of David Brewster, John Herschel, William Henry Fox Talbot, Charles Wheatstone, Antoine-Philibert Masson, Anders Jonas Ångström and William Swan. These investigators examined the origin of the dark lines in the solar spectrum - the so-called Fraunhofer lines - and suggested that they might be created by the selective absorption of light emitted by the sun in its atmosphere. The question then arose as to which chemical substances emitted which particular discrete lines. The final and conclusive steps towards chemical spectral analysis, however, were taken by the chemist Robert Bunsen and the physicist Gustav Kirchhoff" (Mehra & Rechenberg I, p. 157). They concluded that the cool, outer regions of the solar atmosphere contained iron, calcium, magnesium, sodium, nickel and chromium and probably cobalt, barium, copper and zinc as well. ABPC/RBH list only one other copy of this journal issue since 1965 (It is rarer in commerce than the offprint). "Fraunhofer (1787-1826) came from humble parentage in Straubing near Munich and had very little formal education, having lost both parents when he was eleven. In 1807, at the age of 20, he was hired by the Mathematical Mechanical Institute Reichenbach, Utzschneider and Liebherr, a firm founded in 1804 for the production of military and surveying instruments, for which high-quality optical glass for lenses was essential. The optical works of the firm were outside Munich, at a disused monastery in Benediktbeuern, where Fraunhofer received his training from a Swiss named Pierre Guinand (1748-1824). Guinand's considerable reputation rested on his skill in the production of relatively large and optically pure pieces of crown and flint glass. However, owing to a clash of personalities, Guinand resigned his contract in 1814 and returned to Switzerland, and at this time the whole firm passed into the hands of Joseph von Utzschneider and Fraunhofer. "The success of this famous early glass factory lay in the production of optical crown and flint glass free from bubbles and veins. The technique of stirring the molten glass was discovered by Guinand and developed by Fraunhofer. The use of these glasses enabled Fraunhofer to construct achromatic optical instruments of hitherto unsurpassed quality, and this was undoubtedly a key factor in his successful pioneering work in solar spectroscopy. Fraunhofer embarked on a careful examination of the optical properties of his glass, so as to measure the refractive index and dispersion. His work on the solar spectrum can therefore be seen as the means to Fraunhofer's end goal of perfecting optical instruments, for he realized that accurate refractive indices must be measured in monochromatic light. For, having rediscovered the solar absorption lines, he saw that the lines defined the precise wavelength of the light far better than the mere sensation of colour to the human eye. "Fraunhofer observed the solar spectrum using a telescope of 25 mm aperture taken from one of his theodolites. A prism was mounted in front of the objective, and this enabled him to focus a relatively pure spectrum for direct visual inspection through the eyepiece. His introductory words are almost reminiscent of those used by Newton: 'In a shuttered room I allowed sunlight to pass through a narrow opening in the shutters, which was about 15 seconds broad and 36 minutes high, and thence onto a prism of flint glass, which stood on the theodolite . The theodolite was 24 feet from the window, and the angle of the prism measured about 60 degrees . I wanted to find out whether in the colour-image [i.e., spectrum] of sunlight, a similar bright stripe was to be seen, as in the colour-image of lamplight. But instead of this I found with the telescope almost countless strong and weak vertical lines, which however are darker than the remaining part of the colour-image; some seem to be nearly completely black' [p. 202]. "Fraunhofer convinced himself that the lines in no way represent colour boundaries, as the same colour is found on both sides of a line with only a gradual and continuous colour change throughout the spectrum. Ten of the strongest lines were labeled with the letters A, a, B, C, D, E, b, F, G and H from the far red to the limit of the eye's vision in the violet. The last letter was used for the pair of strong violet lines that we now know are due to absorption by calcium. He noted that A was very near the red limit of the spectrum, but he was still able to see some red light beyond this feature. He showed the D feature to be com
LAMBERT, Johann Heinrich
"THE FOUNDATION OF THE SCIENCE OF PHOTOMETRY" (PMM 205) . First edition, very rare, and the finest copy we have seen, of the foundation work of photometry, the measurement of the intensity of light, both objectively and as perceived by the eye; this is one of the rarest of modern science books of this stature. Lambert's discoveries "are of fundamental importance in astronomy, photography and visual research generally . Both Kepler and Huygens had investigated the intensity of light, and the first photometer had been constructed by Pierre Bouguer (1698-1758); but the foundation of the science of photometry - the exact scientific measurement of light - was laid by Lambert's 'Photometry' . In the Photometria he described his photometer and propounded the law of the absorption of light named after him. He investigated the principles and properties of light, of light passing through transparent media, light reflected from opaque surfaces, physiological optics, the scattering of light passing through transparent media, the comparative luminosity of the heavenly bodies and the relative intensities of coloured lights and shadows" (PMM). "It is difficult to overstate how original most of Photometria was and how great was the advance Lambert made with it. He was the first to accurately identify most fundamental photometric concepts, to assemble them into a coherent system of photometric quantities, to define these quantities with a precision sufficient for mathematical statement, and to build from them a system of photometric principles . The behavior of point light sources had been understood since Kepler's time. Lambert was the first to correctly solve the problem posed by extended light sources. He was the first to state the cosine emanation law, which describes how a surface of perfect diffusion emits light, and to see the far-reaching consequences of this idea. Lambert spent one tenth of Photometria developing equations for the calculation of illumination at points and surfaces from luminous areas of various forms - equations that are now used in modern computer graphics, and thermal and lighting engineering . With his emanation law, Lambert calculated the average brightness of the moon and planets, anticipating part of modern astrophysics by a century . Lambert made extensive measurements of the photometric properties of materials by ingenious application of the process of equating two brightnesses. He determined the reflectance and transmittance of glass for a range of angles, the brightness of images produced by lenses, the diffuse reflectance of matte surfaces, and the absorption of light in glass and in the atmosphere. He measured the color composition of white and colored surfaces and was the first to mix colored light and record that the result was different from mixing colored pigments . Lambert was the first to attempt to establish a relationship between the subjective assessment of a luminous stimulus - the brightness - made by the visual system, and the strength - the luminance and size - of that stimulus" (Dilaura, pp. i-ii). ABPC/RBH record the sale of three copies since Norman. OCLC lists copies in US at Brown, Harvard Medical School and Oklahoma. Provenance: Georg Hermann Quincke (1834-1924) (signature on front free endpaper). Quincke received his Ph. D. in 1858 at Berlin, having previously studied also at Königsberg and at Heidelberg. He became privatdozent at Berlin in 1859, professor at Berlin in 1865, professor at Würzburg in 1872, and in 1875 was called to be professor of physics at Heidelberg, where he remained until his retirement in 1907. Quincke did important work in the experimental study of the reflection of light, especially from metallic surfaces. "Lambert began with two simple axioms: light travels in a straight line in a uniform medium and rays that cross do not interact. Like Kepler before him, he recognized that 'laws' of photometry are simply consequences and follow directly from these two assumptions. In this way Photometria demonstrated (rather than assumed) that Illuminance varies inversely as the square of the distance from a point source of light. Illuminance on a surface varies as the cosine of the incidence angle measured from the surface perpendicular. Light decays exponentially in an absorbing medium. "In addition, Lambert postulated a surface that emits light (either as a source or by reflection) in a way such that the density of emitted light (luminous intensity) varies as the cosine of the angle measured from the surface perpendicular. In the case of a reflecting surface, this form of emission is assumed to be the case, regardless of the light's incident direction. Such surfaces are now referred to as 'Perfectly Diffuse' or 'Lambertian'. "Lambert demonstrated these principles in the only way available at the time: by contriving often ingenious optical arrangements that could make two immediately adjacent luminous fields appear equally bright (something that could only be determined by visual observation), when two physical quantities that produced the two fields were unequal by some specific amount (things that could be directly measured, such as angle or distance). In this way, Lambert quantified purely visual properties (such as luminous power, illumination, transparency, reflectivity) by relating them to physical parameters (such as distance, angle, radiant power, and color). Today, this is known as 'visual photometry.' Lambert was among the first to accompany experimental measurements with estimates of uncertainties based on a theory of errors and what he experimentally determined as the limits of visual assessment. "Although previous workers had pronounced photometric laws 1 and 3, Lambert established the second and added the concept of perfectly diffuse surfaces. But more importantly, as Anding pointed out in his German translation of Photometria [Leipzig, 1892], 'Lambert had incomparably clearer ideas about photometry' and with them establis
BONDARCHUK, Lieutenant-General N.S.
A SECRET SOVIET REPORT ON THE CHERNOBYL DISASTER. First edition, extremely rare, of this secret report assessing the immediate aftermath of the nuclear disaster at Chernobyl on 26 April, 1986 - it is one of the very few first-hand accounts by an insider. The book provides a minute-by-minute account of what happened in the period 26-28 April, assesses the damage wrought and the subsequent efforts made to clean up the area. A substantial portion of the book is dedicated to the little known issue of the Diepr River reservoir, fifteen miles downstream from Cheronobyl and ten miles upstream from central Kiev, and to the efforts to procure an alternate water supply for the Ukranian capital. All of these details are illustrated using maps and diagrams that show the progression of radioactivity in different areas and layout the disaster.The book was produced by the Ukranian SSR civil defence corps under the leadership of Lieutenant-General N. S. Bondarchuk, one of the central figures leading the Ukrainian response to the event. He was one of the first to arrive at the power plant, about eight hours after the explosion near reactor 4 and, critically, his "reports of this development were the first clear indication received by GO [civil defense] that the accident was much more serious than Briukhanov [the plant director] had indicated" (Geist, p. 117). Bondarchuk was one of the few to insist the event was announced to the public so that fall out shelters could be readied and potassium iodide tablets be distributed. His wider efforts, such as the evacuation of nearby city of Pripiat and the entire Chernobyl district, were halted due to political interference, and the KGB suppressed his reports. Bondarchuk produced this report for the Ukrainian SSR civil defence corps. This volume is augmented by several maps which separately document exclusion zones and contaminant levels and pollution of the water supply to Pripiat river and Diepr Reservoir. The events documented in this book are of immense importance to the nuclear industry, but also to the field of civil defence. As the book itself states, 'Until recently, in the development of the theory of civil defense, the main attention was paid to its actions in wartime conditions.' No other copy located, and no references have been found to this book in Western literature. Provenance: Stamp on one map reading 'ÑкРNo 016,' indicating that this was the 16th copied issued; deaccession stamp dated to March 6th, 1991; a further manuscript annotation reads 'Num. 581' following a now-illegible stamp, possibly suggesting that the total run of the book was 581 copies; an address on a loose sheet included inthe book indicates that the book remained in Ukraine after 1991. "On April 25 and 26, 1986, the worst nuclear accident in history unfolded in what is now northern Ukraine as a reactor at a nuclear power plant exploded and burned. Shrouded in secrecy, the incident was a watershed moment in both the Cold War and the history of nuclear power. More than 30 years on, scientists estimate the zone around the former plant will not be habitable for up to 20,000 years. "The disaster took place near the city of Chernobyl in the former USSR, which invested heavily in nuclear power after World War II. Starting in 1977, Soviet scientists installed four RBMK nuclear reactors at the power plant, which is located just south of what is now Ukraine's border with Belarus. "On April 25, 1986, routine maintenance was scheduled at V.I. Lenin Nuclear Power Station's fourth reactor, and workers planned to use the downtime to test whether the reactor could still be cooled if the plant lost power. During the test, however, workers violated safety protocols and power surged inside the plant. Despite attempts to shut down the reactor entirely, another power surge caused a chain reaction of explosions inside. Finally, the nuclear core itself was exposed, spewing radioactive material into the atmosphere. "Firefighters attempted to put out a series of blazes at the plant, and eventually helicopters dumped sand and other materials in an attempt to squelch the fires and contain the contamination. Despite the death of two people in the explosions, the hospitalization of workers and firefighters, and the danger from fallout and fire, no one in the surrounding areas-including the nearby city of Pripyat, which was built in the 1970s to house workers at the plant-was evacuated until about 36 hours after the disaster began. "Publicizing a nuclear accident was considered a significant political risk, but by then it was too late: The meltdown had already spread radiation as far as Sweden, where officials at another nuclear plant began to ask about what was happening in the USSR. After first denying any accident, the Soviets finally made a brief announcement on April 28. "Soon, the world realized that it was witnessing a historic event. Up to 30 per cent of Chernobyl's 190 metric tons of uranium was now in the atmosphere, and the Soviet Union eventually evacuated 335,000 people, establishing a 19-mile-wide 'exclusion zone' around the reactor. "At least 28 people initially died as a result of the accident, while more than 100 were injured. The United Nations Scientific Committee on the Effects of Atomic Radiation has reported that more than 6,000 children and adolescents developed thyroid cancer after being exposed to radiation from the incident, although some experts have challenged that claim. "International researchers have predicted that ultimately, around 4,000 people exposed to high levels of radiation could succumb to radiation-related cancer, while about 5,000 people exposed to lower levels of radiation may suffer the same fate. Yet the full consequences of the accident, including impacts on mental health and even subsequent generations, remain highly debated and under study. "What remains of the reactor is now inside a massive steel containment structure deployed in late 2016. Containment effo
DIRAC'S CLASSIC TEXTBOOK ON QUANTUM MECHANICS. First edition, and a fine copy with the dust-wrapper, of Dirac's famous and hugely influential textbook, which "summarized the foundations of a new science, much of which was his own creation. It expressed the spirit of the new quantum mechanics, creating a descriptive language that we still use" (Brown, p. 381). "Physicists immediately hailed it a classic. Nature published a rhapsodic review by an anonymous reviewer who - to judge by the eloquence and sharp turn of phrase - may well have been Eddington. The author made clear that this was no ordinary account of quantum mechanics: '[Dirac] bids us throw aside preconceived ideas regarding the nature of phenomena and admit the existence of a substratum of which it is impossible to form a picture. We may describe this as the application of 'pure thought' to physics, and it is this which makes Dirac's method more profound than that of other writers.' The book eclipsed all the other texts on quantum mechanics written at about the same time - one by Born, another by Jordan - and became the canonical text on the subject in the 1930s. Pauli warmly praised it as a triumph and, although he worried that its abstraction rendered the theory too distant from experiment, described the books as 'an indispensable standard work.' Einstein was another admirer, writing that the book was 'the most logically perfect presentation of quantum theory.' The Principles of Quantum Mechanics later became Einstein's constant companion: he often took it on vacation for leisure reading and, when he came across a difficult quantum problem, would mutter to himself, 'Where's my Dirac?'" (Farmelo, p. ?). The Nobel laureates "Abdus Salam and Eugene P. Wigner declared in their preface of a book commemorating Dirac's seventieth birthday that: 'Posterity will rate Dirac as one of the greatest physicists of all time. The present generation values him as one of its great teachers - teaching both through his lucid lectures as well as through his book The Principles of Quantum Mechanics. This exhibits a clarity and a spirit similar to those of the Principia written by a predecessor of his in the Lucasian Chair in Cambridge . Dirac has left his mark, not only by his observations . but even more by his human greatness . He is a legend in his own lifetime and rightly so'" (Brown, p. 381). Although not a rare book on the market, copies of the first edition of Dirac's Principles in such fine condition as ours are rare - indeed, this copy hardly seems to have been opened - most copies having been studied closely by their owners. "Although not well known to the general public, Paul Adrian Maurice Dirac hardly needs to be introduced to physicists and historians of science. Born in Bristol in 1902 as a Swiss citizen - his father was Swiss and Paul only acquired British nationality in 1919 - he became one of the most important theoretical physicists ever. His impact on modern physics may even have been greater than that of Einstein. Young Dirac made his first breakthrough in the fall of 1925 when he developed his own version of quantum mechanics known as q-number algebra, and over the next few years he established himself as a leading expert in the new quantum physics. In 1927-28 he made pioneering contributions to quantum statistics (Fermi-Dirac statistics), quantum electrodynamics, and relativistic quantum theory. The linear and relativistically-invariant wave equation for the electron that he published in early 1928 not only explained the electron's spin and magnetic moment, but also, three years later, led to the prediction of antielectrons (positrons) and antiparticles more generally. "Dirac's genius was recognized early on. For example, he was part of the exclusive company of physicists invited to the famous Solvay conference in 1927. In 1930, at the unusually young age of 27, he was elected a fellow of the prestigious Royal Society, and the same year he published his monumental Principles of Quantum Mechanics. Two years later he was appointed Lucasian Professor of mathematics at Cambridge University, the chair once held by Isaac Newton and later by Stephen Hawking. Another high point of Dirac's career came in 1933, when he was awarded the Nobel Prize in physics, sharing it with Erwin Schrödinger. Although Dirac's scientific fame is closely linked to his fundamental contributions to quantum theory, and especially to those of the period 1925-34, he also dealt with other subjects, including cosmology, classical electron theory, and the general theory of relativity. Moreover, the influence of his ideas extended beyond physics, especially to mathematics (e.g. the Dirac Î -function, Dirac matrices, and Dirac operators). Paul Dirac remained Lucasian Professor until his retirement in 1969, when he joined the physics department of Florida State University in Tallahassee. He died in 1984, and in 1995 a commemorative stone carrying his name and equation was unveiled at a ceremony in Westminster Abbey. "While still a Ph.D. student [at Cambridge], under the supervision of Ralph Fowler, Dirac was assigned to lecture on the new and exciting developments in quantum theory. The first course ever on quantum mechanics at a British University was given in the Easter term of 1926 . The following year, Dirac started giving a regular course on quantum mechanics, which he would continue to do until the 1960s" (Kragh (2013), pp. 249-250). "Since the fall of 1927, Dirac had given a course of lectures on quantum mechanics at Cambridge. The content of these lectures formed the basis of his celebrated book The Principles of Quantum Mechanics, the first edition of which was published in the summer of 1930. The book was written at the request of Oxford University Press - and not, remarkably, Cambridge University Press - which was preparing a series of monographs in physics. The general editors of the series were two of Dirac's friends, the Cambridge physicists Fowler a
FERMAT'S WORKS - WITH THE RARE PORTRAIT. First edition, very rare, with the even rarer portrait, and the Blenhiem Palace copy, of the first publication of the most important works of Pierre de Fermat (1601-65), arguably the greatest French mathematician of the seventeenth century (Descartes and Pascal notwithstanding), "the father of the modern theory of numbers and herald of differential calculus and analytic geometry" (Grolier). "Fermat shares with Descartes the innovation of analytical geometry by applying algebra to geometry. He, independently, represented a curve by an equation defining its characteristic properties. He published little but, in the manner of his times, announced his discoveries in letters to other mathematicians. Among his discoveries was a general method of solving questions of maxima and minima, a method he used in 1629 and one in use today. He contributed basic concepts in the theory of numbers and probability" (Dibner). This volume contains, inter alia, Fermat's researches in analytic geometry, the methods of maxima and minima, and his techniques of quadrature, together with his correspondence with Pascal, Frénicle, Gassendi, Mersenne, Roberval and other savants. In analytical geometry Fermat, working quite independently, reached much the same results as Descartes, but his presentation was radically different, based as it was on Viète's algebra. In the theory of maxima and minima, on the other hand, Fermat's and Descartes' methods were similar, despite a war of words between the two men on the subject in 1638. Fermat's correspondence with Pascal laid the foundations of modern probability theory, and his letters to Frenicle make him the undisputed father of the modern theory of numbers. Fermat was reluctant to allow any of his work to appear in print, and only two short works were published in his lifetime, most of his work being confined to his correspondence, personal notes, and to marginal jottings in his copy of the 1621 editio princeps, edited by Claude Bachet, of Diophantus' Arithmetica (the latter famously including his statement of 'Fermat's last theorem'). It was only after Fermat's death that his son, Clément-Samuel (1632-90), was able to make public his father's important mathematical contributions by editing the present work. No large paper copy has been traced in auction records. Provenance: The Blenheim Palace copy sold in the Sunderland Library sale 1882 and bought by Quaritch with their label to front paste-down; Royal Society of Edinburgh with their stamp on title and Quaritch's label. Charles Spencer (1675-1722), third Earl of Sunderland, began collecting in the 1690s and by the time of his death in 1722 had amassed one of the finest private libraries in Europe. Comprising some 20,000 volumes, it was particularly rich in incunables (including numerous works on vellum), Bibles, first editions of the Classics, and fifteenth- and sixteenth-century continental literature. It was located at Sunderland House in Piccadilly, occupying two rooms in the house itself and a further five rooms in a purpose-built library. Following Sunderland's death, the library was inherited by his eldest son Robert, the 4th Earl. After lengthy negotiations he sold the manuscripts to the King of Portugal in 1726. When Robert died in 1729 the Sunderland Library passed to his younger brother Charles Spencer (1706-1758), who succeeded as 5th Earl of Sunderland and inherited the Dukedom of Marlborough on the death of his aunt Henrietta in 1733. Marlborough had the collection moved from London to Blenheim Palace in 1749. The library was dispersed in a series of major sales conducted by Puttick & Simpson between 1881 and 1883. The 13,858 lots brought £56,581, of which around £33,000 was paid by Bernard Quaritch alone. Fermat was born near Toulouse in the south of France. After spending some years in Bordeaux, in 1631 he became councillor of the High Court of Justice in Toulouse, an office he held until his death. He developed an enduring friendship with Pierre de Carcavi, who became his colleague at the Toulouse High Court in 1632. Carcavi transferred to Paris in 1636, where he formed a close acquaintance with the scientific circle gathered around Mersenne, Etienne Pascal and Roberval. Fermat's scientific correspondence with the members of that group begins with a letter to Mersenne a few days after Carcavi's arrival in Paris, continuing until around 1662 when Fermat, perhaps for reasons of ill health, allowed "his Geometry to fall into a deep sleep". This correspondence provided Fermat with his main outside incentive for pursuing his mathematical work, as he never met other leading mathematicians in person, with the exception of one brief encounter with Mersenne. "By the time Fermat began corresponding with Mersenne and Roberval in the spring of 1636, he had already composed his 'Ad locos planos et solidos isagoge', in which he set forth a system of analytic geometry almost identical with that developed by Descartes in the Géométrie of 1637. Despite their simultaneous appearance (Descartes's in print, Fermat's in circulated manuscript), the two systems stemmed from entirely independent research and the question of priority is both complex and unenlightening. Fermat received the first impetus toward his system from an attempt to reconstruct Apollonius' lost treatise PlaneLoci (loci that are either straight lines or circles). His completed restoration ['Apollonii Pergaei libri duo de locis planis restituti,' pp. 12-43], although composed in the traditional style of Greek geometry, nevertheless gives clear evidence that Fermat employed algebraic analysis in seeking demonstrations of the theorems listed by Pappus. This application of algebra, combined with the peculiar nature of a geometrical locus and the slightly different proof procedures required by locus demonstrations, appears to have revealed to Fermat that all of the loci discussed by Apollonius could be expressed in the for
"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, none complete;the Horblit copy (lacking the letterpress title) was offered by H. P. Kraus in Cat. 168 (ca. 1984) for $4200. ESTC locates only seven institutional copies: British Library, Cambridge (2), St Andrews, UCL, Harvard (2), US Naval Academy Nimitz, and Williams College. The Canon is just as rare, ABPC/RBH listing only two copies (2004 & 1958), and ESTC listing five (three in the UK, two in the US). Provenance:I. Ownership inscription at head of title page of "John Hope, Tyninghame, 6 October, 1672". A melancholy provenance: John Hope of Hopetoun (1650-1682) was drowned when HMS Gloucester was wrecked off the coast of Norfolk, carrying the Duke of York (the future James II) to Leith. There are several marginal index notes, apparently in Hope's hand. II. Ownership signature of "I Skene" on blank before title; possibly a descendant of Sir John Skene of Curriehall (1549-1617) and a familial connection, as Skene's widow married Thomas Hope of Craighall (1573-1646). III. Imposing armorial bookplate of Sir John Hope, fourth earl of Hopetoun (1765-1823), army officer. Hope had a long and distinguished military career; in 1793 he served with the 25th Foot (later the King's Own Scottish Borderers), one of the regiments assigned to make up the numbers of marines on board the Mediterranean and Channel fleets of lords Hood and Howe (the supporters of his bookplate are two figures with anchors). Wellington called him "the ablest man in the Peninsular army" (cited in ODNB). "Edmund Gunter was born in Hertfordshire in 1581, educated at Westminster School, and then at Christ Church, Oxford. It is probable that while there he was influenced by Sir Henry Savile's lectures on mathematics. At least it is certain that he soon showed himself to be a mathematician of the first order with a gift for instrumental invention. At the age of twenty-two he gained entrée of the mathematical world in England by a manuscript entitled A New Projection of the Sphere . About the time he became Ma
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 a medal struck in his memory, and another medal in his honour was struck as late as 1814. "He contributed important papers to the Academy of Sciences, one, in 1744, describing for the first time an epidemic of scarlet fever in Sweden, a rather late successor to Sydenham's description of an epidemic of scarlet fever in 1675, and in the same year also he described a case of hyoscyamus poisoning in a boy and drew attention to the mydriatic effect of certain drugs. But by far the most important of his writings was his book on diseases of children, Underrattelser om barnasjuk- domar och deras botemedel (Stockholm, 1765). It was at once recognized as a work of great value . "Rosenstein's outlook is evident from the authorities he quotes. Only once, I think, does he mention the name of any of the ancient writers, and that only to give a synonym for epilepsy used by Hippocrates. His references are to the latest writers, and to recent contributions to scientific societies, and to his own personal observations. Now and again the influence of tradition shows itself, and one realizes how strong is the hold of error when it has been inculcated for centuries. Of the mother's milk he says 'it frees the child from many disorders and makes it acquire her own temper and disposition. Therefore we see that young lions who have sucked a cow or a goat have by this means been as it were tamed; and dogs, on the contrary, who have sucked a she-wolf have become beasts of prey' [quotations are from the English edition of 1776]. In the testing of the breast-milk he has gone little further than Soranus. It is to be tested 'By its consistence because when thin it is always better than when thick: therefore a drop of it on your nail ought easily to run off on inclining it, even on shaking the finger hastily there ought not to remain the least white streak on your nail: By the touch, because not any pain ought to be felt on letting a drop of it fall into the eye: With rennet, for if the milk give
CARDANO'S MATHEMATICAL TREATMENT OF MECHANICS. First edition of Cardano's mathematical treatment of mechanics, the Opus novum, together with the revised, second edition of his Ars Magna (first 1545) - the greatest work of 16th century algebra - and with the first edition of a supplement to that work, the De Aliza Regula, in which Cardano was the first to make use of imaginary numbers. The Opus novum was the first significant work to examine mechanics from a largely mathematical basis. Here he sets out to determine what effect different densities might have on missile trajectories; explores the connection between medical efficacy of drugs and their dosage (a geometric or arithmetic relationship?); and formulates the earliest estimate of the relative densities of air and water. He is thus described by the DSB as being one of the earliest to "apply quantitative methods to the study of physics". "His use of the concept of moment of a force in his study of the conditions of equilibrium in balance and his attempt to determine experimentally the relation between the densities of air and water are noteworthy. The value that he obtained, 1:50, is rough; but it is the first deduction to be based on the experimental method and on the hypothesis that the ratio of the distances traveled by bullets shot from the same ballistic instrument, through air and through water, is the inverse of the ratio between the densities of air and water." Cardano's major work "was the Ars magna, in which many new ideas in algebra were systematically presented. Among them are the rule, today called 'Cardano's rule,' for solving reduced third-degree equations (i.e., they lack the second-degree term); the linear transformations that eliminate the second-degree term in a complete cubic equation (which Tartaglia did not know how to solve); the observation that an equation of a degree higher than the first admits more than a single root; the lowering of the degree of an equation when one of its roots is known; and the solution, applied to many problems, of the quartic equation, attributed by Cardano to his disciple and son-in-law, Ludovico Ferrari. Notable also was Cardano's research into approximate solutions of a numerical equation by the method of proportional parts and the observation that, with repeated operations, one could obtain roots always closer to the true ones. Before Cardano, only the solution of an equation was sought. Cardano, however, also observed the relations between the roots and the coefficients of the equation and between the succession of the signs of the terms and the signs of the roots; thus he is justly considered the originator of the theory of algebraic equations. Although in some cases he used imaginary numbers, overcoming the reluctance of contemporary mathematicians to use them, it was only in 1570, in a new edition of the Ars magna, that he added a section entitled De aliza regula (the meaning of aliza is unknown; some say it means 'difficult'), devoted to the "irreducible case" of the cubic equation, in which Cardano's rule is extended to imaginary numbers. This was a recondite work that did not give solutions to the irreducible case, but it was still important for the algebraic transformations which it employed and for the presentation of the solutions of at least three important problems" (DSB). The first edition of the Ars magna is very rare in commerce. Provenance: Königliche Handbibliothek, Tübingen (ink stamp on title). "In the Opus novum de proportionibus . of 1570 there is much of interest and ingenuity. Some questions of statics are taken up with great insight but the novelty of the work lies in its discussions of problems of motion: the possibility of unifying statics with dynamics or at least of mathematically connecting the two disciplines seems to have captured Cardano's imagination . "Cardano's account of acceleration is wholly Aristotelian; he remarks that in natural motion the body has an appetite to approach some end, whence the end must be good, and therefore the body hastens as it approaches the end. He holds that since the medium is divided and driven aside beneath a falling body, it must force upward with it the neighbouring parts of the medium. Those parts then press in above the body to prevent the formation of a vacuum and in so doing they press down on the body and speed its motion. To this concept of antiperistasis he then adds that in both violent and natural motions there is an increase in speed at least up to some point, by which he explains the need in war machines for space through which to act in order to increase the violence of their projectiles. In one proposition, acceleration is linked to time, but Cardano's reasoning for this depends again on antiperistasis. "In discussing the motion of projectiles, Cardano asserts that motion in some part of the horizontal (initial) path is uniform, and he says that, as the path turns downward at the end of that part, the projectile is slowed; hence he believes that it will reach the ground later than it would have reached the corresponding point on the initial horizontal line. This idea is consistent with his argument elsewhere that there is always a conflict between motions of different kinds, rather than a simple composition. But despite its overall Aristotelian orthodoxy, Cardano's discussion of projectile motion is of interest because of his clearly expressed view of speed as a ratio of space to time. This concept, inspired by Cardano's algebraic approach to mathematics, was never grasped by Galileo or his contemporaries. "Still more striking is Cardano's classification of motion into three kinds rather than two: natural, violent, and 'voluntary.' Voluntary motion is exemplified by circulation of the celestial spheres around the centre of the universe; other circular motions, for Cardano, are either violent or mixed motions. In voluntary motions, the body as a whole remains in one place. Cardano considers such motio
RARE OFFPRINT OF GAUSS ON THE CALCULUS OF VARIATIONS. First edition, the rare separately-paginated offprint, and a fine copy in original state, of this early contribution of Gauss (1777-1855) to mathematical physics, which contains a fundamental and groundbreaking contribution to the calculus of variations. "Gauss ranks, together with Archimedes and Newton, as one of the greatest geniuses in the history of mathematics" (Printing & the Mind of Man, p. 155). He is best known today for giving the first satisfactory proof of the fundamental theorem of algebra (1799), for Disquisitiones arithmeticae (1801), which revolutionized number theory, and for Disquisitiones generales circa superficies curvas (1828), which laid the foundations of differential geometry. The present work deals with the theory of capillary action, the rise or fall of liquids in narrow tubes, the foundations of which were laid by Thomas Young in 1805, who provided a qualitative theory for surface tension, and by Pierre-Simon Laplace, who mathematically formalized the relationship described by Young a year later. Gauss wrote that Laplace's "investigations, which have found their confirmation in striking agreement with careful experiments, are among the most beautiful enrichments of natural science that we owe to the great mathematician" (translation from p. 2). However, Laplace's theory depended on hypotheses about molecular forces, which were little known at the time, and so open to criticism, by Young among others. "The principle which [Gauss] adopted is that of virtual velocities, a principle which under his hands was gradually transforming itself into what is now known as the principle of the conservation of energy. Instead of calculating the direction and magnitude of the resultant force on each particle arising from the action of neighbouring particles, he formed a single expression which is the aggregate of all the potentials arising from the mutual action between pairs of particles . With its sign reversed it is now called the potential energy of the system . The condition of equilibrium is that this expression shall be a minimum. This condition when worked out gives not only the equation of the free surface in the form already established by Laplace, but the conditions of the angle of contact of this surface with the surface of a solid. Gauss thus supplied the principal defect in the great work of Laplace" (Britannica). To find the conditions under which the potential energy is a minimum, Gauss used the calculus of variations and his own generalization of d'Alembert's 'principle of virtual work'.In the process he created the method for varying double integrals with variable limits, a problem that both Euler and Jacobi had failed to solve. "In 1830 appeared Principia generalia theoriae figurae fluidorum in statu aequilibrii, his one contribution to capillarity and an important paper in the calculus of variations, since it was the first solution of a variational problem involving double integrals, boundary conditions, and variable limits" (DSB). "Gauss had always been interested in physics .[This] is a theoretical paper, not connected to any experiment . one of Gauss's objectives appeared to be to show how much mathematics could contribute to the elucidation and explanation of nature . Principia generalia should be counted among Gauss's work in the calculus of variations. It also contains interesting results in potential theory . it is closely connected to Gauss's other work in this area" (Bühler, pp. 121-3). This is an offprint from Commentationes Societatis Regiae Scientiarum Göttingensis. It was published in Vol. VII (1832), pp. 39-88 of the Commentationes Classis Mathematicae. As was often the case with the Commentationes, articles appeared in offprint form before the publication of the journal, in this case two years before. Gauss offprints are rarely found in original state as here. ABPC/RBH list only two other copies, both in modern bindings (one with library stamps). "Capillary phenomena and their explanation have undergone a considerable change of status in the physical sciences. Whereas the rise or fall of liquids in tubes or the apparent attraction or repulsion of small floating bodies figure only in subordinate chapters in 20th-century textbooks or in specialized monographs, these phenomena claimed a prominent place in general physics from the early 18th well into the late 19th century. An account of capillarity phenomena formed part of Newton's programme, contained in the last Query in the second English edition of his Opticks (1718), to explain chemical, optical and other phenomena related to cohesion in terms of strong, short-range forces between the microscopic constituents of bodies. For James Clark Maxwell in 1870, the study of capillary action helped to smooth 'the path which leads to the development of molecular physics.' The theory of capillarty was indeed, after the kinetic theory of gases, the most intensively cultivated field of 19th-century molecular physics" (Rüger, p. 1202). At the end of the 18th century, "Laplace developed his programme of reducing 'the phenomena of nature . ultimately to action ad distans between molecules'. Optical refraction and capillary action figured as the first applications of 'Laplacian physics'; elasticity, heat, electricity, magnetism and chemical affinities were to follow. "In the first supplement to book 10 of his Mécanique céleste (1806), Laplace calculated the pressure that a curved surface exerts on the column of liquid in a capillary tube. This capillary pressure is proportional to the mean curvature of the meniscus. According to whether the curvature is negative (concave) or positive (convex), the pressure will be smaller or greater than the pressure under a plane liquid surface, and this pressure difference will cause the liquid in the tube to rise above or sink below the level of the plane surface. Laplace's main result was the differential equation fo
First edition, extremely rare offprint issues, with distinguished provenance, of von Neumann's mathematical formulation of the probabilistic interpretation of quantum mechanics, and of the quantum-mechanical measurement problem, together with its application to quantum thermodynamics. The two papers were presented to the Göttingen Academy on the same day, 11 November 1927. "In the course of his formulation of quantum mechanics in terms of vectors and operators of Hilbert space von Neumann also gave in complete generality the basic statistical rule of interpretation of the theory. This rule concerns the result of the measurement of a given physical quantity on a system in a given quantum state and expresses its probability distribution by means of a simple and now completely familiar formula involving the vector representing the state and the spectral resolution of the operator which represents the physical quantity. This statistical rule, originally proposed by Born in 1926, was for von Neumann the starting point of a mathematical analysis of quantum mechanics in entirely probabilistic terms. The analysis, carried out in a paper of 1927 ['Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechanik'], introduced the concept of statistical matrix for the description of an ensemble of systems which are not necessarily all in the same quantum state. The statistical matrix has become one of the major tools of quantum statistics and it is through this contribution that von Neumann's name became familiar to even the least mathematically minded physicists. In the same paper von Neumann also investigates a problem which is still now the subject of much discussion, viz., the theoretical description of the quantum-mechanical measuring process and of the noncausal elements which it involves. Mathematically speaking von Neumann's study of this delicate question is quite elegant. It provides a clear-cut formal framework for the numerous investigations which were needed to clarify physically the all-important implications of quantum phenomena for the nature of physical measurements, the most essential of which is Niels Bohr's concept of complementarity. The results of the [first] paper were immediately used by the author to lay the foundation for quantum thermodynamics ['Thermodynamik Quantenmechanischer Gesamtheiten']. He gave the quantum analogue of the well-known classical formula for the entropy" (van Hove, pp. 97-98). "That von Neumann has been 'par excellence' the mathematician of quantum mechanics is as obvious to every physicist now as it was a quarter of a century ago. Quantum mechanics was very fortunate indeed to attract, in the very first years after its discovery in 1925, the interest of a mathematical genius of von Neumann's stature. As a result, the mathematical framework of the theory was developed and the formal aspects of its entirely novel rules of interpretation were analyzed by one single man in two years time (1927-1929). Conversely, one could almost say in reciprocity, quantum mechanics introduced von Neumann into a field of mathematical investigation, operator theory, in which he achieved some of his most prominent successes" (ibid., p. 95). Not on OCLC. Only the Samuel Koslov copies (1996) in auction records. Provenance: front wrappers with the signature of mathematician Aurel Friedrich Wintner (1903-1958) who did important work in probability theory and is considered one of the founders of probabilistic number theory. "By 1926, [David] Hilbert's colleagues [at Göttingen] were contending with a proliferation of developments in physics. Heisenberg's new theory of quantum mechanics had been shown by Max Born to be explicable in terms of matrix methods. Schrödinger, at Zurich, had constructed a wave mechanics which, although it led to the same results as Heisenberg, proceeded from an entirely different basis . As was clear to even lay observers, . these conceptual changes in physics resonated deeply in mathematics. In physics, the theory of relativity cast doubt upon many concepts that were central to classical mechanics, such as absolute space and time, and simultaneity, and quantum theory threw mechanistic determinism into question, by demonstrating the impossibility of knowing simultaneously both the position and velocity of a particle, necessary to predicting its future evolution . The first phase of quantum physics had indicated the 'discontinuous character of all micro-events' with energy states of complex structures such as atoms and molecules being seen to consist of a set of discrete values, and to 'jump' from one state to another. The second phase, centered on Born's interpretation of the wave equation, suggested that the basic laws of physics were probabilistic laws, allowing for only statistical predictions. Classical determinism, which had been central to Western scientific culture for more than a century, had been shattered. "Working initially with Hilbert's assistant, [Lothar] Nordheim, von Neumann entered mathematical physics in this, the second phase, beginning with the axiomatisation of Heisenberg's work, and elaborating a mathematical basis for quantum mechanics in Hilbert space" (Leonard, pp. 52-53), contained in his paper 'Mathematische Grundlagen der Quantenmechanik' (pp. 1-57 of the same journal volume as the offered papers). "In another paper the same year ['Thermodynamik Quantenmechanischer Gesamtheiten'], he pushed this probabilistic interpretation in physics further, introducing an idea that remained important in the literature - that of a statistical matrix describing an ensemble of systems of different quantum states. He also broached the question of how to construct a mathematical formalism that would provide an adequate theoretical description of the observation process in quantum mechanics, in which the relationship between the observer and the subatomic phenomenon being observed took on special importance. When a measuring instrument was coupled to
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 published in 1693), which contained Roberval's independent discovery of the method of tangents, a precursor to the differential calculus. Du Verdus was a correspondent of many of the leading European savants, including Evangelista Torricelli whom he met in Rome in 1644; while there he communicated Torricelli's ideas on the vacuum to Marin Mersenne. "With Du Verdus [Thomas] Hobbes seems to have been particularly close. When Hobbes came to write his autobiography it was addressed to 'this candid friend,who knew his ways so well.' While in France he seems to have thought at one pint of remaining permanently in exile and going to stay with Du Verdus in Languedoc. Both men always professed the highest regard for each other; this was to lead Du Verdus to translate one of Hobbes' works, the De Cive; it was to lead Hobbes to dedicate one of his own works to Du Verdus, the mathematical Examinatio et Emendatio" (Skinner). This copy of Six erreurs was probably given to Du Verdus by Desargues - both men were members of Mersenne's circle; Du Verdus became one of the leaders of its successor, the Montmor Academy. Little is known of Desargues' early life. He was born in Lyons in 1591, the youngest son in a large family. It is probable that, some time in the late 1620s, he was employed as an engineer by Cardinal Richelieu. We know that, about 1630, Desargues entered the cadre of savants with whom Marin Mersenne (1588-1648) surrounded himself. This gave Desargues ready access to the leading ideas of his time. Desargues' first publication, and the only one not devoted to geometry and its applications, Un méthode aisée pour apprendre et enseigner a lire et escrire la musique, appeared in Mersenne's monumental Le Harmonie Universelle (1635-36). "At approximately this time (1631-36), Desargues began to tutor the young Blaise Pascal (1623-62) in geometry . That Desargues was now actively engaged in geometry is indicated by his 1636 publication of an Example de l'une des manières universelle
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