Sophia Rare Books Flæsketorvet 68, 1711 København V, Denmark Tel: (+45)27628014 Fax: (+45) 69918469 www.sophiararebooks.com

(The descriptions in this list are abbreviated; full descriptions are available)

Stand no. A-22 Paris International Antiquarian Book Fair 25-28 April 2013

Astronomy ...... 8, 13, 23 Chemistry ...... 15, 30, 31 Computing, Information Theory ...... 3, 40, 41 Electricity, magnetism ...... 4, 9 Geometry ...... 1, 2, 3, 27, 36, 37 Mathematics ...... 1, 2, 3, 10, 12, 21, 22, 23, 24, 25, 27, 36, 37 Mechanics, machinery, technology ...... 33 Medicine, Biology ...... 14, 26, 38 Optics...... 11 Probability, Statistics ...... 28, 34 Physics ...... 5, 6, 7, 9, 10, 12, 15, 16, 17, 18, 19, 20, 24, 29, 32, 35 PMM*, Dibner, Horblit, Evans, Sparrow ...... 1, 4, 12*, 14*, 15*, 20*, 21, 29*, 30*, 35*, 36* Special copies, inscribed, provenance ...... 7, 17, 18, 23, 24, 31, 36, 37 20th century science ...... 7, 16, 17, 18, 19, 20, 25, 26, 29, 32, 35, 39, 40, 41 ‘One of the greatest scientific books of antiquity’ (Stillwell). 1. APOLLONIUS of Perga. Opera, Libri I-IV. Venice: Bernardinus Bindonus, 1537. €48,000 Very rare editio princeps of Apollonius’ Conics, the basic treatise on the subject, “which recognized and named the ellipse, parabola, and hyperbola” (Horblit 4, on the later edition of 1566). This is one of the three greatest mathematical treatises of antiquity, alongside those of Euclid and Archimedes. This first edition is very rare, preceding by 29 years the Commandino edition of the same four books canonized by Horblit (and taken over by Dibner and Norman), and this edition is known to have been used by Tartaglia, Benedetti and, however critically, Maurolico. Books I-IV were the only ones to survive in the original Greek; Borelli discovered Arabic versions of books V-VII and published them, in Latin translation, in 1661 (see item 2). “Apollonius (ca. 245-190 BC) was the last of the great Greek mathematicians, whose treatise on conic sections represents the final flowering of Greek mathematics” (DSB). Only five copies located in America (Harvard, Louisville, MIT, UNC, Yale).

❧Horblit 4; Dibner 101; Norman 57 (citing the 1566 edition); Stillwell 139; Honeyman 117; De Vitry 27.

Large-paper copy, uncut in the original wrappers 2. APOLLONIUS of Perga. Conicorum lib. V. VI. VII. Florence: Cocchini, 1661. €9,500 Editio princeps of books V-VII of the Conics, the most original parts of Apollonius’s treatise on conic sections. Books I-IV were translated and published in 1537 (see item 1), and at the time it was believed that the remaining books were lost. “In the first half of the seventeenth century the Medici family acquired an Arabic manuscript containing Books V-VII of Apollonius’s Conics, which had been lost up to that time. In 1658, with the help of the Maronite scholar Abraham Ecchellensis, Giovanni Borelli prepared an edited Latin translation of the manuscript, which was published three years later. This was a valuable addition to the mathematical knowledge of the time, for whereas Books I-IV of the Conics dealt with information already known to Apollonius’s predecessors, Books V-VII were largely original. Book V discusses normals to conics and contains Apollonius’s proof for the construction of the evolute curve; Book VI treats congruent and similar conics and segments of conics; Book VII is concerned with propositions about inequalities between various functions of conjugate diameters” (Norman). “The fifth book reveals better than any other the giant intellect of its author. Difficult questions of maxima and minima, of which few examples are found in earlier works, are here treated most exhaustively. The subject investigated is to find the longest and shortest lines that can be drawn from a given point to a conic. Here are also found the germs of the subject of evolutes and centres of osculation” (Cajori, A History of Mathematics).

The sheets of our copy measure 368 x 255 mm, significantly larger than all other copies of which we have been able to find descriptions.

❧Norman 58; Honeyman 119; De Vitry 29. Containing a detailed account of how to make Galileo’s geometrical compass 3. ARDÜSER, Johann. Geometriae, theoricae et practicae. Zürich: Bodmer, 1627. €12,000 Very rare first edition, and a fine copy, “of one of the fullest German works on surveying” (Zeitlinger), containing an early and highly detailed account of how to make Galileo’s geometrical compass. This work on geometry, surveying, geometric instruments, mathematical tables, map making etc., gives a full account of the mathematical and geometrical practice in central Europe in the early seventeenth century. Johann Ardüser, highly esteemed by his contemporaries, was in charge of the fortifications of Zürich from 1620, and published several works on fortification and geometry. After introductory chapters on Euclidean geometry and arithmetic the author gives a detailed description (with one plate) of the use and construction of the sector (Cirkelleiter) which is based on Galileo’s invention (dessen erfinder Galileo de Galilei von vilen geachtet wird, f. 53 verso). Illustrations of Galileo’s sector, a sort of primitive analog calculating machine, were kept secret by its inventor to protect the ‘copyright’. Until 1640 there was no authorized illustration of Galileo’s compasso. “Galileo’s sector became a calculating instrument capable of solving quickly and easily every practical mathematical problem that was likely to arise at the time” (Drake).

❧Honeyman 137; Kenney 4078.

One of the most important practical texts on magnets in the seventeenth century 4. BARLOW, William. Magneticall Aduertisements: or divers pertinent obseruations, and approued experiments concerning the nature and properties of the Load-stone... most needfull for practise, of trauelling, or framing of Instruments fit for Trauellers both by Sea and Land. London: Griffin for Barlow, 1616. €18,000 First edition of this rare and important work. The result of forty years’ research into magnetism, with special regard to the manufacture and maintenance of the sea-compass, and containing Barlow’s two fundamental discoveries concerning the directional properties of the compass-needle: the first being that steel made a better needle than iron. Secondly, he devised a method for contact ‘touching’ which increased the directional capabilities of needles.

Barlow “designed navigating instruments, polar charts, and compasses. He explained the difference between iron and steel needles; improved the needle’s shape; made an easily removable card so the needle could be easily remagnetized; gave instructions as to the best method of remagnetizing the needle by stroking it with the lodestone three or four times from the needle’s center to the ends, using the north end of the lodestone for the needle’s north end, and the south for the south. He also designed an azimuth compass for measuring the variations which happened to be an improvement on the instrument designed by Norman and Borough; it was a compass with sights and a verge ring marked in degrees, the first such compass, and was to be used by grateful seamen for over two hundred years” (Gurney, Compass, a Story of Exploration and Innovation, New York, 2004 p.64).

❧Horblit 83; Frank Streeter 19; Penrose 19; Wheeler Gift 89. The six papers in which Becquerel first announced his discoveries on radioactivity 5. BECQUEREL, Antoine Henri. €3,500 1) Sur les radiations émises par phosphorescence; 2) Sur les radiations invisibles émises par les corps phosphorescents; 3) Sur quelques propriétés nouvelles des radiations invisibles …; 4) Sur les radiations invisibles émises par les sels d'uranium; 5) Sur les propriétés différents des radiations invisibles émises …; 6) Émission de radiations nouvelles par l'uranium métallique. Paris: Gauthier-Villars, 1896. First edition.

A very fine copy, in original wrappers, of the Comptes Rendus volume in which Becquerel first announced his discoveries on radioactivity. “On 24 February 1896, Becquerel announced to the French Academy of Sciences that fluorescent crystals of potassium uranyl sulfate had exposed a photographic plate wrapped in black paper after both had lain for several hours in direct sunlight, and on 3 March, he reported similar exposures after both crystals and plate had been kept together in total darkness. In the following two months, Becquerel determined that only crystals containing uranium emitted the penetrating rays, that non-luminescent compounds of uranium also produced radiation, and that the rays were capable of ionizing gases. On 18 May, he reported that a disc of pure uranium produced penetrating radiation three to four times stronger than that produced by the potassium uranyl sulfate crystals. In 1903 Becquerel shared the Nobel Prize for physics with the Curies, as his investigations had opened the way for the Curies’ discovery of radium and polonium.” (Norman).

❧Grolier/Medicine 84a; Norman 157.

Inscribed copy of his doctoral thesis 6. BECQUEREL, Antoine Henri. Recherches sur l'absorption de la lumiere. Paris: Gauthier-Villars, 1888. First edition. €12,000 Presentation copy of his doctoral thesis on the absorption of light in crystals, inscribed by Becquerel to his demonstrator Peignot. “On March 15, 1888 he submitted his thesis ‘Recherches sur l’absorption de la lumière’ (Research on the absorption of light). Antoine Henri had been interested in the absorption of light by crystals since 1886 and showed the importance of crystal symmetry in the absorption spectra of polarized light. He noticed that tetravalent uranium compounds were not phosphorescent, whereas uranyl salts exhibited a bright luminescence under the same conditions of excitation. Interestingly enough this was the second experiment performed by a Becquerel on uranium. Like his father, Antoine Henri was fascinated by the phenomenon of phosphorescence, and at the time nobody suspected the secret hidden in the mysterious element. This strange coincidence might be regarded as a premonitory sign of destiny or as the first step towards a major discovery.” (Adloff: 100 Years after the Discovery of Radiochemistry, p.5).

❧Norman 156 [Norman copy with anonymous inscription]. Bohr’s principle of complementarity, inscribed offprint 7. BOHR, Niels. Das Quantenpostulat und die neuere Entwicklung der Atomistik. Berlin: Julius Springer, 1928. First edition. €17,500 Very rare offprint issue, inscribed presentation copy, of this fundamental paper introducing Bohr’s statement of his ‘complementarity’ principle, the basis of what became known as the ‘Copenhagen interpretation’ of quantum mechanics. “From the epistemological point of view, the discovery of the new type of logical relationship that complementarity represents is a major advance that radically changes our whole view of the role and meaning of science. In contrast with the nineteenth-century ideal of a description of the phenomena from which every reference to their observation would be eliminated, we have the much wider and truer prospect of an account of the phenomena in which due regard is paid to the conditions under which they can actually be observed - thereby securing the full objectivity of the description” (DSB). “The complementarity principle became the cornerstone of what was later referred to as the Copenhagen interpretation of quantum mechanics. Pauli even stated that quantum mechanics might be called ‘complementarity theory’, in an analogy with ‘relativity theory’. And Peierls later claimed that ‘when you refer to the Copenhagen interpretation of the mechanics what you really mean is quantum mechanics’ ... by the mid-1930s Bohr had been remarkably successful in establishing the Copenhagen view as the dominant philosophy of quantum mechanics.” (H. Kragh, Quantum Generations).

‘The most significant treatise between Kepler and Newton’ 8. BOULLIAU, Ismael. Astronomia philolaica. Paris: Simeonis Piget, 1645. €16,000 First edition, very rare, of “the first treatise after Kepler’s Rudolphine Tables to take elliptical orbits as a basis for calculating planetary tables” (The Cambridge Companion to Newton), and the first astronomical work to state that the planetary moving force “should vary inversely as the square of the distance—and not, as Kepler had held, inversely as the first power” (Boyer in DSB). “He claimed that if a planetary moving force existed then it should vary inversely as the square of the distance (Kepler had claimed the first power): ‘As for the power by which the Sun seizes or holds the planets, and which, being corporeal, functions in the manner of hands, it is emitted in straight lines throughout the whole extent of the world, and like the species of the Sun, it turns with the body of the Sun; now, seeing that it is corporeal, it becomes weaker and attenuated at a greater distance or interval, and the ratio of its decrease in strength is the same as in the case of light, namely, the duplicate proportion, but inversely, of the distances that is, 1/d2. “The Astronomia philolaica represents the most significant treatise between Kepler and Newton and it was praised by Newton in his Principia, particularly for the inverse square hypothesis and its accurate tables.” (O’Connor & Robertson).

❧Sotheran I:500 (“This important work according to Newton first mentions the sun’s attraction, which decreases in inverse proportion to its distance”); Favaro, Bibliografia Galileiana #205. The first recognition of electrical repulsion 9. CABEO, Niccolo. Philosophia Magnetica. Ferrara: Francesco Suzzi, 1629. First edition. €12,000 “The first Italian book on magnetism and electricity, and only the second to be published on these subjects, the De Magnete (London, 1600) by William Gilbert being the first. The important discovery of electrical repulsion is here first announced (p. 194), and this phenomenon was later systematically investigated by Otto von Guericke in his Experimenta Nova (Amsterdam, 1672) (see item 27). Electrical repulsion ‘seems to have been noticed incidentally by Cabeus, who … describes how filings attracted by excited amber sometimes recoiled to a distance of several inches after making contact’ (Wolf, I, 303). Cabeo (1585-1650) taught mathematics and theology in Parma for many years and later settled in Genoa, where he taught mathematics. This work … describes many experiments on the possibility of telegraphic communication by means of magnetized needles and gives the first picture of the sympathetic telegraph, which fancifully anticipates the actual telegraph.” (Neville).

❧Wheeler Gift 97; Neville 232; Jesuit Science in the Age of Galileo 14.

With an original contribution by Fermat 10. CASTELLI, Benedetto. Traicté de la mesure des eaux courantes. Castres: F. Barcouda, 1664. €25,000 Rare first edition in French of two works which founded the modern science of hydraulics, and including an original contribution by Fermat which appears here for the first time. Only one other scientific work of Fermat was published in his lifetime. The second work has a preface by the translator Saporta addressed to Fermat. Fermat had prompted Saporta to undertake the translation as a sequel to that of Castelli. The last four pages of the book contain the ‘Observation sur Synesius’ which in translation begins as follows: “The pages which remain empty in this quire made me think of filling them with the splendid observation which I learned some days ago from the incomparable M. Fermat, who does me the honor of being my friend and of frequently talking with me. It is in the fifteenth letter of Synesius, Bishop of Cyrene, which deals with something not understood by any of his commentators, not even by the learned Father Petau, as he himself avows in his notes on this author. I give this observation even more willingly as it has much in common with the treatises here printed.” The ailing Synesius (378-430 AD) wrote in 402 to his friend and teacher Hypatia asking for an instrument he called a hydroscopium or baryllion, and provided detailed instructions as to its construction. When the works of Synesius were published by the Jesuit theologian Denis Petau (1583- 1652) in 1640, Petau confessed that he was unable to understand Synesius’s letter. Castelli asked Fermat for his opinion, and the latter’s response was published as the ‘Observation sur Synesius’. Fermat showed that the instrument described by Synesius was a hydrometer, used to measure the specific gravities of liquids, and he gives a detailed description of its construction, with a diagram. The only other scientific work of Fermat to be published in his lifetime was De linearum curvarum, which appeared as an appendix to Antoine de Lalouvere’s Veterum geometrica promota (1660). The most exhaustive treatise on lens making in the seventeenth century 11. CHERUBIN d’Orléans, Capuchin. La dioptrique oculaire, ou la théorique, la positive, et la mechanique de l’oculaire dioptrique en toutes ses espèces. Paris: Jolly and Benard, 1671 [1670]. €15,000 A very fresh and clean copy, without the browning that usually affects this work, of “the most exhaustive treatise on lens making in the seventeenth century. It is a six-hundred folio page long, comprehensive, cogently-argued treatise on telescope making. It contains an impressive amount of theoretical and practical, first-hand information on all of its facets — from explanations of the telescope’s working principles, to descriptions of lens grinding and polishing, to rules for the right distances between lenses, to methods to find the right apertures, to descriptions of the shapes and articulations of the wooden parts and bolts and screws needed to properly point a telescope to the skies, to the construction of tubes, and so on and so forth. The basic notions and axioms come from Kepler, including the approximate refraction law for angles of incidence no greater than 30º … (pp. 8 & 25). To Kepler’s results about the focus of convex lenses and meniscus, d’Orleans adds a few new results, but not a full treatment of the problem. He takes into consideration only the focus of radiation parallel to the axis of the lens. For it he finds the focal distance for a planoconvex lens, a biconvex symmetrical lens, a biconvex meniscus with two general radius of convexity, and a concavo-convex meniscus whose surfaces have two general radii. He also improves Kepler’s results about the focus of two contiguous equal convex lenses. D’Orleans also takes up in full Kepler’s understanding of magnification, his procedure to measure it, and his explanations for the inversion of the image (pp. 11-13 & 158) …” (Albert et al, The Origins of the Telescope, pp. 289-291).

The copy of Carl Friedrich Gauss 12. CHLADNI, Ernst Florens Friedrich. Entdeckungen über die Theorie des Klanges. Leipzig: Weidmanns Erben und Reich, 1787. First edition. €5,500 A fine copy, with the most distinguished possible provenance, of the book which established the scientific study of acoustics. “The production of sound from solid bodies was not clearly understood until Chladni devised the method of sand figures to illustrate the structure of vibrations in a solid body. He spread sand over glass and copper plates and drew a violin bow over their edges, causing the plates to vibrate; the sand, agitated by vibrations, collected over the nodal curves where no motion occurred. Chladni then classified the sand figures according to geometrical shape and noted for each the corresponding pitch, thus demonstrating that the patterns and sounds of a vibrating plate are analogues of the shapes and tones of the modes in the harmonic series. The strange and beautiful ‘Chladni figures,’ first described in the above work, attracted much scientific attention in the early nineteenth century, inspiring fruitful investigation of the mathematics of elastic vibration.” (Norman). This copy is from the personal library of Gauss. It was sold as a duplicate in 1951 by the Göttingen State and University Library, at which time it passed into private hands.

❧Dibner 150; PPM 233a; Sparrow 39; Norman 480. One of the great landmarks in the history of scientific thought 13. COPERNICUS, Nicolaus. Astronomia instaurata, libris sex comprehensa, qui de revolutionibus orbium coelestium inscribuntur. Nunc demum post 75 ab obitu authoris annum integritati suae restituta, notisque illustrata, opera & studio D. Nicolai Mulerii. Amsterdam: Willem Blaeu, 1617. €45,000 The important third edition, published by Tycho Brahe’s student Blaeu shortly after it was condemned. Copernicus’s De revolutionibus was first printed in 1543 and subsequently in 1566. This edition, however, is the first to contain a commentary; it was extensively corrected and annotated by Mulerius, and includes (for the first time) Copernicus’s biography. “This edition, much improved over the previous two remained the standard edition until the nineteenth century.” (Van Berkel, et al, A history of science in the Netherlands, p.35). “The publication of ‘On the Revolutions of the Celestial Spheres’ in 1543 was a landmark in human thought. It challenged the authority of antiquity and set the course for the modern world by its effective destruction of the anthropocentric view of the universe.” (Printing and the Mind of Man).

❧Cinti 58; De Caro 72; Honeyman 756.

PMM 276 – Comparative Anatomy 14. CUVIER, Georges. Le Règne Animal Distribué D’Après Son Organisation, Pour Servir De Base À L’Histoire Naturelle Des Animaux Et D’Introduction À L’Anatomie Comparée. Paris: Deterville, 1817. €5,400 A beautiful set in fine contemporary French calf. “The most influential exposition of the typological approach to animal classification, representing the greatest body of zoological facts that had yet been assembled; it served as the standard zoological manual for most of Europe during the first half of the nineteenth century” (Norman). “Using the taxonomic system that he had introduced in 1812 in his memoire ‘Sur un nouveau rapprochement à établir entre les classes qui composent le règne animal,’ Cuvier divided the animal kingdom into four main types or embrachements: Vertebrata, Mollusca, Articulata and Radiata, each with its own subgroups. This represented an attempt at a ‘natural’ classification system, based upon the assumption that the characteristic interrelationship between an animal’s function and structure placed it within an exclusive group (i.e., that species were ‘real’), as opposed to the more artificial systems of the past, which had been based upon single features of species. Cuvier’s view of animal organization led him to an early recognition of balance of nature, both with respect to the functional balance of parts in the individual and the interdependence of groups in the ‘network of nature’.” (Norman).

❧PMM 276; Dibner 195; Sparrow, Milestone 42; Norman 567. The foundation work of atomic theory 15. DALTON, John. A New System of Chemical Philosophy. Manchester: S. Russell for R. Bickerstaff; Russell & Allen for R. Bickerstaff; Executives of S. Russell for G. Wilson, 1808; 1810; 1827. First edition. €50,000 Very rare complete set with all half-titles, uncut in original boards. The rarity of complete sets of this work is well known. In 1921 Sotheran’s described a complete set as being ‘excessively scarce’, and during the past thirty years only a handful of copies have appeared on the market, all inferior to ours: Richard Green 2008 (a made-up set lacking the half-titles); Friedman 2001 (modern bindings); the Freilich-Norman copy 2001/1998 (non-uniform cloth-backed boards); Honeyman 1979 (rebacked and made-up). The copy which comes closest in condition to ours is the Freilich-Norman copy (Sotheby’s 2001, $43,875). However, that copy was bound in three different types of boards (plain grey, blue, and marbled), with the cloth laid over the boards, and the spine labels were hand-lettered. All three parts of our copy are bound in uniform cloth-backed plain grey boards, with the cloth laid under the paper of the boards, and have the original printed spine labels intact.

❧PMM 261, Horblit 22, Dibner 44, Evans 54, Sparrow 47.

The inspiration for Richard Feynman's path-integral formalism 16. DIRAC, Paul Adrien Maurice. The Lagrangian in Quantum Mechanics. Charkow: Technischer Staatsverlag, 1933. First edition. €7,500 Extremely rare offprint of this seminal paper which, in the hands of Richard Feynman, gave birth to the path-integral formulation of quantum mechanics and Feynman integrals. “In the autumn of 1932, [Dirac] found another way of [developing quantum mechanics by analogy with classical mechanics], by generalizing the property of classical physics that enables the path of any object to be calculated, regardless of the nature of the forces acting on it. [At the heart of this technique are two quantities.] The first, known as the Lagrangian, is the difference between an object’s energy of motion and the energy it has by virtue of its location. The second, the so-called ‘action’ associated with the object’s path, is calculated by adding the values of the Lagrangian from the beginning of the path to its end. In classical physics, the path taken by any object between two points in any specified time interval turns out... to be the one corresponding to the smallest value of the ‘action’... Dirac thought that the concept of ‘action’ might be just as important in the quantum world of electrons and atomic nuclei as it is in the large-scale domain. When he generalized the idea to quantum mechanics, he found that a quantum particle has not just one path available to it but an infinite number, and they are – loosely speaking – centred around the path predicted by classical mechanics. He also found a way of taking into account all the paths available to the particle to calculate the probability that the quantum particle moves from one place to another... Normally, he would submit a paper like this to a British journal, such as the Proceedings of the Royal Society, but this time he chose to demonstrate his support for Soviet physics by sending the paper to a new Soviet journal... Dirac was quietly pleased with his ‘little paper’ and wrote in early November to one of his colleagues in Russia: ‘It appears that all the important things in the classical [...] treatment can be taken over, perhaps in a rather disguised form, into the quantum theory’” (Farmelo). Feynman’s discovery of Dirac’s paper following a chance conversation with Hernert Jehle at Princeton in 1947, and his derivation of the method of path-integrals from it, is described in his own words in his Nobel Prize address. The journal Physikalische Zeitschrift der Sowjetunion is uncommon even in institutional collections (COPAC lists only eight UK holdings). Autograph scientific notes on relativity theory 17. EINSTEIN, Albert. 1 leaf, written on both sides. With certification in the hand of Helen Dukas, Einstein’s longtime secretary: “A. E.’s handwriting. HD.” From the library of historian of physics Jagdish Mehra (1931-2008). [Zürich or Berlin: ca. 1912-1916]. €37,500 A fascinating Einstein manuscript showing the master at work. While most Einstein autograph material on the market is in the form of letters to friends or colleagues, or drafts of papers to be published, the present manuscript gives us a glimpse of Einstein doing what he did best - original research. It clearly illustrates his highly visual way of thinking - as well as mathematical formulas there are several illustrative diagrams. The present manuscript is also earlier than most such material that appears on the market, probably dating from the period 1912-1916 (see below), during which Einstein was intensely involved in the development of general relativity. The calculations employ compact four-dimensional tensor notation, which Einstein began using only by 1912. Dating the manuscript to the years just after 1912 is confirmed by the existence of thematically similar notes in The Collected Papers of Albert Einstein, vol. 4, Doc. 1, sec. 4 (dated 1912-1914), and vol. 6, Doc. 7, p. 58 (dated Oct. 1914-March 1915). It is difficult to be certain about the scientific content of this manuscript - it was intended to be read by no-one other than Einstein himself, so naturally explanations were unnecessary. The use of four-vector notation is most appropriate (indeed essential) in the context of general relativity. The calculations appear to discuss the motion of point particles and the ponderomotive forces arising from pressure gradients and from stresses. In the period when this manuscript was probably composed, such calculations would make most sense in the context of cosmology. Einstein completed the formal development of general relativity in autumn 1915 and was certainly thinking about cosmology in 1916 when he had a series of discussions with Willem de Sitter on the subject (which led to a notorious controversy).

Offprints of the four papers in which Einstein announced his completion and verification of general relativity in November 1915 18. EINSTEIN, Albert. 1. Zur allgemeinen Relativitätstheorie; 2. Zur allgemeinen Relativitätstheorie (Nachtrag); 3. Erklarung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie; 4. Die Feldgleichungen der Gravitation. Berlin: Verlag der Königlichen Akademie der Wissenschaften, 1915. First edition. €36,000 An exceptional collection of the very rare offprint issues - the perihelion-paper furthermore being the copy that Einstein presented to his son Hans Albert. In these four papers, Einstein announced his final breakthrough after ten years of struggling to incorporate gravitation into relativity. Einstein could proudly state in the fourth paper, ‘finally the general theory of relativity is closed as a logical structure’. The celebrated paper Die Grundlage der Relativitätstheorie, published in Annalen der Physik in May 1916, is actually nothing more than a synopsis of the theory presented in these four papers from November 1915.

❧Weil 75, *76, 77. The EPR paradox

19. EINSTEIN, Albert. PODOLSKY, Boris. ROSEN, Nathan. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Lancaster: American Physical Society, 1935. €15,000 Very rare offprint of the famous ‘EPR paper’ - one of the most discussed and debated papers of modern physics, and the foundation for the new fields of quantum computing and cryptography. “In the May 15, 1935 issue of Physical Review Albert Einstein co-authored a paper with his two postdoctoral research associates at the Institute for Advanced Study, Boris Podolsky and Nathan Rosen. The article was entitled ‘Can Quantum Mechanical Description of Physical Reality Be Considered Complete?’ Generally referred to as ‘EPR’, this paper quickly became a centerpiece in the debate over the interpretation of the quantum theory, a debate that continues today. The paper features a striking case where two quantum systems interact in such a way as to link both their spatial coordinates in a certain direction and also their linear momenta (in the same direction). As a result of this ‘entanglement’, determining either position or momentum for one system would fix (respectively) the position or the momentum of the other. EPR use this case to argue that one cannot maintain both an intuitive condition of local action and the completeness of the quantum description by means of the wave function.” (Stanford Encyclopedia of Philosophy). “The EPR paradox inspired many authors afterwards; in particular, discussion emerged on the revival of the hidden parameter idea by David Bohm and others after the early 1950’s. John Bell’s analysis of the situation in the 1960’s showed that hidden variables resulted in an inequality (for the ‘local condition’) which could be tested by experiment and was found not to be satisfied.” (Pais: Twentieth Century Physics, I, p.229). Technologies relying on quantum entanglement are now being developed. In quantum cryptography, entangled particles are used to transmit signals that cannot be eavesdropped upon without leaving a trace. In quantum computation, entangled quantum states are used to perform computations in parallel, which may allow certain calculations to be performed much more quickly than they ever could be with classical computers.

❧Weil *195.

PMM 408 – General Relativity 20. EINSTEIN, Albert. Die Grundlage der allgemeinen Relativitätstheorie. Leipzig: Johann Ambrosius Barth, 1916. First edition, first printing, journal issue. €12,000 A fine copy in unrestored wrappers, as it originally appeared in the May issue of Annalen der Physik. “This paper was the first comprehensive overview of the final version of Einstein’s general theory of relativity after several expositions of preliminary versions and latest revisions of the theory in November 1915. It includes a self-contained exposition of the elements of tensor calculus that are needed for the theory” (Sauer, Landmark Writings in Western Mathematics). “Whereas Special Relativity had brought under one set of laws the electromagnetic world of Maxwell and Newtonian mechanics as far as they applied to bodies in uniform relative motion, the General Theory did the same thing for bodies with the accelerated relative motion epitomized in the acceleration of gravity. But first it had been necessary for Einstein to develop the true nature of gravity from his principle of equivalence...Basically, he proposed that gravity was a function of matter itself and that its effects were transmitted between contiguous portions of space-time… In addition, gravity affected light...exactly as it affected material particles. Thus the universe which Newton had seen, and for which he had constructed his apparently impeccable mechanical laws, was not the real universe...Einstein’s paper gave not only a correct picture of the universe but also a fresh set of mechanical laws by which its details could be described” (R.W. Clark, Einstein: The Life and Times).

❧Grolier/Horblit 26c; Norman 695; PMM 408; Weil 80. Creation of the Calculus of Variations 21. EULER, Leonhard. Methodus inveniendi Lineas Curvas Maximi Minimive proprietate gaudentes, sive Solutio Problematis isoperimetrici latissimo sensu accepti. Lausanne & Geneve: Bosquet & Socios, 1744. First edition. €11,500

An exceptionally fine copy of “Euler’s most valuable contribution to mathematics in which he developed the concept of the calculus of variations.” (Norman). “This work displays an amount of mathematical genius seldom rivaled.” (Cajori). “The book brought him immediate fame and recognition as the greatest living mathematician.” (Kline). “Starting with several problems solved by Johann and Jakob Bernoulli, Euler was the first to formulate the principal problems of the calculus of variations and to create general methods for their solution. In Methodus inveniendi lineas curvas … he systematically developed his discoveries of the 1730’s (1739, 1741). The very title of the work shows that Euler widely employed geometric representations of functions as flat curves. Here he introduced, using different terminology, the concepts of function and variation and distinguished between problems of absolute extrema and relative extrema, showing how the latter are reduced to the former. (DSB). “Basel had achieved enough glory in the history of mathematics through being the home of the Bernoullis, but she doubled her glory, when she produced Léonard Euler.” (Smith).

❧Horblit 28; Evans 9; Dibner 111; Sparrow 60; Norman 731.

Second only to Euclid’s Elements 22. EULER, Leonhard. Vollständige Anleitung zur Algebra, I-II. St. Petersburg: Kaiserliche Academie der Wissenschaften, 1770. €7,500 First edition of Euler’s great textbook of algebra in its language of composition, preceded only by an extremely rare Russian translation published in 1768-9 by two of his students. “Euler’s Vollständige Anleitung zur Algebra is not only the most popular textbook on elementary algebra, with the exception of Euclid’s Elements it is the most widely printed book on mathematics” (Truesdell). Euler composed his famous ‘Algebra’ in German in 1765-6, soon after his return to St Petersburg from Berlin. He was by then partially blind, and dictated the work to a young valet. Publication of the original German version (as offered here) was, however, delayed until 1770 and thus came to be preceded by a Russian translation by his students Peter Inokhodtsev and Ivan Yudin which was issued in 1768-9. This Russian translation is practically unobtainable; OCLC locates just one copy worldwide. The offered original German edition is also very rare with just two copies being auctioned in the past fifty years.

❧Norman 735; Honeyman 1075; Eneström 387 & 388 An important Gauss manuscript, signed and dated 1800 23. [GAUSS] PFAFF, Johann Friedrich. Programma inaugurale in quo peculiarem differentialia investigandi rationem ex theoria functionum deducit. Helmstedt: J. H. Kühlin, 1788. €65,000 With Gauss’s autograph signature and two geometrical diagrams on front endpaper, and a 12-line mathematical proof in his hand on rear endpaper. Gauss’s own personal copy of the inaugural dissertation of Johann Friedrich Pfaff, who supervised Gauss’s doctoral thesis and was a close personal friend. This is an important Gauss manuscript, signed and dated 1800 by him, and with a mathematical calculation in his hand relating to orbital mechanics, performed at a time when Gauss was deeply involved in the calculation of the orbit of the minor planet Ceres. “In 1801 the creativity of the previous years was reflected in two extraordinary achievements, the Disquisitiones arithmeticae and the calculation of the orbit of the newly discovered planet Ceres” (DSB). The mathematical calculations performed by Gauss at the rear of the present volume are difficult to interpret precisely – they were intended only for Gauss himself so naturally detailed explanations were unnecessary. They are titled Determinatur curva per aequationem inter radios vectores...,” the determination of curves by equations given in polar coordinates (in modern terminology). Moreover, the calculations bear a close resemblance to some of those eventually published in his Theoria motus corporum coelestium (1809), the mature expression of his work on the calculation of planetary orbits. Together with the dating of the manuscript, the conclusion is inescapable that we have here an early expression of Gauss’s thoughts on the determination of orbits, the topic which first brought his genius to the attention of the wider scientific world.

Gauss’s own personal copy 24. GAUSS, Carl Friedrich Allgemeine Lehrsätze in Beziehung auf die im verkehrten Verhältnisse des Quadrats der Entfernung wirkenden Anziehungs- und Abstossungs-Kräfte. Leipzig: Weidmann, 1840. First edition. €30,000 Gauss’s own personal copy, of “the first systematic treatment of potential theory as a mathematical topic, [which] recognized the necessity of existence theorems in that field, and reached a standard of rigor that remained unsurpassed for more than a century” (DSB). In Allgemeine Theorie der Erdmagnetismus, his general theory of terrestrial magnetism, Gauss determined the magnetic force at the earth’s surface by expressing the magnetic potential as the sum of a converging series of spherical functions (Gauss retained only the first few terms as an approximation). “A year after the publication of his general theory of earth magnetism, Gauss published a systematic presentation of the mathematical tool he had used in that work, the potential. Here Gauss formally introduced the term ‘potential’ to designate the function from which the components of forces varying as the inverse square of the distance can be derived. He wrote the function as V = Σ µ/r, which expresses the action at any point of a collection of point ‘masses’ or, in general, ‘agents’, and he developed a collection of theorems concerning the behavior of this function. The significance of V is that its properties are the ‘key to the attracting or repelling forces’ of nature. Potential theory applies to the phenomena of nature described by inverse- square forces between particles, to the phenomena of gravitation, electricity and magnetism. Gauss even considered its application to electrodynamic phenomena, since Ampère’s force between current elements depends on the inverse square of the distance; but the action of this force is complicated by the directionality of currents, and Gauss did not treat it here and only spoke of discussing it in a later paper, which he never did. “Gauss showed that despite the striking differences of the observed phenomena of gravitation, electricity and magnetism, their mathematical description draws on a common body of theorems. Potential theory provided mathematical methods of impressive generality: by studying the behavior of one function, abstracted from any one domain of phenomena, physicists could learn at once the mathematical structures relating the phenomena belonging to several domains. The conservation of energy principle, enunciated soon after Gauss’s potential theory, made the potential an even more important aid in developing physical laws” (Jungnickel & McCormmach, pp. 68-9. ‘The Copernicus of logic’ 25. GÖDEL, Kurt. Ergebnisse eines mathematischen Kolloquiums, unter Mitwirkung von Kurt Gödel und Georg Nöbeling. Herausgegeben von Karl Menger. Heft 1-7. Leipzig & Berlin: B.G. Teubner, 1931-1936. All first editions. €7,500 An absolutely mint set, in the original wrappers, of these rare proceedings to which Gödel contributed fifteen important papers and remarks on the foundations of logic and mathematics. “By invitation, in October 1929 Gödel began attending Menger’s mathematics colloquium, which was modeled 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 coeditor 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).

❧See Dawson’s Bibliography of the Published Works of Kurt Gödel for a detailed account of the fifteen Gödel contributions.

Inscribed offprints of her Nobel papers 26. HODGKIN, Dorothy Mary Crowfoot. Structure of Vitamin B12; The X-ray Crystallographic Investigation of the Structure of Penicillin (together with six other offprints). 1945-65. €9,500 Exceptional collection of inscribed offprints, from the library of crystallographer Jack D. Dunitz, of Hodgkin’s most important papers, in which she solved the molecular structure of penicillin and vitamin B12, the last of which revealed the existence of a hitherto- unsuspected chemical grouping, the corrin nucleus. Lawrence Bragg compared these achievements with ‘breaking the sound barrier’, and in 1964 Hodgkin received the Nobel Prize in Chemistry for this work. Provenance: All items are from the library of Jack David Dunitz, British chemist and one of the greatest chemical crystallographers. Together with Sydney Brenner, Dorothy Hodgkin, Leslie Orgel, and Beryl M. Oughton he was one of the first people in April 1953 to see the model of the structure of DNA, constructed by Francis Crick and James Watson. A turning point in the history of non-Euclidean geometry 27. LAMBERT, Johann Heinrich. Theorie der Parallellinien. Leipzig: 1786. First edition. €12,500 In this paper Lambert was the first to realize “that Euclid’s Parallel Postulate cannot be proved from the other Euclidean postulates and that it is possible to build a logically consistent system satisfying the other postulates but explicitly rejecting the Parallel Postulate” (Parkinson, Breakthroughs, 1766 & 1786). “In the second half of the 18th century, Johann Lambert … wrote a special treatise under the title Theory of parallel lines … In the introductory part of his treatise Lambert write: ‘This work deals with the difficulty encountered in the very beginnings of geometry and which, from the time of Euclid, has been a source of discomfort for those who do not just blindly follow the teachings of others but look for a basis for their convictions and do not wish to give up the least bit of the rigor found in most proofs. This difficulty immediately confronts every reader of Euclid’s Elements, for it is concealed not in his propositions but in the axioms with which he prefaced the first book”. (Rosenfeld, A History of Non- Euclidean Geometry. See pp. 99-101 for a detailed account of Lambert’s treatise). Lambert became interested in the parallel postulate after having heard of Georg Klügel’s dissertation from 1763, in which he had shown the flaws of all proofs so far of the parallel postulate. This inspired Lambert to take up the subject himself. Just as Saccheri had done in 1733, he explored the consequences of adopting the hypothesis of the obtuse angle and that of the acute angle. Like Saccheri, he quickly obtained a logical contradiction in the first case. But unlike Saccheri, Lambert did not accept consequences of the second hypothesis, no matter how absurd or repugnant they seemed, as formal proof of the invalidity of the acute angle hypothesis. Unable to obtain a formal contradiction, Lambert continued to explore the path, on which Saccheri had turned around. Even though hyperbolic geometry was first discovered by Gauss, Lobachevsky, and Bolyai half a century later, Lambert derived several fundamental results belonging to this subject and “no one else came so close to the truth without actually discovering non-Euclidean geometry.” (Boyer, History of Mathematics, pp. 504). This statement is due to the important observation which Lambert made after having discovered the formula for the area of a triangle under the acute angle hypothesis. As he noted, the formula is exactly the same as on the surface of a sphere except for the fact that the radius-term of the sphere must be substituted with the square root of -1. To this Lambert remarked “from this I should almost conclude that the (acute angle) hypothesis holds on the surface of an ‘imaginary’ sphere”. Here Lambert was prevented from discovering hyperbolic geometry only by the insufficient notion of curvature of his time. What Lambert is lacking when he stands on the surface of his ‘imaginary’ sphere is the notion of curvature of a surface developed by Gauss in his Disquisitiones generales circa superficies curvas (1828). Undoubtedly, it would then have been obvious to Lambert that his formula for the area of a triangle is simply Gauss’ area-curvature formula applied to the proper surface of the pseudo-sphere, and that the acute angle hypothesis does hold in the hyperbolic plane.

‘The most influential book on probability and statistics ever written’ 28. LAPLACE, Pierre Simon. Théorie Analytique des Probabilités. Paris: Courcier, 1812. First edition. €22,500 “In the Théorie Laplace gave a new level of mathematical foundation and development both to probability theory and to mathematical statistics. … [It] emerged from a long series of slow processes and once established, loomed over the landscape for a century or more.” (Stephen Stigler: Landmark Writings in Western Mathematics, p.329-30). “Laplace’s great treatise on probability appeared in 1812, with later editions in 1814 and 1820. Its picture of probability theory was entirely different from the picture in 1750. On the philosophical side was Laplace’s interpretation of probability as rational belief, with inverse probability as its underpinning. On the mathematical side was the method of generating functions, the central limit theorem, and Laplace’s technique for evaluating posterior probabilities. On the applied side, games of chance were still evidence, but they were dominated by problems of data analysis and Bayesian methods for combining probabilities of judgments, which replaced the earlier non-Bayesian methods of Hooper and Bernoulli.” (Grattan-Guinness: History and Philosophy of the Mathematical Sciences, p.1301). “It was the first full–scale study completely devoted to a new specialty, … [and came] to have the same sort of relation to the later development of probability that, for example, Newton’s Principia Mathematica had to the later science of mechanics.” (DSB).

❧Evans 12; Landmark Writings in Western Mathematics 24. Discovery of the diffraction of X-rays by crystals – ‘one of the most beautiful discoveries in physics’ (Einstein) 29. LAUE, Max von, Walter FRIEDRICH & Paul KNIPPING. Interferenz-Erscheinungen bei Röntgenstrahlen. [with:] Eine quantitative Prüfung der Theorie für den Interferenz-Erscheinungen bei Röntgenstrahlen. München: F. Straub, 1912. €15,000 Very rare first edition, offprint issue, of Laue’s Nobel Prize-winning papers. X-rays had been in wide use since their discovery in 1895 but their exact nature as electromagnetic waves of short wavelength was first elucidated by Laue and his collaborators in the present papers. “Laue had the crucial idea of sending X-rays through crystals. At this time scientists were very far from having proven the supposition that the radiation that Röntgen had discovered in 1895 actually consisted of very short electromagnetic waves. Similarly, the physical composition of crystals was in dispute, although it was frequently stated that a regular structure of atoms was the characteristic property of crystals. Laue argued that if these suppositions were correct, then the behavior of X-radiation upon penetrating a crystal should be approximately the same as that of light upon striking a diffraction grating” (DSB), an instrument used for measuring the wavelength of light, inapplicable to X-rays because their wavelength is too short. Sommerfeld was initially skeptical but Laue persisted, enlisting the help of Sommerfeld’s experimental assistant Walter Friedrich in his spare time as well as that of the doctoral student Paul Knipping. On April 12, 1912, Friedrich and Knipping succeeded in producing a regular pattern of dark spots on a photographic plate placed behind a copper sulphate cyrstal which had been bombarded with X- rays. “The awarding of the Nobel Prize in physics for 1914 to Laue indicated the significance of the discovery that Albert Einstein called ‘one of the most beautiful in physics.’ Subsequently it was possible to investigate X-radiation itself by means of wavelength determinations as well as to study the structure of the irradiated material. In the truest sense of the word scientists began to cast light on the structure of matter” (DSB). The following year the Prize was granted to the father and son team W. H. and W. L. Bragg for their exploration of crystal structure using X-rays.

❧PMM 406a; Norman 1283.

PMM 238 – A new epoch in chemistry 30. LAVOISIER, Antoine-Laurent de Traité élémentaire de Chimie, présenté dans un ordre nouveau, et d'après les découvertes modernes. Paris: Chez Cuchet, 1789. First edition. €5,800 A fine copy of “one of the great milestones in the history of chemical literature. By common consent modern chemistry begins with this work” (Neville), “which finally freed the science from its phlogiston chains and formed the starting point of its modern progress. It may be said to have done almost as much for chemistry as Newton’s Principia did for physics.” (Zeitlinger). “Lavoisier’s chemical textbook includes the unified exposition of his four most significant contributions to chemistry. These are first, the use of accurate measurements for chemical researches, such as the balance for weight distribution at every chemical change; second, researches on combustion which effectively overthrew the phlogiston theory of Stahl; third, the law of conservation of mass; and fourth, the reform of chemical nomenclature, whereby every substance was assigned a definite name based upon the elements of which it was composed.” (Norman).

❧PMM 238; Grolier/Horblit 64; Dibner 43; Evans 53; Sparrow 127. With the two unpublished plates 31. LAVOISIER, Antoine Laurent. Mémoires de chimie. [Paris: Du Pont, 1792/1805]. €13,500 First edition of this very rare work; copy of the Lavoisier scholar and antiquarian Lucien Scheler, with prints of the two copper plates meant to illustrate the work but never issued, which Scheler and Duveen discovered and described together in the 1950’s (see below), finely bound by Lobstein with a three page manuscript letter by Scheler about the work, together with the original wrappers. We know of just one other copy accompanied by these two plates (Haskell F. Norman). “The collection contains thirty-nine memoirs, twenty-nine by Lavoisier, of which twelve appear here for the first time; the remaining memoirs are by Séguin, Meusnier, Brisson, Vauquelin, Macquart and Fourcroy. The fifth memoir in Vol. II contains Lavoisier’s claim to the discovery of the theory of oxidation” (Norman). The contents of this important and final work by Lavoisier are discussed in detail by Duveen and Klickstein. Provenance: This copy belonged to the Lavoisier scholar and famous antiquarian Lucien Scheler (1902-1999), and is accompanied by a three page letter by him about the work and the two plates bound in with this copy. There are references to illustrations in the Mémoires but no plates accompanied the work when Mme. Lavoisier distributed copies. In 1950 two copper plates were discovered in the addict of Mme P. de Chazelles. Scheler had prints taken of these plates and together with Denis Duveen he published an article describing these hitherto unknown illustrations for the Mémoires. The original copper plates are now, together with 108 prints, at the Lavoisier Archive in Cornell University. ❧Norman 1297; Duveen & Klickstein 186-200; Neville p.17; Thornton & Tully 168.

‘The paper that led to Einstein being awarded the Nobel Prize’ 32. MILLIKAN, Robert Andrews. A Direct Photoelectric Determination of Planck’s “h”. [Lancaster: American Physical Society], 1916. First edition. €4,000 Rare offprint issue of Millikan’s famous determination of Planck’s constant “that led to Einstein being awarded the Nobel Prize for his theory of the photoelectric effect (the citation of Einstein’s prize specifically mentions Millikan’s work), and to the notion of light quanta becoming firmly established as respectable physics.” (Gribbin). “In 1915, Millikan experimentally verified Einstein’s all-important photoelectric equation, and made the first direct photoelectric determination of Planck’s constant h. Einstein’s 1905 paper proposed the simple description of ‘light quanta,’ or photons, and showed how they explained the photoelectric effect. By assuming that light actually consisted of discrete energy packets, Einstein proposed a linear relationship between the maximum energy of electrons ejected from a surface, and the frequency of the incident light. The slope of the line was Planck’s constant, introduced 5 years earlier by Planck. Millikan was convinced that the equation had to be wrong, because of the vast body of evidence that had already shown that light was a wave. If Einstein was correct, his equation for the photoelectric effect suggested a completely different way to measure Planck’s constant. Millikan undertook a decade-long experimental program to test Einstein’s theory by careful measurement of the photoelectric effect, and even devised techniques for scraping clean the metal surfaces inside the vacuum tube needed for an uncontaminated experiment. For all his efforts Millikan found what to him were disappointing results: he confirmed Einstein’s predictions in every detail, measuring Planck’s constant to within 0.5% by his method. … [Millikan] received the Nobel Prize in part for this discovery.” (APS biography of Millikan). ‘The most important book on mechanics published in the sixteenth century’ (Drake) 33. MONTE, Guidobaldo, Marchese Del. Mechanicorum Liber. Pesaro: Hieronymus Concordia, 1577. €15,000 First edition. Monte’s theories were most influential for Galileo’s discoveries in the field of applied mechanics as expressly stated by Galileo in his Discorsi. According to Lagrange (Mécanique analytique, 1811) Monte was the first to apply the theory of momentum to simple machines, and to discover the principle of virtual velocities in the lever and the pulley. “From the time of its publication in 1577 [it was] the most authoritative treatise on statics to emerge since antiquity, and it remained pre-eminent until the appearance of Galileo’s Two New Sciences in 1638. It marks the high point of the Archimedean revival of the Renaissance.” (Rose). The Liber mechanicorum “was regarded by contemporaries as the greatest work on statics since the Greeks. It was intended as a return to classical Archimedean models of rigorous mathematical proof and as a rejection of the ‘barbaric’ medieval proofs of Jordanus de Nemore (revived by Tartaglia in his Quesiti of 1546), which mixed dynamic principles with mathematical analysis.” (DSB). A fine copy with contemporary annotations.

❧Bibliotheca Mechanica 229.

One of the most important landmark works on probability theory 34. MONTMORT, Pierre Rémond de. Essay d'Analyse sur les Jeux de Hazard. Paris: J. Quilau, 1708. €6,500 Rare first edition, first issue (i.e., without plates and with significant textual differences in comparison with the second issue also from 1708 which has plates). Based on the problems set forth by Huygens in his famous treatise De Ratiociniis in Ludo Aleae (1657), it spawned the publication of De Moivre’s two important works De Mesura Sortis (1711) and Doctrine of Chances (1718) as well as Bernoulli’s celebrated Ars Conjectandi (1713). “In 1708 [Montmort] published his work on Chances, where with the courage of Columbus he revealed a new world to mathematicians.” (Todhunter). “The greatest value of Montmort’s book lay perhaps not in its solutions but in its systematic setting out of problems about games, which are shown to have important mathematical properties worthy of further work. The book aroused Nikolaus I Bernoulli’s interest in particular and the 1713 edition includes the mathematical correspondence of the two men. This correspondence in turn provided an incentive for Nikolaus to publish the Ars conjectandi of his uncle Jakob I Bernoulli, thereby providing mathematics with a first step beyond mere combinatorial problems in probability. The work of De Moivre is, to say the least, a continuation of the inquiries of Montmort. Montmort put the case more strongly—he accused De Moivre of stealing his ideas without acknowledgment. De Moivre’s De mensura sortis appeared in 1711 and Montmort attacked it scathingly in the 1713 edition of his own Essay… Pierre Rémond de Montmort (1678-1719) was born into a wealthy family of the French nobility. As a young man he traveled in England, the Netherlands, and Germany. Shortly after his return to Paris in 1699 his father died and left him a large fortune. He studied Cartesian philosophy under Malebranche and studied the calculus on his own. … Montmort corresponded with Leibniz whom he greatly admired. He was also on good terms with Newton whom he visited in London. In 1709 he printed 100 copies of Newton’s De Quadratura at his own expense. As noted earlier, through John Bernoulli, he also offered to print Ars Conjectandi. He was on friendly terms with Nicholas Bernoulli and Brook Taylor.” (Hald, A History of Probability and Statistics and their Applications before 1750). The beginning of quantum theory 35. PLANCK, Max. Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum. Leipzig: Johann Ambrosius Barth, 1900. First edition, first printing. €16,500 A fine copy of the founding document of quantum theory, “marking the dividing line between classical and modern physics” (Norman). In this celebrated first announcement of quantum theory, Planck derived his radiation law based upon the assumption that energy is emitted and absorbed in discrete quanta. “In this important paper he stated that energy flowed not in continuous, indefinitely divisible currents, but in pulses or bursts of action [or quanta]” (Dibner). Planck determined a unit of energy in a system showing a natural frequency and proposed a constant of angular momentum, the value of which is known as ‘Planck's constant.’ This ‘quantum’ of energy led to explanations of the specific heats of solids, the photo-chemical effects of light, the orbits of electrons in the atom, the spectra of Röntgen rays, the velocity of rotating gas molecules, and the distances between the particles of a crystal. “It contradicted the mechanics of Newton and the electromagnetics of Faraday and Maxwell. Moreover it challenged the notion of the continuity of nature” (PMM). Published by the Berlin Physics Society, the first appearance of Planck’s revolutionary work is very rare. (It was later published, in 1901, in the more widely distributed Annalen der Physik).

❧PMM 391, Dibner 166, Horblit 26a, Evans 47, Sparrow 162.

The copy of Pierre Daniel Huet 36. PROCLUS Diadochus. Procli... in primum Euclidis Elementorum librum commentariorum libri IIII. Padua: Perchacino, 1560. €25,000 A magnificent copy, with a very distinguished provenance, of the first Latin edition of Proclus’ commentary on the first book of Euclid’s Elements, edited by Federico Barozzi. The text appeared previously in the Greek Euclid of 1533 (Basel), but lacked illustrations, and contained other deficiencies, remarked upon by Barozzi in the preface to the present edition. Proclus’ commentary can be regarded as the first work on non-Euclidean geometry (Sommerville). It gives a penetrating discussion of Euclid's fifth postulate, also known as the ‘parallel postulate’. He criticizes Ptolemy’s proof of the fifth postulate, and points out with the example of the straight line asymptote to a hyperbola that it is possible for two lines to get closer and closer together without ever meeting. He goes on to show that the parallel postulate is equivalent to what later became known as Playfair’s axion (introduced in John Playfair’s 1795 commentary on Euclid), that ‘Through a given point, only one line can be drawn parallel to a given line’. He then attempts a proof of this new postulate, but his proof is vitiated by his assumption that parallel lines are a bounded distance apart (which can be shown to be equivalent to the parallel postulate). Provenance: Pierre Daniel Huet, Bishop of Avranches with bookplate commemorating his legacy in 1692 to; Jesuit College at Paris, with printed pressmark label XLVII.C, and with label on title-page ‘Ne extra hanc bibliothecam efferatur. Ex obedientia.’; Michel Chasles (bookplate), bought at his sale Paris, 7 July 1881 by; P. Laffite. Bound in sixteenth century red morocco 37. PTOLEMAEUS, Claudius. Clavdii Ptolemaei liber de analemmate. Rome: Paulum Manutius, 1562. €9,500 First edition of Ptolemy’s Analemma, which “explained how to determine the position of the sun at a given moment in any latitude by an orthogonal projection using three mutually perpendicular planes… [The] Analemma [survives], apart from a few palimpsest fragments, only in William of Moerbeke’s Latin translation from the Greek. It is an explanation of a method for finding angles used in the construction of sundials, involving projection onto the plane of the meridian and swinging other planes into that plane. The actual determination of the angles is achieved not by trigonometry (although Ptolemy shows how that is theoretically possible) but by an ingenious graphical technique which in modern terms would be classified as nomographic. Although the basic idea was not new (Ptolemy criticizes his predecessors, and a similar procedure is described by Vitruvius ca. 30 BC), the sophisticated development is probably Ptolemy’s... [As] in the case of Ptolemy’s Planisphere, no Greek text was available to Commandino (a portion was later recovered from a palimpsest); but an Arabic version had been translated into Latin. This was edited from the manuscript by Commandino (Rome, 1562). Besides his customary commentary, he added his own essay On the Calibration of Sundials of various types, since he felt that Ptolemy’s discussion was theoretical rather than practical” (DSB).

Presentation copy 38. RAMÓN Y CAJAL, Santiago. Estudios sobre la degeneración y regeneración del sistema nervosio. Madrid: Hijos de Nicolás Moza, 1913-14. First edition. €12,500 Exceptional presentation copy, the copy of neuroanatomist Jean Nageotte (1866-1948), of the extremely rare first edition of this this classic work on the degeneration and regeneration of nervous tissue by the father of modern neuroscience. “The most complete work on the subject so far written.” (Garrison- Morton 560.1). The preface to the first English edition of 1928 asserts that ‘This book may be considered, without exaggeration, as unpublished in Europe and North America’ since nearly all the copies of the 1913-1914 edition were distributed to South American subscribers. We know of just one other copy (not inscribed by Cajal as here) auctioned in 1995. Cajal presentations are very rare. After having published his Textura (1899-1904) “Ramón y Cajal next turned his attention to the problem of traumatic degeneration and regeneration of nervous structures. He did this in response to what he considered a dangerous revival of the reticularist theory. The main facts had not been in dispute since the work of Waller, Rainier, and others nearly half a century earlier; but there were two schools of thought about precisely how the degenerated peripheral end of the cut axon was restored to structural and functional continuity with its nerve cell. The polygenesists, who earlier had included E. F. A. Vulpian and C. E. Brown-Séquard and whose leader at the time was A. T. J. Bethe, maintained that the regenerated peripheral fibers were the result of progressive transformation and eventual fusion of the Schwann cells which had sheathed the degenerated fibers. The monogenesists, to whom Ramón y Cajal belonged, said that the regenerated fibers were the result of sprouting from the cylinders of the central stump, still in continuity with their nerve cells, and saw their opponents as reviving the reticular theory of nerve continuity in thinly disguised form. Ramón y Cajal, using his reduced silver nitrate method of staining, fully confirmed the monogenesist theory. The results of these researches were collected and published in 1913–1914 as Estudios sobre la degeneración y regeneración del sistema nervioso, still the fullest account of the subject. (D.W. Taylor in DSB). Very rare pre-publication of this hugely influential book 39. SIMON, Herbert A. Administrative Behavior: A Study of Decision-Making Processes in Administrative Organization. Preliminary Edition. Chicago: Illinois Institute of Technology, 1945. €3,600 Preliminary edition of this classic which the Royal Swedish Academy cited as “epoch-making” in awarding the 1978 Nobel Prize in Economics to Simon “for his pioneering research into the decision- making process within economic organizations”. OCLC locates just one copy of this edition (Yale). “Simon’s theories and observations about decision-making in organizations apply very well to the systems and techniques of planning, budgeting and control that are used in modern business and public administration. These theories are less elegant and less suited to overall economic analysis than is the classic profit-maximizing theory, but they provide greater possibilities for understanding and predictions in a number of areas. They have been used successfully to explain and predict such diverse activities as the distribution of access to information and decision-making within companies, market adjustment to limited competition, choosing investment portfolios and choosing a country in which to establish a foreign investment. Modern business economics and administrative research are largely based on Simon’s ideas.” (Nobel Press Release). The first edition was published by Macmillan in 1947; the second, in 1957; the third, in 1976; and the fourth, in 1997. A 1990 article in Public Administration Review named it the “public administration book of the half century” (1940- 1990). It was voted the fifth most influential management book of the 20th century in a poll of the Fellows of the Academy of Management.

The founding paper of communication theory 40. SHANNON, Claude Elwood. A Mathematical Theory of Communication. New York: ATTC, 1948. €9,500 Rare “separate offprint of the most famous work in the history of communication theory” (Norman). Based on research begun during World War II, “Shannon developed a general theory of communication that would treat of the transmission of any sort of information from one point to another in space or time. His aim was to give specific technical definitions of concepts general enough to obtain in any situation where information is manipulated or transmitted - concepts such as information, noise, transmitter, signal, receiver, and message. “At the heart of the theory was a new conceptualization of information. To make communication theory a scientific discipline, Shannon needed to provide a precise definition of information that transformed it into a physical parameter capable of quantification. He accomplished this transformation by distinguishing information from meaning. He reserved ‘meaning’ for the content actually included in a particular message. He used ‘information’ to refer to the number of different possible messages that could be carried along a channel, depending on the message’s length and on the number of choices of symbols for transmission at each point in the message. Information in Shannon’s sense was a measure of orderliness (as opposed to randomness) in that it indicated the number of possible messages from which a particular message to be sent was chosen. The larger the number of possibilities, the larger the amount of information transmitted, because the actual message is distinguished from a greater number of possible alternatives ... “What began as a study of transmission over telegraph lines [by Nyquist and Hartley] was developed by Shannon into a general theory of communication applicable to telegraph, telephone, radio, television, and computing machines - in fact, to any system, physical or biological, in which information is being transferred or manipulated through time or space” (Aspray). ❧Hook & Norman: Origins of Cyberspace 880; Mount & List, Milestones, 65. The Turing test

41. TURING, Alan Mathison. Computing Machinery and Intelligence. Edinburgh: Thomas Nelson & Sons, 1950. First edition. €2,500 A very fine copy, in original wrappers, of Turing’s landmark paper on artificial intelligence. “With the advent of the electronic digital computer came much speculation as to whether or not in processing information these machines were actually thinking. In this paper Turing considered this question from a behavioristic standpoint, proposing an experiment, later called the Turing test, that would allow unbiased comparison of a machine’s ‘thinking behavior’ with that of a normal human being. The test involves two parties, ‘X’ and ‘Y’, who engage in a conversation by teletype. Human X cannot know whether Y is a machine or a person. If X believes that Y is responding like a person after a specified period of time, and Y turns out to be a machine, then that machine may be defined as having the capacity to ‘think.’ From the time he wrote his paper on computable numbers in which he modeled his ‘Turing’ machines after the way people carry out computations, Turing believed that every human thought that could be expressed in language could be mimicked by a universal machine, or computer, if it was suitably programmed. Concerning the future of artificial intelligence, Turing wrote in this paper published in 1950, ‘I believe that in about fifty years’ time it will be possible to program computers with a storage capacity of about 109, to make them play the imitation game so well that an average interrogator will not have more than 70 per cent chance of making the right identification after five minutes of questioning. The original question, ‘Can machines think?’ I believe to be too meaningless to deserve discussion. Nevertheless I believe that at the end of the century the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted’ (p. 442). (Hook & Norman: Origins of Cyberspace, p.467). “Turing's work at Manchester [from 1948 onward] was among the earliest investigations of the use of electronic computers for artificial-intelligence research. He was among the first to believe that electronic machines were capable of doing not only numerical computations, but also general-purpose information processing. He was convinced computers would soon have the capacity to carry out any mental activity of which the human mind is capable. He attempted to break down the distinctions between human and machine intelligence and to provide a single standard of intelligence, in terms of mental behavior, upon which both machines and biological organisms could be judged. In providing his standard, he considered only the information that entered and exited the automata. Like Shannon and Wiener, Turing was moving toward a unified theory of information and information processing applicable to both the machine and the biological worlds ...” (Aspray, Scientific Conceptualization of Information, p.132).

❧From Gutenberg to the Internet, 11.2; Origins of Cyberspace, 936.

Sophia Rare Books Flæsketorvet 68, 1711 København V, Denmark Tel: (+45)27628014 Fax: (+45) 69918469 www.sophiararebooks.com