Booth 313 California International Antiquarian Book Fair 7-9 February 2014

Home , Christopher Clavius, Kepler conjecture

Rare and important books & manuscripts in science, by Christian Westergaard, M.Sc.

Flæsketorvet 68 *1711 København V * Denmark Tel: (+45)27628014 / Fax: (+45)69918469 www.sophiararebooks.com

Astronomy...... 4, 12, 13, 15, 17, 18, 22, 26, 29, 34, 37, 44, 46, 49, 57, 63, 65, 67, 73 Chemistry...... 45, 60 Computing, Arithmetic...... 5, 6, 20, 68, 71, 72 Electricity, magnetism...... 14, 51, 52 Geometry...... 3, 22, 41, 48, 54, 66, 69 Manuscripts...... 24, 35, 52, 60, 74 Mathematics...... 2, 3, 6, 9, 20, 22, 23, 27, 30, 31, 35, 36, 38, 40, 41, 43, 46, 48, 50, 54, 55, 65, 66, 67, 68, 69, 71, 73 Mechanics, machinery, technology...... 1, 3, 28, 29, 42, 50, 56, 74 Medicine, Biology...... 16, 19, 26, 47, 59, 60, 61 Navigation...... 70, 73 Optics...... 17, 26, 39 Probability, Statistics ...... 8, 43, 46, 55, 62, 64, 65 Physics...... 1, 3, 7, 8, 9, 10, 11, 21, 22, 24, 25, 26, 28, 29, 32, 33, 37, 39, 40, 51, 52, 56, 58, 65 PMM*, Dibner, Horblit, Evans...... 2, 3*, 9*, 16*, 19*, 21*, 22*, 25, 30, 33, 39, 42, 43, 45*, 47, 51*, 53*, 59, 61* Special copies, inscribed, provenance...... 8, 10, 13, 16, 23, 28, 34, 66, 72 20th century science ...... 7, 31

(The descriptions in this list are abbreviated; full descriptions are available) Francesco Villamena’s 1606 engraving of Christopher Clavius - the first Jesuit portrait of a scientist ‘One of the greatest scientific books of antiquity’ (Stillwell). 1. APOLLONIUS of Perga. Opera per doctissimum Philosophum Ioannem Baptistam Memum patritiumVenetum, mathematicharumque artium in urbe Veneta lectorum publicum. De Graeco in Latinum Traducta & Noviter impressa. Venice: Bernardinus Bindonus, 1537. $65,000 Rare editio princeps of Apollonius’s 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. “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.

Editio princeps of the greatest mathematician and physicist of antiquity 2. ARCHIMEDES of Syracuse. Opera, quae quidem extant, omnia. Basel: J. Hervagius, 1544. $80,000 An outstanding copy, in a fine contemporary binding, of the first complete edition of the greatest classical work on mathematics and physics - fully complete with both Latin and Greek text. Prior to this edition only two small tracts in Latin translation (1501 and 1503) and a partial translation (1543) had appeared. The publication of the present edition marked a decisive step forward in the history of mathematics in that it made Archimedes’ knowledge and sophisticated techniques readily available for study. “Archimedes – together with Newton and Gauss – is generally regarded as one of the greatest mathematicians the world has ever known, and if his influence had not been overshadowed at first by Aristotle, Euclid and Plato, the progress of modern mathematics might have been much faster. As it was, his influence began to take full effect only after the publication of this first printed edition which enabled Descartes, Galileo and Newton in particular to build on what he had begun.” (Printing and the Mind of Man). ❧ PMM 72; Evans 2; Grolier/Horblit 5; Dibner 137; Sparrow 9; Norman 6.

3 The earliest English book on rocketry 3. ANDERSON, Robert. The Making of Rockets. in Two Parts. The first containing the Making of Rockets for the meanest Capacity. The other to make Rockets by a Duplicate Proposition, to 1000 pound Weight or higher. Experimentally and Math- ematically Demonstrated. London: for R. Morden, 1696. $23,500 First edition, exceptionally rare, of the first English book on rocketry and the first book to propose the use of metal rocket casings. This development, which enabled the thrust of the rocket to be greatly increased, was principally responsible for the subsequent use of rockets as major weapons of war, and in the twentieth century for space exploration. Only one other copy has appeared at auction for more than a century. Only five copies located in America (Harvard, Louisville, MIT, UNC, Yale). This is an extremely rare book. ESTC lists Glasgow and BL only, and the only other copy in auction records is the Andrade-Norman copy. The catalogue of the Andrade sale (Sotheby’s, 12 July 1965) states (lot 16): “There is no record of the sale by auction in England of this work since the beginning of BAR” (i.e. Brit- ish Auction Records, which began in 1903). The present copy must have entered the Macclesfield library via John Collins, with whom Anderson was associated. Although this copy has some slight cropping to a few gatherings, it is actually taller than the Andrade-Norman copy, and is unrestored (the Andrade-Norman copy was rebacked). ❧Norman 54; Macclesfield 3328 (this copy); ESTC R1638.

The first proponent of the heliocentric hypothesis

4. ARISTARCHUS of Samos. De Magnitudinibus et Distantiis Solis et Lunae. Pesaro: Franciscanus, 1572. $19,250 This treatise is the sole extant work of Aristarchus - the first proponent of a heliocentric system - and marks “the first attempt to determine astronomical distances and di- mensions by mathematical deductions based upon a set of assumptions.” (DSB). “This treatise is also of great mathematical interest because of it containing the calculation of ratios which are in fact trigonometrical ratios.” (Sarton, I p.156-57). “The propositions of Aristarchus are also of particular mathematical interest because the ratios of the sizes and distances which have to be calculated are really trigonometrical ratios, sines, cosines, &c., although at the time of Aristarchus trigonometry had not been invented, while no reasonably close approximation to the value of π had been made (it was Archimedes who first obtained the value 22/7). Exact calculation of the trigonometrical ratios being therefore impossible for Aristarchus, he set himself to find upper and lower limits for them, and he succeeded in locating those which emerge in his propositions within tolerably narrow limits.” (Heath, Aristarchus of Samos, The Ancient Copernicus, p.328). Provenance: The Macclesfield copy, fine 17th-century calf with crowned monogram of Gaston, Duke of Orléans (1608-1660), initials F.S.L.A. on title. Exceptionally fine and clean throughout. ❧Sparrow, Milestones of Science 10; Barchas Collection 82; Stanitz 19.

4 A main source of the Difference and Analytical Engines 5. BABBAGE, Charles. Passages from the Life of a Philosopher. London: Longman, Roberts & Green, 1864. $6,750 A superb copy, untouched in the original publisher’s cloth, of “Babbage’s final book, and the principal source, along with the posthumous Babbage’s Calculating Engines, of our knowledge of Babbage’s Difference and Analytical Engines. Chapters V-VII contain Babbage’s accounts of his Difference Engines nos. 1 and 2, along with Sir Nicholas Harris Nicolas’s statement on the Difference Engine drawn up from Babbage’s papers. Chapter VIII contains Babbage’s only published description of the design of his Analytical Engine, a universal cal- culator capable of any type of mathematical calculation, which embodied “all the important functions of the modern digital computer” (Campbell-Kelly, 1994, p. 23). The frontispiece shows the only portion of Babbage’s first Difference Engine to be constructed, and the final four pages contain Babbage’s own bibliography of his published works” (Hook & Norman). ❧Origins of Cyberspace 84; From Gutenberg to the Internet 6.2.

The revival of British mathematics

6. BABBAGE, Charles and HERSCHEL, John. Memoirs of the Analytical Society. Cambridge: Smith, 1813. $15,500 First edition, extremely rare, of the only volume of the Memoirs of the Ana- lytical Society. “Babbage, Herschel, George Peacock and several other math- ematlly minded students at Cambridge University founded the Analytical So- ciety, dedicated to the reform of mathematics in Britain, in 1812. This is the only volume of its Memoirs. It is also Babbages first publication. Mathemat- ics at British universities—and by extension the entire country—had become stagnant over the previos century, due to the universities’ partisan adherence to Newton’s dot-notation and method of fluxions over the powerful Leibnitz- ian differential methods and d-notation used in Europe. The first objective of the Society was to promote the continental method as embodied in Lacroix’s Sur le calcul differentiel et integrale (1802), which Babbagc deemed “so per- fect that any comment was unncccssary”. In 1813 the Society published its single volume of Memoirs, written entirely by Babbage and Herschel; in de- ciding upon a title for the work, Babbage punningly suggested that it should be called “The Principle of pure D-ism in opposition to the Dot-age of the University”. Babbage and Herschel cowrote the preface, which gives a brief history of analysis since the time of Newton, and draws attention to what was to be a lasting preoccupation for Babbage—“the importance of adopting a clear and comprehensive notation”, Babbage’s first published work, a paper entitled ‘On continued products,’ also appeared in the Memoirs. ❧Origins of Cyberspace 17 (lacking last two leaves of the Babbage paper). OCLC lists two copies in the US (Brown and NYPL) and one in UK.

5 Very rare offprint issue of this milestone in 20th century physics 7. BARDEEN, J., COOPER, L. & SCHRIEFFER, J. R. Theory of Superconductivity. Lancaster: American Physical Soci- ety, 1957. $13,750 Exceptional offprint of this famous paper announcing the ‘BCS’ theory of superconductivity, the first successful quantum-mechanical explanation of the disappear- ance of electrical resistance in certain metals at very low temperatures. Supercon- ductivity was first observed by Kammerlingh Onnes in 1911. “In the competitive world of theoretical physics, the BCS theory was the triumphant solution of a long-standing riddle. Between 1911 and 1957, all the best theorists in the world, among them [Richard] Feynman, Albert Einstein, Niels Bohr, Werner Heisenberg, Wolfgang Pauli and Lev Landau had tried and failed to explain superconductivity” (Hoddesdon & Daitch). Bardeen, Cooper and Schrieffer were awarded the 1972 Nobel Prize in Physics for this work, earning Bardeen the singular distinction of being the only person to be awarded the Nobel Prize in Physics twice. His team completed the work on superconductivity just a few months after he returned from Stockholm to collect the 1956 Prize for the invention of the transistor (shared with William Shockley and Walter Brattain). ❧Brandt, Harvest of a Century, Episode 78.

His thesis inscribed to his demonstrator Peignot 8. BECQUEREL, Antoine Henri. Recherches sur l’absorption de la lumiere. Thèses presentees a la faculté des sciences de Paris pour obtenir le grade de docteur ès sciences physiques. Paris: Gauthier-Villars, 1888. First edition. $16,200 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 Discov- ery of Radiochemistry, p.5). ❧Norman 156 [Norman copy with anonymous inscription].

6 His most famous work 9. BERNOULLI, Daniel. Hydrodynamica, sive De Viribus et Motibus Fluidorum Commentarii. Strasbourgh: Johann Re- inhold Dulsseker, 1738. $17,800 First edition of Bernoulli’s epochal work on fluid dynamics and kinetic gas theory. “Bernoulli’s Hydrodynamica [was] one of the major works initiating the mathematical study of fluid flow. Bernoulli presents the following equations for steady, non viscous, incompressible flow:p + ρ v2/2 + ρ gy = A, where p symbol- izes pressure, ρ density, v velocity, g the acceleration of gravity, y height, and A a constant. He also examines the equilibrium oscillation of an interialess ocean, and explicitly states that the flow equations are appropriate not only for the more common applications of fluid dynamics but also for the flow of blood in veins and arteries. Bernoulli, like Galileo Galilei in 1638 and Christian Huygens, assumes conservation of mv2 rather than conservation of momentum mv, m and v symbolizing a body’s mass and velocity respectively” (Parkinson, Break- throughs). TheHydrodynamica also “initiates the mathematical study of the kinetic theory of gases ... and analytically deduces Boyle’s Law that volume and presuure of a gas are inversely related, a law originally obtained emperically. To establish the analytical derivation, Bernoulli follows Robert Hooke in visualiz- ing the pressure of a gas as resulting from huge numbers of impacts on the walls of the container by hard, fast-moving gas particles. Bernoulli’s explanation, based on random motions of the gas particles, is more modern than an earlier attempt by Isaac Newton to explain Boyle’s Law by assuming relatively motionless particles which repel each other with a force inversely proportional to the distance between them” (ibid). ❧Norman 215; PMM 179n; Barchas 175; Parkinson pp 155-6; Roberts and Trent, pp 34-5.

The birth of modern atomic physics 10. BOHR, Niels. On the Constitution of Atoms and Molecules, I-III. London: Taylor & Francis, 1913. $59,500 Extremely rare author’s presentation offprints of his great trilogy, which constitutes the birth of modern atomic physics. “Bohr’s three- part paper postulated the existence of stationary states of an atomic system whose behavior could be described using classical mechanics, while the transition of the system from one stationary state to another would represent A non-classical process accompanied by emission or absorption of one quantum of homogeneous radiation, the frequency of which was related to its energy by Planck’s equation” (Norman). Bohr’s atomic theory inaugurated two of the most adventurous decades in the history of science. In 1922 Bohr was awarded the Nobel Prize “for his services in the investigation of the structure of atoms and of the radiation emanating from them”. ❧Norman 258 (ordinary journal issues).

7 The foundation work of statistical thermodynamics 11. BOLTZMANN, Ludwig. Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmtheorie und der Wahrscheinlichkeitsrechnuung, respective den Sätzen über das Wärmegleichgewicht. Vienna: Karl Ger½old, 1878. $3,400 First edition of this seminal paper, containing the Boltzmann principle expressing the relation between entropy and probability, S = k log W, where S is the entropy of a system, W the thermodynamic probability of the same system, and k a universal constant (later named the ‘Boltzmann constant’ by Planck). “This formula connects a thermodynamic or macroscopic quantity, the entropy, with a statistical or microscopic quantity, probability... These results gave rise to a paradox. If Newtonian mechanics held on the molecular level, interactions between particles had to be reversible, whereas thermodynamic changes on the macroscopic lever were irreversible. The answer to this ‘reversibility paradox’ lay in the statistical character of the second law” (Oxford Com- panion to the History of Modern Science). This work is fundamental to all subsequent developments in statistical mechanics and especially in quantum mechanics. “Each microscopic configuration possible for a gas with a given energy content is presumed to have an equal likelihood, and therefore the probability of any particular macroscopic condition is proportional to the number of microstates yielding it. Hence, in contrast to the original formulation of the second law, there is a finite, albeit small, probability for the entropy of a system to decrease” (Parkinson). “The result of this investigation, the theorem that entropy is proportional to the logarithm of the probability, is one of the most beautiful theorems of theoretical physics, indeed of all science” (Fritz Hasenöhrl). This paper was presented in October 1877, but in fact not printed until the beginning of 1878. ❧Parkinson: Breakthroughs, p. 393

‘The most significant treatise between Kepler and Newton’ 12. BOULLIAU, Ismael. Astronomia philolaica. Paris: Simeonis Piget, 1645. $22,000 First edition, very rare, of “the first treatise after Kepler’sRudolphine Tables to take elliptical orbits as a basis for calculating planetary tables” (The Cam- bridge 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 inDSB ). “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 attenu- ated 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/d “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.

8 The basis of Kepler’s laws 13. BRAHE, Tycho. Astronomiae Instauratae Mechanica. Nuremberg: Levinus Hulsius, 1602. $65,500 First trade edition, a fine copy with provenance, of one of Brahe’s most important works, a description of his famous astronomical instruments (the most advanced in the world for their time), his globe, and his observatory on the island of Hven. “Brahe’s observations formed the basis upon which Kepler established his three laws of planetary motion” (Sparrow). “The first edition of 1598 was printed by Philip de Ohr on Brahe’s own press at Heinrich Rant- zov’s castle at Wandbeck, near Hamburg, where Brahe spent a year after quitting Denmark; it consisted of about 40 copies which Brahe distributed privately. With the exception of the portrait and the engraving on C6c, replacing a woodcut, the illustrations of this published edition were printed from the blocks and plates of the first edition, sold by the author’s heirs to Levinus Hulsius.” (Norman). Provenance: The Danish astronomer John Louis Emily Dreyer (1852-1926), wrote the standard biography of Brahe and published in 1864 a supplement of approximately 1000 new ‘nebulae’ to Her- schel’s A General Catalogue of Nebulae and Clusters of Stars (Lon- don 1864). ❧Norman 320; Sparrow, Milestones of Science 29.

The first recognition of electrical repulsion 14. CABEO, Niccolo. Philosophia Magnetica. Ferrara: Francesco Suzzi, 1629. $16,500 “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). 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.

9 Cassini’s theory of comets 15. CASSINI, Giovanni Domenico. Theoriae motus cometae anni MDCLXIV ea præferens, quæ ex primis obseruationi- bus ad futurorum motuum prænotionem deduci potuere, cum noua inuestigationis methodo, tum in eodem, tum in comete nouissimo anni MDCLXV ad praxim reuocata. [bound with:] Lettere astronomische di Gio: Domenico Cassini al Signor Abbate Ottavio Falconieri sopra il confronto di alcune osservazioni delle comete di questo´ anno M.DC.LXV. Rome: Fabio di Falco, 1665. $48,000 First editions of these two exceptionally rare Cassini publications on the comet of 1664-5. Cassini observed the comet “in the presence of Queen Christina [to whom the first work is dedicated] and formulated on this occasion a new theory (in agreement with the Tychonian system) in which the orbit of the comet is a great circle whose center is situated in the direction of Sirius and whose perigee is beyond the orbit of Saturn” (DSB). Cassini’s detailed observations of the comet were made with a powerful new telescope. “Through his friendship with the famous Roman lensmakers Giuseppe Campani and Eusta- chio Divini, Cassini, beginning in 1664, was able to obtain from them powerful celestial telescopes of great focal length. He used these instruments—very delicate and extremely accurate for the time—with great skill, and made within several years a remarkable series of observations…” In the preface to the work Cassini describes the telescopes, and the first observations made with them. The large engraved plate depicts the course of the comet in the southern celestial hemisphere from December 13, 1664 through the middle of January, 1665. It also shows the appearance and direction of the comet’s tail in a series of nightly dated observations. The great comet of 1664-5 was observed by many astronomers, including Auzout, Borelli, Fabri, Hevelius, Hooke and Petit. The second work, addressed to the archaeologist Falconieri, presents further observations on the comet, and Cassini remarks about the observations made by Auzout and Hevelius. ❧OCLC: Brown (lacking plate) for the first work, and Brown, Cornell, Ohio State for the second work.

PMM 420 - Penicillin 16. CHAIN, Ernst; FLOREY, Howard; HEATLEY, Norman; et al. Penicillin as a Chemotherapeutic Agent. [with:] Fur- ther Observations on Penicillin. London: The Lancet, 1940-41. $9,500 First edition, offprint issue, of the paper which established penicillin as an anti- bacterial agent for medical application, one of the greatest medical advances of the twentieth century. It is here accompanied by an offprint of the paper, published a year later, which reported the first medical trials of penicillin. Provenance: both offprints by direct descent from the library of Norman Heatley (1911-2004), one of the scientists in the Oxford research group which developed penicillin. ‘Without Fleming, no Chain or Florey; without Florey, no Heatley; without Heatley, no penicillin’ (Professor Sir Henry Harris). Fleming, Florey and Chain were jointly awarded the Nobel Prize for physiology or medicine in 1945, recog- nising the tremendous contribution of penicillin to human welfare. But Heatley’s contribution, which had been no less essential, went largely unrecognised during his working life. However in later years, following an OBE in 1978, the University of Oxford awarded him with the first Penicillin Fellowship at Lincoln College, and renamed the laboratory in which he had worked for 42 years in his honour, as well as instituting an annual lecture and a lectureship in his name. ❧PMM 420b; Norman 437; GM 1934.

10 The most exhaustive treatise on lens making in the 17th century 17. CHERUBIN d’Orléans, Capuchin. La dioptrique oculaire, ou la théorique, la positive, et la mechaniquede l’oculaire dioptrique en toutes ses espèces. Paris: Jolly and Benard, 1671 [1670]. $20,000 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 Ori- gins of the Telescope, pp. 289-291). ❧Albert et al 412; Krivatsy 2427

By one of the best makers of terrestrial globes 18. CORONELLI, Vincenzo. Epitome Cosmographica, o compendiosa introduttione All’Astronomia. Colonia [i.e. Venice]: Ad istanza di Andrea Poletti, 1693. $22,000 First and only edition of this sumptuously illustrated work, a singular source for the documentation of several of the most elaborate large-scale globes, inventions used to make celestial and terrestrial maps, and astronomical mechanisms, some now lost, constructed during the latter decades of the seventeenth century. The work contains 4 large fold-out celestial maps in circular format engraved in a spectacular baroque style. These celestial maps are especially note- worthy because they were based upon the most recent astronomical observations and were copied into the eighteenth century. Also included are two large terrestrial maps – the western and eastern hemispheres. Of the 37 double-page plates, many illustrate globes, spheres, astronomical diagrams and instruments. ❧Riccardi I: 374-5; Houzeau & Lancaster 8006; Nordenskiold Collection 57 (28 plates only)], Armao, Vincenzo Coronelli, p. 189; Warner, The Sky Explored, pp. 56-7.

11 PMM 276 – Comparative Anatomy 19. CUVIER, Georges. 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. $7,000 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” (Nor- man). “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 embrache- ments: 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, Milestones of Science 42; Norman 567.

‘One of the most important algorithms of the 20th century’ 20. DANTZIG, George Bernard. Linear Programming: Invited paper presented before the Symposium on Numerical Meth- ods July, 1948, Los Angeles, California. [National Bureau of Standards], 1948. First edition, pre-print. $7,500 Extremely rare mimeographed typescript of the paper (published three years later) in which Dantzig gave the first general description of linear programming and his famous ‘simplex’ method - declared as one of the most important algorithms of the 20th century. Dantzig was the recipient of the first Von Neumann Theory Prize “for his work on linear programming”. When it was announced that the 1975 Nobel Prize in Economics would be awarded jointly to Kantorovich and Koopmans “for their contributions to the theory of optimum allocation of resources”, the latter wrote first that he would deny the prize, as a protest towards the exclusion of Dantzig. Harvard economist Robert Dorfman, in his paper ‘The Discovery of Linear Programming’ (Annals of the History of Computing, vol. 6, pp. 283-295, 1984), clearly refers to the offered 1948 pre-print by Dantzig as the first in which he discovered the “basic strat- egy of the simplex method and all its variants, … Thus Dantzig described the basic step in climbing the beanpole in the summer of 1948”, citing the published version of this paper. The contents of this mimeographed typescript is identical to the 1951 publication [also offered here] and is with all probability the version handed out to the attendees of the symposium (National Bureau of Standards) in July 1948 – the first and last page are marked with the rubberstamp of statistician, and specialist in numerical methods, Dr. Clifford J. Maloney (who worked for different gov- ernmental institutions) and who would have been a very likely participant at this symposium. Included is, furthermore, one mimeographed typed sheet being an abstract of (a seemingly unpublished) paper by Dantzig, ‘Application of the SEAC to Linear Programming’, given before the Association for Computing Machinery, Sept. 7-9, 1950. ❧Gass & Assad, An Annotated Timeline of Operations Research, p. 64.

12 The wave theory of matter confirmed 21. DAVISSON, Clinton. & GERMER, Lester. The Scattering of Electrons by a Single Crystal of Nickel. London: Macmil- lan, 1927. $3,750 A fine copy, in original wrappers, of the first announcement of the discovery of elec- tron diffraction in crystals, i.e., the famous Davisson–Germer experiment which confirmed de Broglie’s hypothesis of the wave-particle duality of matter. “This idea was tested and confirmed by Davisson and Germer in 1927. They directed a beam of electrons on to a crystal of metal, and found that instead of bouncing off, as particles would, the beam was diffracted; just as the X-rays had been in the experiments of von Laue and Braggs [1912]...Thus the duality of both light and matter had been established, and physicists had to come to terms with fundamental particles which defied simple theories and demanded two sets of ‘complementary’ descriptions, each applicable under certain circumstances, but incompatible with one another.” (Print- ing and the Mind of Man). ❧ PMM 417 (note); A Century of Nature, Twenty-One Discoveries that Changed Science and the World, 28; Parkinson, Breakthroughs, p. 505; Brandt, Harvest of a Century, p. 13

Exceptionally large copy in the original Dutch vellum 22. DESCARTES, René. Discours de la methode pour bien conduire sa raison, & chercher la verité dans les sciences. Plus la Dioptrique, les Meteores, et la Geometrie. Qui sont des essais de cete Methode. Leiden: Jan Maire, 1637. $192,000 A very fine and exceptionally large copy, entirely unrestored, in its original Dutch vellum binding - the birth of analytical or co-ordinate geometry, designated by John Stuart Mill as “the greatest single step ever made in the progress of the exact sciences”. “It is no exaggeration to say that Descartes was the first of modern philosophers and one of the first modern scientists; in both branches of learning his influence has been vast. ... The revolution he caused can be most easily found in his reassertion of the principle (lost in the middle ages) that knowledge, if it is to have any value, must be intelligence and not erudition. His application of modern algebraic arithmetic to ancient geometry created the analytical geometry which is the basis of the post-Eu- clidean development of that science. His statement of the elementary laws of matter and movement in the physical universe, the theory of vortices, and many other speculations threw light on every branch of science from optics to biology. Not least may be remarked his discussion of Harvey’s discovery of the circulation of blood, the first mention of it by a prominent foreign scholar. All this found its starting point in the ‘Discourse on the Method for Proper Reasoning and Investigating Truth in the Sciences’. Descartes’s purpose is to find the simple indestructible proposition which gives to the universe and thought their order and system. Three points are made: the truth of thought, when thought is true to itself (thus cogito, ergo, sum), the inevitable elevation of its partial state in our finite consciousness to its full state in the infinite existence of God, and the ultimate reduction of the material universe to extension and local movement.” (PMM). ❧PMM 129; Grolier/Horblit 24; Dibner 81; Evans 5; Sparrow 54.

13 Presentation copy in contemporary morocco, inscribed by the author 23. DOUAT, Dominique. Méthode pour faire une infinité de desseins differens, avec des carreaux mi-partis de deux couleurs par une ligne diagonal. Paris: Laulne, Jombert & Cailleau, 1722. $16,000 First edition of “the earliest (and perhaps the rarest) treatise on the theory of design” (Gom- brich). Douat’s book is the first book which gives a systematic graphical treatment of the theory of patterns, permutations and combinatorics, a subject that under the influence of Pascal, Fer- mat and Leibnitz was at the forefront of mathematics at the time. “There are few places where the approaches of the artist and the scientist intersect more intimately than in the production and analysis of tiling patterns” (Smith), and certainly in not many works is this intersection more evident than in this book… The mathematical background of Douat’s theory is based on the quite simple observation that a square diagonally divided in two triangles of different colors, can be rotated (90 degrees, clockwise) in four different positions: these four variants (indicated by Douat as A, B, C and D) represent the basis for any further development. Sets of two of such variants can be arranged in 16 different ways; sets of three variants give 64 permutations; sets of all four variants result in 256 permutations. Taking each one of the 256 possibilities to be further combined with each other one we obtain 2562 = 65536 … and so on ad infinitum. The book is divided in four parts: the first giving the necessary background to produce the different variants; the second one gives several different patterns as example; the third one provides the necessary explanations for the previous part and the fourth one gives instructions to obtain different patterns without the use of the permutations table and without a previous drawing of the desired design. ❧Gombrich, The Sense of 0rder. A study in the psychology of decorative Art, p. 70.

Autograph scientific notes on relativity theory 24. EINSTEIN, Albert. One 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]. $52,000 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 in- tensely involved in the development of general relativity. The calculations employ com- pact 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 pon- deromotive 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. ❧ We are grateful to Prof. P. West and Dr A. Recknagel of the Theoretical Physics Group, King’s College London, and to Dr. Tilman Sauer of the Einstein Papers Project at CIT, for helping with the discription of this manuscript.

14 ‘One of the most remarkable volumes in the whole scientific literature’ (Max Born) 25. EINSTEIN, Albert. 1) Zur Elektrodynamik bewegter Körper; 2) Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt; 3) Über die von der molekularkinetischen Theorie der Warme -ge forderte Bewegung von in ruhenden Flussigkeiten suspendierten Teilchen. Leipzig: Johann Ambrosius Barth, 1905. $22,500 A fine and unsophisticated copy without stamps or other markings, of the famous volume 17 of the Annalen der Physik. “It is probably no exaggeration to say that Einstein and Newton have been the greatest physicists of all times. Einstein’s name is generally associated with the theory of relativity, which has profoundly revolutionized man’s ideas of space and time. But as Max Born said in one of his articles, Einstein would probably have been one of the greatest scientists, even had he not written a single line on relativity. Einstein made a spectacular appearance on the physics scene in 1905 [his ‘annus mirabilis’] when he published these three papers in one and the same volume [i.e., the offered] of theAnnalen der Physik, the three papers having been submitted within a period of only three and half months.” (Wolff). ❧Dibner 167; Grolier/Horblit 26b; Norman 691a.

The foundation work of optical systems 26. EULER, Leonhard. Dioptricae Pars prima ... De explicatione principorum; Pars secunda...De constructione telescopio- rum dioptricorum; Pars tertia...De constructione microscopiorum. St. Petersburg: Imperial Academy of Sciences, 1769-177 $16,250 First edition, and a very fine copy, of Euler’s rare work on optics, ‘widely known and important in the physics of the eighteenth century’ and which ‘laid the foundations of the calculation of optical systems’ (DSB). The first volume presents his general theory of optics, including his prediction of the possibility of constructing achromatic lenses. The second and third volumes discuss the construction of the telescope and the microscope. “Next to the lunar theory, the most important subject which exercised the genius of [18th century] mathematicians was the improvement of the achromatic telescope” (Edinburgh Encyclo- pedia, Vol. 6). “In the second half of his life, from 1750 on and throughout his sixties, Leonhard Euler worked intensively on problems in geometric optics. His goal was to improve in several ways optical instruments, in particular, telescopes and microscopes. Besides the determination of the enlargement, the light intensity and the field of view, he was primarily interested in the deviations from the point-by-point imaging of objects (caused by the diffraction of light passing through as system of lenses), and also in the even less tractable deviations which arise from the spherical shape of the lenses… As was his cus- tom, he collected his results in a grandly conceived textbook, the Dioptrica (1769-1771). ❧Eneström 367, 386, 404; Arnaud de Vitry 377.

15 Second to only Euclid’s Elements 27. EULER, Leonhard. Vollständige Anleitung zur Algebra. St. Petersburg: Kaiserliche Academie der Wissenschaften, 1770. $9,800 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 (practically unobtainable). “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). It “was translated into Russian (1768-9), Dutch (1773), French (1774), Latin (1790), English (1797, 1822) and Greek (1800). The popular German edition from Reclam Verlag sold no less than 108,000 copies between 1883 and 1943 (Reich, 1992). After 240 years this algebra textbook is still in print today, available in several languages and editions” (Heeffer). 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. ❧Norman 735; Honeyman 1075; Eneström 387 & 388

The sequel to Euler’s Mechanica 28. EULER, Leonhard. Theoria motus corporum solidorum seu rigidorum. Ex primis nostrae cognitionis principiis stabilita et ad omnes motus, qui in huiusmodi corpora cadere possunt, accommodata. Rostock & Greifswald: A. F. Röse, 1765. $9,800 First edition, the copy of mathematician Friedrich Engel, of this con- tinuation of Euler’s Mechanica (1736), in which he moves on from the treatment of the motion of point-masses in the earlier work to that of rigid bodies, studying rotational problems (some motivated by the problem of the precession of the equinoxes) and introducing many now familiar concepts such as the ‘moment of inertia,’ ‘principal axes’ and ‘Euler angles.’ “The Theoria motus corporum solidorum, published almost thirty years later (1765), is related to the Mechanica. In the introduction to this work, Euler gave a new exposition of punctual mechanics and followed Maclaurin’s example (1742) in projecting the forces onto the axes of a fixed orthogonal rectilinear system. Establishing that the instantaneous motion of a solid body might be regarded as composed of rectilinear translation and instant rotation, Euler devoted special attention to the study of rotatory motion. Euler thus laid the mathematical foundation of the numerous studies on variational principles of mechanics and physics which are still being carried out” (DSB). Provenance: With the signature of the eminent German mathematician Friedrich Engel (1861–1941) to the front free end-paper, dated 1894/ Leipzig. Front paste-down with extensive pencil notes in German. ❧Parkinson, Breakthroughs, p. 154; Roberts and Trent, pp. 105-6.

16 One of Euler’s rarest publications 29. EULER, Leonhard. Theoria Motus Lunae Exhibens Omnes Eius Inaequalitates.St. Petersburg: Academiae Imperialis Scientiarum, 1753. $16,400 Very rare first edition of Euler’s ‘first lunar theory’, the theoretical basis for Tobias Mayer’s lunar tables that won the British Parliament prize for the longitude problem (see below). “Based on Newton’s universal law of gravitation, Euler first developed his first lunar theory with the aid of his method of variation of orbital parameters. This method is fairly general in the sense that it cannot only be applied to the theory of lunar motion, but also to the planetary motion. Euler published his first lunar theory in his celebrated treatise ‘Theory of lunar motion’ in 1753. He continued his research for almost the next three decades to make significant improvement of his first lunar theory including the lunar orbit, Moon’s position, equations for the Moon’s motion, lunar eclipses and the period of revolution of the Moon.” (Debnath: The Legacy of Leonhard Euler, p.365). “Astronomy owes to Euler the method of variation of arbitrary constants. By it he attacked the problem of perturba- tions, explaining, in case of two planets, the secular variations of eccentricities, nodes, etc. He was one of the first to take up with success the theory of the moon’s motion by giving approximate solutions to the ‘problem of three bodies’. He laid a sound basis for the calculation of tables of the moon.” (Cajori, History of Mathematics, p.240). ❧Eneström 187.

Creation of the calculus of variations 30. EULER, Leonhard. Methodus inveniendi Lineas Curvas Maximi Minimive proprietate gaudentes, sive Solutio Prob- lematis isoperimetrici latissimo sensu accepti. Lausanne & Geneve: Bosquet & Socios, 1744. $15,500 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.

17 Feynman’s most important work 31. FEYNMAN, Richard. Six papers constituting the development of the ‘Feynman diagram’ approach to quantum electrodynamics (QED): 1) A Relativistic Cut-Off for Classical Electrodynamics; 2) Relativistic cut-off for quantum electrodynamics; 3) The Theory of Positrons; 4) Space-Time Approach to Quantum Electrodynamics; 5) Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction; 6) An Operator Calculus Having Applications in Quantum Electrodynam- ics. Lancaster: American Physical Society, 1948-5 $11,500 First editions, in original wrappers, of the six papers which constitute Feynman’s formulation of QED, involving the famous ‘Feynman diagrams.’ Feynman “published an extended set of papers - they would stretch over three years and one hundred thousand words - that defined the start of the modern era for the next generation of physicists. After his path-integral paper came, in the Physical Review, ‘A Relativistic Cut-Off for Classical Electrodynamics,’ ‘Relativistic Cut-Off for Quantum Electrodynamics,’ ‘The Theory of Positrons,’ ‘Space-Time Approach to Quantum Electrodynamics,’ ‘Mathemat- ical Formulation of the Quantum Theory of Electromagnetic Interaction,’ and ‘An Op- erator Calculus Having Applications in Quantum Electrodynamics.’ As they appeared, the younger theorists... devoured them... [and] felt invigorated by his images... “No as- piring physicist could read these papers without thinking about what space was, what time was, what energy was. Feynman was helping physics live up to the special promise it made to its devotees: that this most fundamental of disciplines would bring them face to face with the primeval questions” (Gleick). ❧Brandt, The Harvest of a Century; Gleick, Genius pp. 271-272.

Fermat’s Last Theorem 32. [FERMAT, Pierre de] DIOPHANTUS of Alexandria. Arithmeticorum libri sex, et de numeris multangulis liber unus. Cum commentariis C.G. Bacheti V.C. & observationibus D.P. de Fermat senatoris Tolosani. Toulouse: Bernard Bosc, 1670. $65,000 First edition of Fermat’s discoveries in number theory and first printing of his celebrated ‘last theorem’, one of the most famous problems in mathematics and unsolved for over 325 years until its solution in 1995. Fermat showed not the slightest interest in publishing his work, which remained confined to his correspondence, personal notes, and to marginal jottings in a copy of the 1621 editio princeps, edited by Claude Bachet, of Diophantus’ Arithmetica. Fermat’s marginalia included not only arguments against some of Bachet’s conclusions, but also new problems inspired by Diophantus. After his death, Fermat’s eldest son Clement-Samuel published in 1670 his father’s marginalia in this new edition. Most famous of the 48 observations by Fermat included here is the tantalizing note that appears on fol. H3r; stating one of the most famous problems in mathematics; the impossibility of finding a positive integern > 2 for which the equation xn + yn = zn holds true for the positive integers x, y, and z. Fermat noted that he had discovered a ‘truly marvelous demonstration’ of this proposition, but that the margin was too narrow to transcribe it. The proposition, so simple in form, became known as the single most difficult problem in mathematics, and for over 325 years no mathematician succeeded either in disproving it or in finding Fermat’s mysterious proof. In 1995 Andrew Wiles, professor of mathematics at Princeton, who had been obsessed with Fermat’s proposition since the age of 10, completed a 130-page proof of the theorem (first presented in 1993, with a flaw that required revision), using the most advanced techniques of modern mathematics. His achievement was described by fellow mathematicians as the mathematical equivalent ‘of splitting the atom or finding the structure of DNA’ (Simon Singh). Nonetheless, Wiles had had to resort to sophisticated 20th-century techniques not available to Fermat. The exact form of Fermat’s proof, if indeed he had a genuine one, thus remains one of the great unsolved puzzles of mathematics. ❧Norman 777.

18 ‘The source of all modern methods in mathematical physics’ 33. FOURIER, Jean-Baptiste-Joseph. Théorie Analytique de la Chaleur.Paris: Firmin Didot, 1822. $35,000 A fine copy of the first mathematical study of heat diffusion and a landmark in the development of mathematical physics. “This work marks an epoch in the history of both pure and applied mathematics. It is the source of all modern methods in mathematical physics … The gem of Fourier’s great book is ‘Fourier series’.” (Cajori, A History of Mathematics, p.270). Fourier showed that heat diffusion was subject to simple physical constants that could be discerned through observation and expressed mathematically. His theory of heat became one of the most important branches of general physics. Fourier’s achievements were twofold: the first was his “formulation of the physical problem as boundary-value problems in linear partial differential equations, which... achieved the extension of rational mechanics to fields outside those defined by Newton’s Principia;... second, the powerful mathematical tools he invented for the solution of the equations... yielded a long series of descendants and raised problems in mathematical analysis that motivated much of the leading work in that field for the rest of the century and beyond.” (DSB). ❧Dibner 154; Evans 37; Sparrow 68; Landmark Writings in Western Mathematics 26; Norman 824.

With numerous contemporary annotations 34. GAURICUS, Lucas. Ephemeridies recognitae et ad vngem Castigatae... Eiusdem schemata & praedictiones ad Annum vsque virginei partus 1552 Eiusdem Isagogicus in totam ferme Astrolgiam Libellus... Venice: Sumptibus Lucentonii Juntae Typographi, 1533. $11,500 A fine copy of these very rare ephemerides, containing tables as well as astrologi- cal prognostications for the years 1534 through 1551, each preceded by a special title page. According to Houzeau and Lancaster, the ephemerides are calculated after the Alphonsine Tables, and for the meridian of Venice. Astrologer and mathematician, Luca Gaurico was born at Giffoni, near Naples, in 1476 and died at Rome in 1558. As a mathematician he is best known for the first published Latin translations of Archimedes’ works De Mensura Circuli and De Quadratura Parab- olae (1503). He went on to publish an edition of Pecham’s Perspectiva Commu- nis (Venice, 1504), and Trapezuntius’s translation of the Almagest (Venice, 1528). Rose (p. 120) suggests that Gaurico may have met Copernicus at Padua, as they were both at the university in the early years of the 16th century, and would have shared a common interest in Ptolemy and Archimedes. In 1531 he was appointed professor of mathematics at Ferrara, where Scaliger was one of his pupils. ❧Horblit 447 (two leaves in in facsimile); Honeyman 1448 (10 leaves defective). OCLC lists six copies in America (Brown, Chicago, Columbia, Cornell, Harvard, Michigan).

19 An important Gauss manuscript, signed and dated 1800 35. [GAUSS, Carl Friedrich] PFAFF, Johann Friedrich. Programma inaugurale in quo peculiarem differentialia investi- gandi rationem ex theoria functionum deducit. Helmstedt: J. H. Kühlin, 1788. $87,500 Pfaff’s dissertation 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), the mathematics required to describe planetary orbits. ❧ The present volume 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.

‘The Copernicus of logic’ 36. GÖDEL, Kurt [VON NEUMANN, John; WALD, Abraham]. Ergebnisse eines mathematischen Kolloquiums, unter Mitwirkung von Kurt Gödel und Georg Nöbeling. Herausgegeben von Karl Menger. Heft 1-8. Leipzig & Berlin: B.G. Teub- ner, 1931-1937. $10,000 Extremely rare fully complete 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 dis- cussed 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). The th8 issue contains John von Neumann’s seminal economics paper on ‘Über ein ökonomisches Gleichungssystem und eine Ve- rallgemeinerung des Brouwerschen Fixpunktsatzes.’ and Abraham Wald’s important statistics paper ‘Die Widerspruchsfreiheit des Kollektivbegriffes der Wahrscheinli- chkeitsrechnung’. ❧See Dawson’s Bibliography of the Published Works of Kurt Gödel for a detailed account of the fifteen Gödel contributions.

20 Six first editions by Huygens 37. HUYGENS, Christiaan. Opuscula postuma, quae continent dioptricam, commentarios de vitris figurandis, disserta- tionem de corona & parheliis, tractatum de motu, tractatum de VI centrifuga, descriptionem automani planetarii. Leiden: Cornelius Boutesteyn, 1703. $11,500 A very fine copy of these six important works by Huygens published here for the first time. The first work, theDioptrica, is one of the author’s most significant optical treatises; in it he discusses “the law of refraction, the determination of the focuses of lenses and spheres and of refraction indices, the structure of the eye, the shape of lenses for spectacles, the theory of magnification, and the construction of telescopes.” (DSB). The second work describes Huygens’ methods of grinding lenses (illustrated in the fine plates). Huygens had acquired great technical skill in the grinding and polishing of spherical lenses and his telescopes were the best of the time. De Motu Corporum ex percussione, his study on collision of elastic bodies, amounted to a refutation of Descartes’ laws of impact. De Vi Centrzfuga, written in 1659, contains Huy- gens’ results of his studies on centrifugal force. It was here that he concluded that centrifugal force and the force of gravity are similar. The final treatise describes his construction of a mechanical planetarium. ❧Houzeau & Lancaster 3427.

The first published work on probability theory 38. HUYGENS, Christian; SCHOOTEN, Frans van. Exercitationum Mathematicarum libri quinque...Quibus accedit Christiani Hugenii tractatus de ratiociniis in aleae ludo. Leiden: Elzevir, 1657. $19,500 Rare first edition of Schooten’s book which contains the first printing of Huy- gens’ famous appendix on games of chance De Ratiociniis in Ludo Aleae; “the first published work on probability theory. It won immediate recognition and became the standard text on probability theory for the next 50 years.” (An- ders Hald: A History of Probability). (Stephen Stigler, Chance is 350 Years Old): “Huygens’ presentation dominated the literature for half a century due to its accessibility and near monopoly. And his solutions to the problems of Pascal and Fermat previously solved were fine examples of the work of a good mathematical mind. But there was one part of the tract that was strik- ingly original, and even today appears surprisingly modern.” When Huygens began his treatise by listing the elementary first principles of probability, e.g., when you have equal chances to win a or b, then your expectation (the fair price to play the game) is (a+b)/2, etc. Huygens did not present these principles as definitions or axioms as is customary but as “propositions: assertions that required - and were given – proofs. And the proofs were extraordinary for the time, with strong hints of late 20th Century financial mathematics. [For details on these proofs see Stigler’s article]. Three hundred fifty years ago, Huygens was the first published scientific probabilist, as well as the first financial engineer, constructing hedges and derivative contracts in order to extend probability theory from common notions of fairness in symmetric situations to very different asymmetric markets. Sociologist of Science Robert K. Merton introduced the term ‘obliteration by incorporation’ to describe the phenomenon in which a scientist’s work becomes so widely incorporated that he or she is seldom referred to in connection with it. Such was the fate of Huygens’ work on probability after the first decade of the 18th Century. But unlike many scientific pioneers, his work set off ripples that are still felt today.” (Stephen Stigler). ❧Stanitz 394.

21 The wave theory of light 39. HUYGENS, Christian. Traité de la Lumière. Leyden: Pierre vander Aa, 1690. $36,500 Huygens’s path breaking exposition of his wave theory of light. “Light, according to Huygens, is an irregular series of shock waves which proceeds with very great, but finite, velocity through the ether. This ether consists of uniformly minute, elastic particles compressed very close together. Light, therefore, is not an actual transference of matter but rather of a ‘tendency to move’, a serial displacement similar to a collision which proceeds through a row of balls ... Huygens therefore concluded that new wave fronts originate around each particle that is touched by light and extend outward from the particle in the form of hemispheres...” (DSB). Huygens was able to explain reflection and refraction using this theory, of which he became completely convinced in August 6, 1677, when he found that it explained the double refraction in Iceland spar. His view of light was opposed to the corpuscular theory of light advanced by Newton. In the second part of the work, the Discours de la cause de la pesanteur, written in 1669, Huygens expounded his vortex theory of gravity, a purely mechanistic theory that also contrast- ed markedly with Newton’s notion of a universal attractional force intrinsic to matter. ❧Grolier/Horblit 54; Dibner 146; Evans 32; Sparrow 111.

The founding work of crystallography 40. KEPLER, Johannes. Strena seu de nive sexangula. Frankfurt: Godefrid Tampach, 1611. $47,500 First edition of this Kepler rarity, the first scientific treatise concerning crystallography. Written in the form of a letter, this small tract was presented as a New Year’s gift to Kepler’s friend at court, Matthaus Wackher von Wack- enfels (who had informed Kepler of the discoveries Galileo had made with the telescope in 1610). “It is not only a charming letter, light-hearted and full of puns, but also a perceptive, pioneering study of the regular arrangement and the close packing that are fundamental in crystallography” (DSB). In the course of this study, Kepler is led to formulate ‘Kepler’s conjecture,’ one of the “greatest unsolved problems in mathematics” (Singh), which was the 18th of the problems David Hilbert presented to the mathematical world at the International Congress of Mathematicians in 1900. Kepler’s conjecture remained undecided for almost four centuries until in 1998 Professor Thomas Hales of Michigan University, together with his student Samuel Ferguson, announced that they had proved the conjecture. The proof is extremely long (282 pages!) and requires extensive computer calculations, and it is therefore a challenge to test its correctness. It is now generally accepted by the mathematical community. ❧Caspar 39; Cinti 30.

22 One of the most influential works in the history of non-Euclidean geometry 41. KLÜGEL, Georg Simon. Conatuum praecipuorum theoriam parallelarum demonstrandi recensio. Göttingen: Schultz, 1763. $28,600 Extremely rare first edition of Klügel’s thesis in which he criticized some thirty attempted proofs of the Parallel Postulate. “If one means by the creation of non-Euclidean geometry the recognition that there can be geometries alternative to Euclid’s then Klügel and Lambert deserve the credit” (Kline, Mathematical Thought from Ancient to Modern Times). Klügel’s most detailed analysis is reserved for Girolamo Saccheri’s Eu- clides ab omni naevo vindicates (1733). In this work, Saccheri denies the truth of the Parallel Postulate and draws a series of conclusions which, in retrospect, constitute many of the basic results of non-Euclidean geometry. Saccheri believed he had reached a contradiction, thus establishing the truth of the Parallel Postulate by reductio ad absurdam, but Klügel showed that he had done so by assuming certain properties of figures at infinite distance that are only known at finite distances. Despite its -im portance, Saccheri’s work was not widely known, and it was largely via Klügel’s thesis that its influence began to be felt. Johann Heinrich Lam- bert (1728-77) quotes Klügel’s thesis in his important Theorie der Paral- lellinien and probably learned of Saccheri’s work from it. It is probable that Janos Bolyai learned of Saccheri’s work from his father Farkas, who studied at Göttingen in 1796-8 and became interested in the parallel postulate under Kästner’s influence; he will inevitably have been directed by Kästner to study his student Klügel’s thesis. Bonola speculates that the other founder of non-Euclidean geometry, Nicolai Lobachevsky, may also have learned about Saccheri’s work via Klügel’s thesis. Thus, Klügel’s thesis provided the starting point for the most important developments in non-Euclidean geometry in the second half of the eighteenth and the first half of the nineteenth centuries. ❧ Kline, Mathematical Thought from Ancient to Modern Times, p. 869.

The first scientific work on the mechanics of flight 42. LANA TERZI, Francesco. Prodromo overo saggio di alcune inventioni nuove premesso all’arte maestra.Brescia: Riz- zardi, 1670. $12,800 An excellent copy the first scientific work on the mechanics of flight. “In this volume is presented the earliest concept of flight derived from demonstrable aerostatic principles.” (Norman). An important work in the history of aeronautics, in the Prodromo Lana Terzi presented several technological innovations, of which the best known is his proposal for a ‘flying boat:’ to be airborne by four spheres of thin copper from which air had been exhausted. Although the vehicle was never tested, and would have proved unworkable, since the copper would not have been able to withstand the atmospheric pressure, Lana Terzi’s reasoning was correct. In surmising that a vessel containing a semi-vacuum would weigh less than the surrounding air and would consequently become buoyant, Lana Terzi formulated the earliest concept of flight based on aerostatic principles. “While Lana apparently originated the method of reducing air density in a vessel by heating it, the implications of this phenomenon in relation to flight were not fully understood until the advent of the Montgolfier brothers a century later” (Nor- man). ❧Dibner 125; Norman 127.

23 ‘The most influential book on probability and statistics ever written’ (Hald) 43. LAPLACE, Pierre Simon. Théorie Analytique des Probabilités.Paris: Courcier, 1812. $33,000 “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 pos- terior probabilities. On the applied side, games of chance were still in 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 Math- ematica had to the later science of mechanics.” (DSB). ❧Evans 12; Landmark Writings in Western Mathematics 24.

On the origin of the solar system 44. LAPLACE, Pierre Simon. Exposition du Systême du Monde. Paris: De l’Imprimerie du Cercle-Social, 1796. $5,400 A fine copy, with the very rare errata leaves, of Laplace’s classic work on the origin and formation of the solar system in which he first stated his celebrated ‘nebular hypothesis.’ “One of the most successful popularizations of science ever composed.” (DSB). “An elegant, non-mathematical classic on astronomy. It is in this work that Laplace introduced one of his most notable contributions (although he himself did not take it very seriously at first) -- the so-called nebular hypothesis, which provided a con- jectural account of the origin of the solar system. This remained through the 19th century the most widely accepted view on the subject” (PMM). As mentioned in the 2004 Christie’s sale of the library of Jean-Louis Mosès: “A pair of errata leaves was added to very few copies [not present in the Mosès-Barrillot copy]”. Both of these errata leaves are present in our copy. We can find no copy in the auction records having the errata leaves. ❧Sparrow, Milestones of Science 123; Honeyman 1919.

24 PMM 238 – A new epoch in chemistry 45. LAVOISIER, Antoine-Laurent de. Traité élémentaire de Chimie, présenté dans un ordre nouveau, etd’après les décou- vertes modernes. Paris: Chez Cuchet, 1789. $7,800 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.

The method of least squares 46. LEGENDRE, Adrien Marie. Nouvelles méthodes pour la determination des orbites des comètes. Paris: Huzard-Cour- cier, 1806-1820. $8,400 First edition, second issue [with the supplements], of the invention of the method of least squares – “the automobile of modern statistical analysis” (Stigler). A rare complete copy including both supplements (in first issue) and Legendre’s 1820 note in which he attacked Gauss for having claimed the method his own - “the most famous priority dispute in the history of statistics” (ibid). “In 1805 Legendre published the work by which he is chiefly known in the history of statistics, Nou- velles méthoedes pour la determination des orbites des comètes. At eighty pages this work made a slim book, but it gained a fifty-five page supplement (and a- re printed title page [i.e., the offered issue]) in January of 1806, and a second eighty- page supplement in August 1820. The appendix presenting the method of least squares occupies nine of the first eighty pages; it is entitled ‘Sur la méthode des moindres quarrés.’ For stark clarity of the exposition the presentation is unsur- passed; it must be counted as one of the clearest and most elegant introductions of a new statistical method in the history of statistics.” (Stigler). ❧Parkinson, Breakthorughs, p. 247.

25 The foundation of zoological and entomological nomenclature 47. LINNAEUS, Carl. Systema Naturae per Regna tria Naturae, secundum classes, ordines, genera, species cum characteri- bus, differentiis, synonymis, locis. Editio Decima, reformata. Stockholm: Laurent Salvi, 1758-59. $12,500 “The Tenth Edition of Linnaeus’s ‘Systema Naturae’ is one of the great books in the history of science because it marked the start of an epoch in two essential fields of zoological study: systematics or taxonomy, and nomenclature. ... especially as the system of nomenclature which Linnaeus published in 1758, has been universally recognised as the first consistent general application of the principle of giving binomial names to animal species. Without it, progress in Zoology would have been impossible, and by establishing this practice Linnaeus performed a service of inesti- mable value. The tenth edition of the Systema‘ Naturae’ is therefore accepted as the starting-point of zoological nomenclature” (Gavin de Beer). The tenth edition is in fact the fourth original edition of the ‘Systema’. “Carolus Linnaeus established the binomial system of nomenclature and was originator of the modern classification of insects. No scientific name is considered valid if it appeared before the tenth edition of his ‘Systema Naturae’ in 1758” (E. Essig. A history of entomology, p. 688). Provenance: Bookplate of Gregory M. Mathews, author of ‘The Birds of Australia’. ❧Dibner 27n; Norman 1359; Soulsby 58; Dance, 194.

The most authoritative defense of Newton’s fluxions 48. MACLAURIN, Colin. A Treatise of Fluxions. In Two Books. Edinburgh: T.W. and T. Ruddimans, 1742. $18,000 A very fine copy of “the earliest logical and systematic publication of the Newtonian methods. It stood as a model of rigor until the appearance of Cauchy’s Cours d’Analyse in 1821.” (DSB). “Despite the great progress of analysis during the 18th century, foun- dational questions remained largely unsolved. … The most influential criticism of the new analysis was put forward by the famous English philosopher George Berkeley [in his pamphlet The Analyst, 1734]. … Berkeley’s criticism was well informed and efficient. Rooted in the tradition of English sensualism, he showed that many definitions in the infinitesimal calculus are paradoxical and cannot be justified by intuition. He explained the success of the new calculus by a repeated neglect of infinitely small quantities leading through a compensation of errors to a correct answer.” (Jahnke). “The most authoritative answer to Berkeley came from Maclaurin, one of the most talented of Newton’s disciples. In his Fluxions, he tried to show that infinitesimals were used by Newton only to abbreviate proofs; these proofs could be re-expanded, following the style of the De Quadratura (1704), in terms of limits. Furthermore, Ma- claurin elaborated the idea that Newtonian proofs in terms of limits were equivalent to the venerated method of exhaustion of the ancient Greek mathematicians. Newton’s ‘method of prime and ultimate ratios’ was just the direct version of the indirect (ad absurdum) method of Archimedes. ” (Grattan-Guinness). ❧Norman 1408; Honeyman 2084.

26 ‘New Theories of the Celestial Orbs Agreeing with the Observations of Copernicus’ 49. MAGINI, Giovanni Antonio. Novae coelestium orbium theoricae congruentes cum observationibus N. Copernici. Venice: ex officina Damiani Zenarii, 1589. $12,800 A very fine copy, from the Riccati library, of Magini’s principal astronomical treatise. The work is of interest for the sixteenth century reception of Coper- nicus: although Magini endorsed the unprecedented accuracy of Copernicus’ calculation of celestial movements he nevertheless publically retained his belief in geocentrism, referring in the present work to “absurd hypotheses as Copernicus has imagined.” He is the target in much of Galileo’s revolution- ary embrace of the Copernican system. However, there is strong evidence that Magini later embraced Copernicanism, in private if not in public. In this work Magini “took the position that Copernicus had so reformed astronomy that no correction of equal motions, or a very slight one, was now required... For although Copernicus had devised hypotheses which wandered far from verisimilitude, yet they corresponded closely to the phenomena... He, therefore, collated the ideas of Ptolemy and Copernicus, adding new hypotheses of his own where they seemed necessary, and has written an introductory text or theory of the planets along these lines. He asserts that there was a great demand for such a theory of the planets which would abandon the outmoded Alfonsine hypotheses and conform his recent observations without such absurd hypotheses as Copernicus had imagined.” (Thorndike). ❧Honeyman 2098; Houzeau & Lancaster 12741; Gingerich, Science in the Age of Copernicus.

The principle of least action 50. MAUPERTUIS, Pierre-Louis; EULER, Leonhard; KÖNIG, Samuel; VOLTAIRE. Maupertuisiana. Hambourg [Leiden]: 1753. $8,800 Rare complete collection, and a fine copy, of the 16 pamphlets relating to the ‘König affair,’ the celebrated polemic on the principle of least action, “perhaps the ugliest of all the famous scientific disputes” (DSB). The texts in this collection are all in their first printed state with the exception of Appel au public (first printed in the Nova Acta Eruditorum for 1751) and Diatribe du Docteur Akakia, the first edition of which was ordered to be publicly burned by the ‘philosopher King’ Frederick II of Prussia. The König affair is of considerable importance in the history of physics, since the principle of least action “was clarified and underwent important developments at the hands of Hamilton and Jacobi in the 19th century… [It] has come to play a fundamentally important part in twentieth-century Physics… the discovery of its atomicity is the basis of the Quantum Theory” (Wolf,A History of Science, Technology, and Philosophy in the Eighteenth Century, p. 69). Although initially a quarrel between Maupertuis and König, the dispute drew in, among others, Euler, Voltaire and the King. Beginning as a narrow scientific priority dispute, it became a battleground of love and jealousy, patronage, academic freedom and the control of knowledge and of print. ❧Bibliothèque Jean-Louis Mosès 129.

27 The ‘Principia’ of electromagnetism 51. MAXWELL, James Clerk. A Treatise on Electricity and Magnetism. Oxford: Clarendon Press, 1873. $16,800 A fine copy of the rare first issue of the work which did for electromagnetism what Newton’s Principia had done for classical mechanics. “In 1873, Maxwell published a two-volume Treatise on Electricity and Magnetism that was destined to change the orthodox picture of physical reality. This treatise did for electromagnetism what Newton’s Principia had done for classical mechanics. It not only provided the mathematical tools for the investigation and representation of the whole electromagnetic theory, but it altered the very framework of both theoretical and experimental physics. It was this work that finally displayed action-at-a-distance physics and substi- tuted the physics of the field.” Historical( Encyclopedia Of Natural And Mathematical Sciences). Provenance: Front free end-papers and half titles inscribed ‘A. H. F. Boughey / Trin: Coll: Camb.’ (i.e, Anchitel Harry Fletcher Boughey 1849-1936, Rural Dean of Trin- ity College Cambridge). Maxwell graduated from Trinity College in 1854. There are numerous pages throughout with technical and mathematical annotations in a contemporary hand (probably Boughey’s). ❧Grolier/Horblit 72; Norman 1666; PMM 355; Wheeler Gift Catalogue 187.

Exceptional letter by the greatest theoretical physicist of the century

52. MAXWELL, James Clerk. Three page ALS to Scottish mathematician Archibald Smith on a problem in electromagnetism. Dated 13 May 1869. $47,500 An outstanding autograph letter discussing an important problem in electromagnetism and its relation to work of predecessors and contemporaries, including Michael Faraday, George Green and Simeon-Denis Poisson. The content of the letter is highly technical, including several formulas and equations, and was later incorporated into Maxwell’s Treatise on Electricity and Magnetism (1873). Maxwell autograph material is of extreme rarity on the market, especially with significant scientific content as here. Widely regarded as the greatest theoretical physicist of the nineteenth century, Maxwell’s most important contribution to science is his theory of electromagnetism, which first appeared in his ‘Dynamical theory of the electromagnetic field’ (1865) and in mature form in the Treatise (1873). The present letter is situated chronologically mid-way between these two great milestones, a time at which Maxwell was indisputably the world’s leading expert on electricity and magnetism. The topic considered in the letter is the problem of determining the magnetization which would be acquired by a cylinder of soft iron when situated in an external magnetic field. Referring to the work of Green, who had considered this problem in Sect. 17 of An Essay on the Application of Mathemati- cal Analysis to the Theories of Electricity and Magnetism (1828), Maxwell states the solution to the problem in a series of formulas and equations which were published in Sects. 439-440 of his Treatise. The final result involves the solution of a numerical equation relating two of the parameters of the problem; after the end of the letter Maxwell adds in a postscript that he has ‘just calculated’ three solutions which he sets out in a small table. The letter was undoubtedly occasioned by Smith’s work on the effect of the magnetization of a ship’s hull on a compass needle, important in navigation, the contribution for which he is best known today. ❧Grolier/Horblit 72; Norman 1666; PMM 355; Wheeler Gift Catalogue 187 (all refering to the ‘Treatise’).

28 PMM 260 – The metric system 53. MÉCHAIN; DELAMBRE; BIOT & ARAGO. Base du Système Mètrique Décimal. I-IV. Paris: Baudouin & Garnery, 1806-21. $40,000 Rare complete set (in four volumes) of the foundation work of the metric system. “In 1790, at the request of Talleyrand, the Academie des Sciences set up a commission to consider the problem of finding a fundamental unit of measurement to replace the various diverse regional systems that had been in use throughout Europe for centuries. The members of the commission included J.C. Borda, Lagrange, Laplace, G. Monge and Condorcet. ‘In 1791 they reported that the fundamental unit of length should be derived from a dimension of the earth: it should be the ten-millionth part of a quadrant of the earth’s meridian extending between Dunkirk and Barcelona ... The Constituent Assembly set up a general commission of weights and meas- ures to carry these proposals into effect and in 1795 a law was passed introducing the metric system into France with provisional standards’ (PMM). The astronomers Delambre and Mechain were appointed to make accurate measurements of the meridian passing through Dunkirk and Barcelona, and their measurements were completed in 1799. The project had numerous delays, including France’s political revolution, the tedious calculations in converting one system to another, and the death of Mechain in 1804. Delambre completed the final volume of their report in 1810.” (Norman). ❧PMM 260 (lacking the fourth volume); Norman 1481 (lacking half-titles).

Anticipating Newton and Leibniz 54. MENGOLI, Pietro. Geometriae Speciose Elementa. Bologna: Giovanni Battista Ferroni, 1659. $32,250 Very rare first edition, and a fine copy from the library of Pietro Riccardi, of this important work on limits of geometrical figures. In this work Mengoli “set up the basic rules of the calculus thirty years before Newton and Leibniz. Both of these were influenced by his contribution, in the case of Leibniz the influence was direct as he read Mengoli’s work while in the case of Newton he knew of it indirectly through studying Wallis.” (MacTutor History of Mathematics). “In the ‘Geometriae speciosae elementa’ (1659), Mengoli set out a logical arrangement of the concepts of limit and definite integral that anticipated the work of 19th-century mathematicians. In establishing a rigorous theory of limits, he considered a variable quantity as a ratio of magnitudes and hence needed to consider only positive limits. He then made the following definitions: a variable quantity that can be greater than any assignable number is called ‘quasi-infinite’; a variable quantity that can be smaller than any positive number is ‘quasi-nil’; and a variable quantity that can be both smaller than any number larger than a given positive number a and greater than any number smaller than a is ‘quasi-a.’ Using these precise concepts of the infinite, the infinitesimal, and the limit, and working from simple inequalities valid between numerical ratios, he demonstrated (as Agostini recognized by translating his obscure exposition into modern symbols and terminology) the properties of the limit of the sum and the product, and showed that the properties of proportions are conserved also at the limit. The proofs obtain when such limits are neither0 nor ∞ for this case Mengoli set out the properties of the infinitesimal calculus and the calculus of infinites some thirty years before Newton published them in his ‘Principia.’ Provenance: Ex libris of the Biblioteca Riccardi to front pastedown. OCLC records just one copy in the US (New York Public Library). ❧ DSB, IX, pp.303-304.

29 De Moivre’s law 55. MOIVRE, Abraham de. Annuities upon Lives: or, The Valuation of Annuities upon any Number of Lives; as also, of Reversions. To which is added, An Appendix concerning the Expectations of Life, and Probabilities of Survivorship. London: W.P., 1725. $4,800 A very nice copy of the first edition of de Moivre’s influential study of annuities based upon the mortality statistics gathered by Edmund Halley in the 1690s. “De Moivre’s contribution to annuities lies not in his evaluation of the demographic facts then known but in his derivation of formulas for annuities based on a postulated law of mortality and constant rates of interest on money. Here one finds the treatment of joint annuities on several lives, the inheritance of annuities, problems about the fair division of the costs of a tontine, and other contracts in which both age and interest on capital are relevant. This mathematics became a standard part of all subsequent commercial applications in England” (DSB). ❧Norman 1530; Garrison-Morton 1690.

‘The most important book on mechanics published in the sixteenth century’ (Drake) 56. MONTE, Guidobaldo, Marchese Del. Mechanicorum Liber. Pesaro: Hieronymus Concordia, 1577. $20,000 A fine copy of the first edition with contemporary annotations. Monte’s theories were most influential for Galileo’s discoveries in the field of applied -me chanics 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 veloci- ties 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). TheLiber 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). ❧Bibliotheca Mechanica 229.

30 The Greatest Influences on Galileo 57. MONTE, Guidobaldo, Marchese Del. Problematum Astronomicorum Libri Septem. Venice: Bernardo Giunta & G.B. Ciotti, 1609. $20,000 First edition of the main astronomical work by one of the greatest influences on Galileo. “Guidobaldo was Galileo’s patron and friend for twenty years and was possibly the greatest single influence on the mechanics of Galileo.” (Rose in DSB). In this work...Guidobaldo deals with mathematical and observational astronomy and the improvement of astronomical instruments. “Guidobaldo helped to develop a number of mathematical instruments, including the proportional compass, the elliptical compass, and a device for dividing the circle into degrees, minutes, and seconds [described and illustrated in this work].” (DSB). “In general Guido- baldo’s attitude to mathematical instruments paralleled his attitude towards machines. Through these material devices, he felt, abstract mathematical truth could be made completely visible.” (Rose). ❧Houzeau & Lancaster 2912.

The air-pump 58. PAPIN, Denis. Nouvelles experiences du vuide. Avec la description des machines qui servent a les faire. Paris: J. Cusson, Fils, 1674. $25,000 First edition, very rare and a fine copy, of one of the most important documents in the early history of the air-pump, and the primary source (besides letters published half a century later in Christiaan Huygens’ Oeuvres) for information on Huygens’ improvements on Boyles’ first air- pump. “Among further improvements in the air-pump during the latter part of the seventeenth century were the two way tap, introduced by Papin; and the double cylindered pump, probably introduced by Papin and perfected by Hauksbee, through whom the air-pump assumed what long remained its standard form” (Wolf, A History of Science, Technol- ogy, and Philosophy, Vol. I, p. 107). The work is contained in a sammel- band from the Macclesfield Library, bound in mid-eighteenth-century polished mottled calf, with six other works. OCLC lists Brandeis and Harvard only in US. ❧ Ernst Weil stated (his Cat. 27, item 162) that this book is to be “always regarded as one of the Classics in Science; it is without doubt one of the rarest of all of them.”

31 Dibner 125 - ‘The best and most complete edition’ (Neville) 59. PARACELSUS, Theophrastus.Opera Omnia Medico-Chemico-Chirurgica, tribus voluminibus comprehensa. Geneva: Sumptibus Joan. Antonii, & Samuelis De Tournes. 1658. $19,500 A very fine copy, in contemporary vellum and with the often missing portrait, of “the best and most complete edition of Paracelsus’s collected works” (Neville). “According to Sudhoff, bibliographer of Paracelsus’s works, this com- pendium of the works of Paracelsus, edited by Friedrich Bitiskius, is the most complete of the Latin collected editions. It contains virtually all of Paracelsus’s medical and philosophical writings, as well as Tintoretto’s beautiful portrait of Paracelsus, which is often missing” (Heirs of Hippocrates). “Philippus Aureolus Theophratus Bobastus von Hohenheim, also known as Paracelsus, remains one of the most controversial and remarkable personalities of the Renaissance. He has been described as a quack, a magician, an astrologer, and alchemist, as well as a brilliant physician, prophet, and genius. Sir William Osler called him the ‘Luther of medicine,’ and Fielding Garrison lauded him as ‘the most original thinker of the sixteenth century.’ “Paracelsus was a voluminous writer …, but his controversial views and antagonistic personality alienated publishers, and only a few of his books appeared during his lifetime.” (Haskell F. Norman in One Hundred Books Famous in Medicine). ❧Dibner 124; Heirs of Hippocrates 215; Neville 250.

Eight pages of research notes on the brewing of beer

60. PASTEUR, Louis. Highly important group of autograph manuscript research notes by Pasteur relating to his early studies and experiments with beer, probably carried out in the first half of 1871 at the Kuhn brewery in Clermont-Ferrand, which revolutionized beer production. $36,250 In 1876, Louis Pasteur published his groundbreaking volume, Études sur la Bière, soon translated into English as Studies On Fermentation. This book changed the course of brewing during the late 19th and early 20th centuries, representing an enormous leap forward in the scientific understanding of the processes involved in beer making. Brewers around the globe put Pasteur’s findings to work in their breweries, and thus plunged the industry headlong into the modern era. In his preface, Pasteur modestly wrote, “I need not hazard any prediction concerning the advantages likely to accrue to the brewing industry from the adop- tion of such a process of brewing as my study of the subject has enabled me to devise, and from an application of the novel facts upon which this process is founded. Time is the best appraiser of scientific work, and I am not unaware that an industrial discovery rarely produces all its fruits in the hands of its first inventor.” But, of course, the brewing industry recognized almost immediately the impact that Pasteur’s work would have on the art and science of beer making. Frank Faulkner, the British brewing scholar who translated Pasteur’s volume explains: “The more I studied the work, the more I was convinced of its immense value to the brewer as affording him an intelligent knowledge of the processes and materials with which he deals . . . The debt which we English brewers owe to M. Pasteur can hardly be over-estimated.” ❧ Patrice Debré, Louis Pasteur, 1998. DSB X: 373-4.

32 Pavlov’s dogs 61. PAVLOV, Ivan Petrovitch. Lektsii o rabotie glavnikh pishtshevaritelnikh zhelyos. St. Petersburg: I. N. Kushnereff & Ko. $27,000 A fine copy, in contemporary Russian binding, of this famous work on di- gestive juices by the demonstrator of the ‘conditioned reflex’. “Mouthwa- tering is a familiar experience and may be induced without the sight or smell of food. The sounds of a table being laid for lunch in another room may induce salivation in man, and the rattle of a dish in which its food is usually served will cause similar reaction in a dog. “By detailed analysis of such facts as these Pavlov made great contributions to our knowledge of the physiology of digestion in a series of lectures delivered in St Petersburg and published in the following year [i.e., the offered work]. In the course of these lectures he described the artificial stomach for dogs used by him to produce for the first time gastric juices uncontaminated by food. Fur- ther experiments led him to the conclusion that salivation and the flow of gastric juice ensuing upon the sight or smell of food was due to a reflex process. This simple form of reaction he called first a ‘psychic’, later an ‘un- conditioned’, reflex. Reflex action was familiar to physiologists, but it had never been invoked to explain such a complicated process…” (PMM). ❧PMM 385; Grolier/Horblit 83; Dibner 135; Grolier/Medicine 85; Lilly, Notable Medical Books 24.

The foundation for modern census techniques

62. PETTY, William. Several Essays in Political Arithmetick. London: R. Clavel & H. Mortlock, 1699. $11,500 Very rare complete copy of this collection of Petty’s essays on demography and economics, “including the influential Political Arithmetick (first published 1690), a major comparative study of the wealth and economic policies of Eng- land and her rivals France and Holland. This was the first of Petty’s works to contain in its title the phrase he had coined to describe the application of statistics to economic theory and policy. Petty was the first to employ numerical evaluation in economics, and his work provided the decisive impulse toward econometrics and the general application of statistics” (Norman). ❧Garrison-Morton 1688; Norman 1688 (lacking several of the part- titles).

33 The Ramsden vertical circle 63. PIAZZI, Giuseppe. Della Specola Astronomica de’ Regi Studi di Palermo Libri Quattro. Palermo: Reale Stamperia, 1792. $6,500 A fine copy, uncut in the original boards, of Piazzi’s account of the Palermo Ob- servatory, which he established, and where he made the observations that led to his discovery, on January 1, 1801, of the minor planet Ceres. Specola Astronomica includes Piazzi’s description of the astronomical instruments he had commissioned and assembled for the Palermo Observatory, the most famous of which was Jesse Ramsden’s vertical circle, illustrated on the plates in this volume. A “large theodo- lite-type instrument was the 5-foot vertical circle which Ramsden made for Piazzi’s new observatory at Palermo. Both Ramsden and Piazzi worked at this instrument, twice abandoned before its completion in August, 1789. The horizontal circle gave readings in azimuth read by a micrometer microscope, and the vertical, readings in altitude by two diametrically opposed microscopes. The divisions on the cir- cles were illuminated by an inclined silver mirror fixed to each microscope, and the wires in the telescope eyepiece by transmitting light from a small instrument through the hollow tube-axis – two Ramsden innovations. This instrument, the fin- est complete circle hitherto made, formed the basis of Piazzi’s astronomical work. With it he catalogued nearly 8000 stars, compiled a valuable table of refractions, and attempted to measure the parallax of several bright stars. The great labour involved in the catalogue is the more remarkable when we consider that each star was observed several times before its position was decided” (King, History of the Telescope, pp. 166-8, with the circle illustrated). ❧Lalande, p. 622 (‘Ce grand et précieux ouvrage’).

The Poisson distribution 64. POISSON, Siméon-Denis. Recherches sur la probabilité des jugements en matiere criminelle et en matierecivile, précé- dées des règles générales du calcul des probabilités. Paris: Bachelier, 1837. $3,250 A fine copy of “Poisson’s major work on probability... The book was in large part a treatise on probability theory after the manner of Laplace, with an emphasis on the behavior of means of large numbers of measurements. The latter portion (p. 318- 415) dealt with the subject matter of the title. Some of this material was taken from memoirs Poisson published in the two preceding years. Only a charitable modern reading could identify a new concept in the work; yet the book contains the germ of the two things now most commonly associated with the Poisson’s name. The first of these is the probability distribution now commonly called the Poisson distribution. In a section of the book concerned with the form of the binomial distribution for large numbers of trials, Poisson does in fact derive this distribution in its cumula- tive form, as a limit to the binomial distribution when the chance of a success is very small. The distribution appears on only one page in all of Poisson’s work (here, p. 206). The second most common appearance of Poisson’s name in modern literature is in connection with a generalization of the Bernoulli law of large numbers.” (Stigler). ❧Stigler, The History of Statistics: The Measurement of Uncertainty Before 1900, p. 183.

34 Offprint collection assembled by Binet 65. POISSON, Siméon-Denis. Exceptional collection of almost forty Poisson offprints assembled by the mathematician, and successor of Poisson, Jacques Philippe Marie Binet (1786-1856). The collection includes offprints of Poisson’s most important papers in which he: created the mathematical theory of electrostatics; made his fundamental contributions to celestial mechanics; was a co-founder of the mathematical theory of elasticity; published his milestone investigations of definite integrals and Fourier series; first announced his ‘law of large numbers’; and made significant contributions to the mathematical theory of heat. Paris, 1808-1839. $32,500 Simeon Dennis Poisson (1781–1840) was “one of the greatest of nineteenth century analysts and a first-class mathematical physicist” (Kline). He was principal successor to Laplace, both in interests and position. “There are few branches of mathematics to which he did not contribute something, but it was in the application of mathematics to physical subjects that his greatest services to science were performed. He considered such matters as physical astronomy, stability of planetary orbits, heat con- duction, analytical mechanics, the attraction of ellipsoids, probability theory, definite integrals, Fourier series and theory of elasticity. One encounters Poisson Brackets, Poisson’s Constant, Poisson Integral, Poisson Equation, Poisson Summation Formula and the Poisson Distribution. He was first to predict the existence of longitudinal and transverse elastic waves and deduced, in an alternative way to that of Navier, the basic equations of a viscous fluid. He also studied the propagation of waves in anisotrop- ic media (crystals). He derived the equation satisfied by the gravitational potential within a distribution of matter, which now bears his name.” (Historical Encyclopedia of Natural and Mathematical Sciences). Provenance: Book plates of the mathematician Jacques Binet (1786-1856); the French engineer and book collector Henri Viellard (1840-1886); and the Institut Catholique de Paris to whom Viellard’s wife in 1902 donated his collection of important science books. ❧DSB, XV, pp. 480-490.

The copy of Pierre Daniel Huet 66. PROCLUS Diadochus. Procli... in primum Euclidis Elementorum librum commentariorum libri IIII. Padua: Percha- cino, 1560. $34,000 A magnificent copy, with a very distinguished provenance, of the first Latin edition of Proclus’ commentary on the first book of Euclid’sElements , 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 Col- lege 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. ❧For Huet’s library, see F. Pelisson-Karo, ‘La bibliotheque de Pierre-Daniel Huet...’, in B. Blasselle & L. Portes, Melanges autour de l’histoire des livres imprimees et periodiques, Paris: BNF, 1998, pp. 107-131.

35 Bound in sixteenth century red morocco 67. PTOLEMAEUS, Claudius. Clavdii Ptolemaei liber de analemmate. Rome: Paulum Manutius, 1562. $12,800 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 Mo- erbeke’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 in- genious 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). ❧ Adams P2216; Riccardi I 360; Renouard 173:4.

Only one complete copy in OCLC 68. RECORD, Robert. The Grounde of Artes ... And now of late diligently ouerseene and augmented with new and neces- sarie additions. I.D. [John Dee]. London: John Harison, 1579. $25,000 A very rare and early edition of “the first commercial arithmetic of any note used in the English schools” (Smith), by “the founder of the English school of mathematical writers” (DSB). All sixteenth-century editions of this book are rare. There are two variants of this edition. Both have the colophon with the joint imprint of Henry Binneman and Harison, and the date 1577; the other variant has Binneman’s name only on the title-page. Only one other complete copy of the present issue is known (Princeton); BL holds a ‘copy’ with the title leaf only. Three copies of the other issue are recorded: Columbia, National Li- brary of Wales, and UCL (imperfect). Remarking on the date at the colophon, Smith states ‘this is therefore one of the cases where a large edition was printed, and a new title-page was added from year to year as necessary. This [Binneman] edition is rarer than the date would suggest.’ Binneman and Harison first issued the book in 1575, and again in 1582, but no edition of 1577 is recorded. ❧Smith, Rara Arithmetica, p. 217 (for the Binneman issue). For an account of the evolution of the text see J. B. Easton, ‘The Early Editions of Robert Recorde’s Ground of Artes,’ in Isis, 58 (1967), 515–532.

36 ‘One of the most important achievements of 19th century mathematics’ 69. RIEMANN, Bernhard. Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichencomplexen Grösse. Göttingen: E. A. Huth, 1851. $29,500 First edition of Riemann’s Dissertation, “one of the most important achievements of 19th century mathematics” (Laugwitz), “which marked a new era in the development of the theory of analytic functions” (Kolmogorov & Yushkevich, p. 199), introducing geometric and topological methods, notably the idea of a ‘Rie- mann surface’. “Riemann’s doctoral thesis is, in short, a masterpiece” (Derbyshire, p. 121). It is also of great rarity, for “although [it] was a printed booklet, it was not published or publicised in the normal way; the candidate had to pay for the print-run, and sales and marketing were executed on an infinitesimal scale. So the first printing of Riemann’s thesis consisted only of the obligatory copies he had to hand in at Göttingen University, and a few copies for his personal use” (Peter Ullrich in Landmark Writings in Western Mathematics). The present copy is evidently one of those handed to the University. ❧Landmark Writings in Western Mathematics, no. 34.

Navigation 70. STEVIN, Simon. Limeneuretike sive Portuum investigandorum ratio. Metaphraste Hug. Grotio Batavo. Leiden: Of- ficina Plantiniana, 1599. $25,000 First Latin edition, very rare, of Stevin’s important contribution to the art of mari- time position finding by use of the compass and its deviation, published at the same time as the original Dutch edition (De Havenvinding). “In a seafaring nation like the Dutch republic matters of navigation were, of course, of great importance... in a short treatise entitled De Havenvinding, [Stevin] ap- proached the subject of determining the longitude of a ship, a problem that was not fully solved until the nineteenth century. Several previous authors had suggested that longitude might be determined by measuring the deviation of the magnetic needle from the astronomical meridian, a suggestion based on the assumption that the earthwide distribution of terrestrial magnetism was known. Since the determination of latitude was well known, such a measurement would allow the sailor to chart longitudinal position against the latitudinal circle...Stevin, in his booklet, gave a clear explanation of this method; he differed from Petrus Plancius and Mer- cator in that he did not rely upon a priori conceptions of the way in which geo- magnetic deviation depends upon geographical position. Although he was willing to offer a conjecture about this dependence, Stevin insisted on the necessity of col- lecting actual measurements from all possible sources and urged the establishment of an empirical, worldwide survey. His method was sound, although as data began to accumulate it became clear that the magnetic elements were subject to secular variation. The problem was at last solved more simply by the invention of the ship’s chronometer” (DSB). Christoffel Raphelengius was granted the privilege to print the work, in any language, in August 1599. An English edition was prepared by Edward Wright on the advice of Richard Hakluyt, while a French edition was entitled Le Trouve Port. The Latin translation was entrusted to the young and highly precocious Hugo Grotius, whose father Jan had been a long-standing associate of Stevin’s. One of his very earliest works, Grotius’ translation began an enterprise which culminated in his great Mare Liberum (On the Freedom of the Seas) of 1609. All editions of Stevin’s work are of exceptional rarity, only a single copy of any edition having appeared at British and American auctions in over 30 years. OCLC lists no copy in America. ❧Bierens de Haan 4565; Dijksterhuis, p. x and pp. 87-92.

37 With numerous contemporary annotations 71. STIFEL, Michael. Die Coss Christoffs Rodolff; mit schönen Exempeln der Coss durch Michael Stifel gebessert und sehr gemehrt. Königsberg: Alexandrum Behm von Lutomysl, 1553. $30,500 A magnificent copy, in contemporary blind stamped pigskin and heavily annotated, of the first edition of Stifel’sCoss . “This work did for Germany what Cardan’s and Tartaglia’s did for Italy” (Smith). This is the first edition by Stifel of Rudolff ’s Behend vnnd Hubsch Rechnung durch die kunstreichen regeln Algebre so gemeincklich die Coss genennt warden (Strasbourg, 1525), the first German book on algebra, usually referred to simply as the Coss. Rudolff ’s book having become unavailable, Stifel took on the task of producing a new version, not only reproducing Rudolff ’s text in its entirety, but adding commentary and additions of his own, which more than doubled the length of the book (Rudolff ’s 208 pages grew to 494 in Stifel’s edition). Stifel’s work served for at least the next 150 years as the principal text from which many mathematicians learned their algebra, including Frans van Schooten (1615-1660) (DSB) and, as late as the eighteenth century, Leonhard Euler (1707-1783); in fact, it formed the basis of Euler’s own algebra textbook, Vollständige anleitung zur Algebra (1770). “[Stifel] was, in fact, the greatest German algebraist of the sixteenth century” (DSB). ❧Smith, Rara Arithmetica, pp. 258-260; Honeyman 2916.

Offprint of his PhD thesis - the copy of Robin Gandy 72. TURING, Alan Mathison. Systems of Logic Based on Ordinals. London: C.F. Hodgson & Son, 1939. $37,800 First edition, the incredibly rare offprint issue, and the copy of Robin Gandy, of Turing’s PhD thesis, “one of the key documents in the history of mathematics and computer science” (Appel), and perhaps Turing’s most formi- dable paper. “Systems of logic based on ordinals is a profound work of first rank importance. Among its achievements are the exploration of a means of circumventing Gödel’s incompleteness theorems; the introduction of the concept of an ‘oracle machine,’ thereby opening the field of relative comput- ability; and, in the wake of the demolition of the Hilbert programme (by Gödel, Turing and Church), an analysis of the place of intuition in mathematics and logic” (Copeland). “Turing’s 1938 Princeton PhD thesis, Systems of logic based on ordinals, which includes his notion of an oracle machine, has had a lasting influence on computer science and mathematics... A work of philosophy as well as mathematics, Turing’s thesis envisions a practical goal – a logical system to formalize mathematical proofs so that they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms... Turing’s vision of ‘constructive systems of logic for practical use’ has become reality: in the twenty-first century, automated ‘formal methods’ are now routine” (Appel). Offprints of Turing’s papers are extremely rare in institutional holdings, and even more so in commerce. We have located only three copies: one in the Alan Turing Archive at King’s College Cambridge (AMT/B/15), one at St. Andrew’s, and one in the Max Newman collection at Bletchley Park. ❧Andrew Appel, Alan Turing’s Systems of Logic: The Princeton Thesis; Brian Jack Copeland, The Essential Turing; Solomon Feferman, Turing’s Thesis; Andrew Hodges, Alan Turing: The Enigma, pp. 142-3.

38 The Werner map projection 73. WERNER, Johannes. In hoc opere haec co[n]tinentur: Noua translatio primi libri Geographiæ Cl. Ptolomæi Geograph- ia quæ quidem translatio ... Nürnberg: Stuchs, 1514. $75,000 First edition of Werner’s most important book, an extremely rare and highly influential work on cartography and navigation, containing the first published direct translation of any part of Ptolemy’s Geography from the original Greek. It includes the first publication of the Werner map projection, which was widely used for world and continental maps through the sixteenth and seventeenth centuries, notably by Mercator, Oronce Finé and Ortelius. The book also contains the invention of the lunar distance method of longitude determination, and of the cross-staff, an instrument designed to make the necessary astronomical observations at sea. Werner’s greatest personal input in this edition were his mathematical notes to the first book, where he criticized Ptolemy, often on the grounds that taking him literally would result in ‘deforming the earth’s shape’. Drawing inspiration from Ptolemy and from astronomical usage, Werner also made an original contribution to cartographical projections with his Libellus de quatuour ... Here Werner gave a theoretical discussion of two generalizations of Ptolemy’s second conic projection. His Propositio IV modifies Ptolemy’s methodology by requiring that lengths be preserved on all parallels, represented by concentric arcs, and on all radii. Werner further modified the projection in a way that makes the North Pole the centre of what in modern terms would be called a system of polar coordinates. In Propositio V he also requires that a quadrant of the equator have the same length as the radius between a pole and the equator. These modifications provided the first solution to the problem of representing the surface of a sphere within a finite area. ❧ Bagrow, History of Cartography, pp. 34-35 & 209-10. Sabin 66479. Stillwell, The Awakening Interest in Science during the First Century of Printing, 212n & 25.

Defending their claim to be the first to fly 74. WRIGHT, Wilbur. Important signed autograph letter from Wilbur to the editor of Aeronautics magazine, written just seven months before his death, in which he validates the Wright brothers’ claim to being the first men to fly, refuting the French claim that this was done by Clément Ader in 1897. Dayton, Ohio: 21 October 1911. $84,500 Ever since their successful 17 December 1903 flight at Kitty Hawk, Wilbur and Orville Wright were challenged as to their claim that they were the first to fly by the French who claimed that Clément Ader (1841-1926) had flown in his Avion III airplane on 14 October 1897. The French claim was accepted by many, even in the United States. In this letter, Wilbur Wright makes the case that the French claims are unfounded. Ader, together with two assistants, completed his first flying machine, the Éole, in 1890. Its first test, at Armainvilliers on 9 October 1890, was the first legitimate attempt to fly a powered human-carrying airplane. Ader managed to accelerate to lift-off speed and skim the earth at a height of about 30cm for 50 metres in a machine that had essentially no forward vision and no flight control system. “Three criteria characterize a successful heavier-than-air airplane flight: it must be powered, sustained, and controlled. Ader met the first of these criteria, came close to but still missed the second, and definitely failed the third” (Hallion, p. 130). After securing 550,000 Francs of government fund- ing, Ader completed the more advanced Avion III in 1897, it’s first attempted flight vein in the afternoon of 14 October. . “The results were unambiguous failure: unlike the earlier Éole, theAvion III could not gain the air... Ader’s machine accelerated enough that the tail wheel rose, for its track disappeared. But the other wheels remained firmly grounded. Things rapidly got worse, and Ader and his airplane nearly came completely to grief when contrary winds blew it off course” (Hallion, p. 134). ❧ Richard Hallion, Taking Flight: Inventing the Aerial Age, from Antiquity Through the First World War, 2003.

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