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

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

Stand no. 306 San Francisco International Antiquarian Book Fair 15-17 February 2013

Astronomy ...... 14, 16, 22, 31, 50, 56 Chemistry ...... 3, 9, 10, 25, 39, 42, 43, 52, 61, 54 Commercial arithmetics, probability, statistics ...... 6, 12, 18, 41, 49, 55 Communications, Computing, Information ...... 4, 5, 20, 59, 63, 64 Electricity, magnetism ...... 8, 17, 33, 38 Geometry ...... 2, 21, 26, 30 Mechanics, machinery, technology ...... 1, 4, 5, 48 Medicine, Biology ...... 39, 44, 52, 54, 61 Mathematics ...... 2, 6, 11, 12, 19, 21, 24, 26, 29, 30, 31, 32, 36, 37, 41, 45, 50, 62, 63, 64 Navigation...... 15, 38, 46, 50 Optics...... 9, 22, 31, 35, 40, 51, 58 Physics ...... 7, 8, 9, 10, 13, 17, 19, 23, 25, 26, 27, 28, 31, 33, 34, 35, 38, 40, 47, 48, 51, 53, 57, 60 PMM*, Dibner, Horblit, Evans, Sparrow ...... 1*, 8, 12*, 16, 23*, 25*, 26*, 28, 30, 33*, 40, 41, 43*, 44, 46*, 51, 52, 53*, 62* Special copies, inscribed, provenance ...... 21, 23, 24, 29, 36, 39, 42, 49 20th century science ...... 7, 13, 20, 27, 28, 34, 37, 39, 47, 53, 57, 60 PMM 79 - The first systematic treatise on mining and metallurgy 1. AGRICOLA, Gerorgius. De Re Metallica. Basel: Froben & Bischoff, 1556. $60,000

A fine copy, in contemporary binding, of “the first systematic treatise on mining and metallurgy and one of the first technological books of modern times” (Printing and the Mind of Man). “The De Re Metallica embraces everything connected with the mining industry and metallurgical processes, including administration, prospecting, the duties of officials and companies and the manufacture of glass, sulphur and alum. The magnificent series of two hundred and seventy-three large woodcut illustrations by Hans Rudolph Manuel Deutsch add to its value. Some of the most important sections are those on mechanical engineering and the use of water-power, hauling, pumps, ventilation, blowing of furnaces, transport of ores, etc., showing a very elaborate technique.” (PMM).

Copies in unrestored contemporary binding are rare.

❧PMM 79, Horblit 2b, Dibner 88, Sparrow 4.

Large-paper copy, uncut in the original wrappers 2. APOLLONIUS of Perga. Conicorum Lib. V. VI. VII. Florence: Cocchini, 1661. $12,000 Editio princeps of books V-VII of the Conics, the most original parts of Apollonius’s treatise on conic sections. Books I-IV were translated and published in 1537, and at the time it was believed that the remaining books were lost. “In the first half of the seventeenth century the Medici family acquired an Arabic manuscript containing Books V-VII of Apollonius’s Conics, which had been lost up to that time. In 1658, with the help of the Maronite scholar Abraham Ecchellensis, Giovanni Borelli prepared an edited Latin translation of the manuscript, which was published three years later. This was a valuable addition to the mathematical knowledge of the time, for whereas Books I-IV of the Conics dealt with information already known to Apollonius’s predecessors, Books V-VII were largely original. Book V discusses normals to conics and contains Apollonius’s proof for the construction of the evolute curve; Book VI treats congruent and similar conics and segments of conics; Book VII is concerned with propositions about inequalities between various functions of conjugate diameters” (Norman). “The fifth book reveals better than any other the giant intellect of its author. Difficult questions of maxima and minima, of which few examples are found in earlier works, are here treated most exhaustively. The subject investigated is to find the longest and shortest lines that can be drawn from a given point to a conic. Here are also found the germs of the subject of evolutes and centres of osculation” (Cajori, A History of Mathematics).

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

❧Norman 58, Honeyman 119, De Vitry 29. A foundation work of physical chemistry 3. AVOGADRO, Amadeo. Fisica de’ Corpi Ponderabili ossia Trattato della Costituzione Generale de’ Corpi del Cavaliere. 4 vols. Torino: Stamperia Reale, 1837-41. First edition. $28,000 A very fine set of one of the great milestones of chemical literature. This monumental work is the only major publication of Avogadro (1776- 1856), one of the founders of physical chemistry in the early 19th century. The famous hypothesis which bears his name - that equal volumes of all gases and vapors contain the same number of ultimate molecules at the same pressure and temperature - demonstrated the link between Gay- Lussac’s law of volume and Dalton’s atomic theory, and provided a much needed key to the problems of 19th-century chemistry by distinguishing between atoms and molecules. The very title of this book indicates that he was concerned with atomic weights. His molecular hypothesis is widely considered to be Italy’s great contribution to chemistry in the 19th century. Emil Offenbacher, the distinguished dealer who specialized in chemistry, wrote (cat. 39, item 4, 1986) ‘a complete set is today of great rarity’.

❧Norman 89; Honeyman 168; Neville Historical Chemical Library 52.

The very rare pre-publication offprint 4. BABBAGE, Charles. On a Method of Expressing by Signs the Action of Machinery. London: W. Nicol, 1826. First edition. $12,800 Offprint issue of “Babbage’s first publication of his system of mechanical notation that enabled him to describe the logic and operation of his machines on paper as they would be fabricated in metal.” (Norman). Babbage later stated that ‘Without the aid of this language I could not have invented the Analytical Engine; nor do I believe that any machinery of equal complexity can ever be contrived without the assistance of that or some other equivalent language. The Difference Engine No. 2 … is entirely described by its aid’. “While making designs for the Difference Engine, Babbage found great difficulty in ascertaining from ordinary drawings – plans and elevations – the state of rest or motion of individual parts as computation proceeded: that is to say the following in detail succeeding stages of a machine’s action. This led him to develop a mechanical notation which provided a systematic method for labeling parts of a machine, classifying each part as fixed or moveable; a formal method for indicating the relative motions of the several parts which was easy to follow; and means for relating notations and drawings so that they might illustrate and explain each other. As the calculating engines developed the notation became a powerful but complex formal tool. Although its scope was much wider than logical systems, the mechanical notation was the most powerful formal method for describing switching systems until Boolean algebra was applied to the problem in the middle of the twentieth century. In its mature form the mechanical notation was to comprise three main components; a systematic method for preparing and labeling complex mechanical drawings; timing diagrams; and logic diagrams, which show the general flow of control.” (Hyman).

❧ Origins of Cyberspace, no. 37 (ordinary journal issue, i.e., not the offprint as here). The most important paper in the in the history of digital computing 5. BABBAGE, Charles. & LOVELACE, Ada. Sketch of the Analytical Engine invented by Charles Babbage. London: Richard & John Taylor, 1843. $37,500 In 1840 Babbage traveled to Torino to present to a group of Italian scientists an account of his Analytical Engine. In attendance at Babbage’s lecture was the young Italian mathematician Luigi Federico Menabrea (later Prime Minister of Italy), who prepared from his notes an account of the principles of the Analytical Engine, which he published in French in 1842. “After the appearance of Menabrea’s paper, the daughter of Lord Byron, Augusta Ada King, Countess of Lovelace, became interested in preparing an English translation… At Babbage’s suggestion, Lady Lovelace added seven explanatory notes to her translation, which run three times the length of the original. Because Babbage never published a detailed description of the Analytical Engine, Ada’s translation of Menabrea’s paper, with its lengthy explanatory notes, represents the most complete contemporary account in English of the intended design and operation of the first programmable digital computer. Her annotated translation has been called ‘the most important paper in the in the history of digital computing before modern times’ (Allan George Bromley). Babbage considered this paper a complete summary of the mathematical aspects of the machine, proving ‘that the whole of the development and operations of Analysis are now capable of being executed by machinery’. As part of his contribution to the project, Babbage supplied Ada with algorithms for the solution of various problems. These he had worked out years ago, except for one involving Bernoulli numbers, which was new. Ada illustrated these algorithms in her notes in the form of charts detailing the stepwise sequence of events as the hypothetical machine would progress through a string of instructions input from punched cards. These procedures, and the procedures published in the original edition of Menabrea’s paper, were the first published examples of computer ‘programs’.” (Norman).

Theory of speculation 6. BACHELIER, Louis. Calcul des Probabilités. Paris: Gauthier-Villars, 1912. $4,000 Very rare first edition of Bachelier’s first book, in which he elaborated and further developed the ideas from his celebrated thesis Théorie de la Spéculation (1900). Bachelier considered this book as the first to surpass Laplace’s great treatise Théorie Analytique des Probabilités (1812). Louis Bachelier (1870- 1946) is nowadays generally credited with being the first person to model the stochastic process now called Brownian motion, which was part of his PhD thesis. His thesis, which discussed the use of Brownian motion to evaluate stock options, is historically the first paper to use advanced mathematics in the study of finance. “Five years before Einstein’s famous 1905 paper on Brownian Motion, in which Einstein derived the equation (the partial differential heat/diffusion equation of Fourier) governing Brownian motion and made an estimate for the size of molecules, Bachelier had worked out, for his Thesis, the distribution function for what is now known as the Wiener stochastic process (the stochastic process that underlies Brownian Motion) linking it mathematically with the diffusion equation. The probabilist William Feller had originally called it the Bachelier-Wiener Process. It appears that Einstein in 1905 was ignorant of the work of Bachelier. “Seventy three years before Black and Scholes wrote their famous paper in 1973, Bachelier had derived the price of an option where the share price movement is modelled by a Wiener process and derived the price of what is now called a barrier option (namely the option which depends on whether the share price crosses a barrier).” (MacTutor History of Mathematics). “However, not only was his thesis remarkable, but his later researches were even more so ... Bachelier introduced an interesting theory of ‘invers probability’ and of ‘probability causes,’ that is of statistical estimation, which he pursued in a treatise on the calculus of probabilities published in 1912 [the offered volume], which is as clear as it is remarkable.” (Statisticians of the Centuries). 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 Society, 1957. $13,500 Exceptional offprint of this famous paper announcing the ‘BCS’ theory of superconductivity, the first successful quantum-mechanical explanation of the disappearance of electrical resistance in certain metals at very low temperatures. Superconductivity 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). The offprint is accompanied by copies of the two earlier Physical Review papers which announced the essential ideas leading to the BCS theory (each contained in a complete journal issue in the original printed wrappers).

❧Brandt, Harvest of a Century, Episode 78.

One of the most important practical texts on magnets in the seventeenth century 8. BARLOW, William. Magneticall Aduertisements: or divers pertinent obseruations, and approued experiments concerning the nature and properties of the Load-stone... most needfull for practise, of trauelling, or framing of Instruments fit for Trauellers both by Sea and Land. London: Griffin for Barlow, 1616. $24,000 First edition of this rare and important work. The result of forty years’ research into magnetism, with special regard to the manufacture and maintenance of the sea-compass, and containing Barlow’s two fundamental discoveries concerning the directional properties of the compass-needle: the first being that steel made a better needle than iron. Secondly, he devised a method for contact ‘touching’ which increased the directional capabilities of needles.

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

❧Horblit 83; Frank Streeter 19; Penrose 19; Wheeler Gift 89. Inscribed copy of his doctoral thesis 9. BECQUEREL, Antoine Henri. Recherches sur l'absorption de la lumiere. Paris: Gauthier-Villars, 1888. First edition. $16,000 Presentation copy of his doctoral thesis on the absorption of light in crystals, inscribed by Becquerel to his demonstrator Peignot. “On March 15, 1888 he submitted his thesis ‘Recherches sur l’absorption de la lumière’ (Research on the absorption of light). Antoine Henri had been interested in the absorption of light by crystals since 1886 and showed the importance of crystal symmetry in the absorption spectra of polarized light. He noticed that tetravalent uranium compounds were not phosphorescent, whereas uranyl salts exhibited a bright luminescence under the same conditions of excitation. Interestingly enough this was the second experiment performed by a Becquerel on uranium. Like his father, Antoine Henri was fascinated by the phenomenon of phosphorescence, and at the time nobody suspected the secret hidden in the mysterious element. This strange coincidence might be regarded as a premonitory sign of destiny or as the first step towards a major discovery.” (Adloff: 100 Years after the Discovery of Radiochemistry, p.5).

❧Norman 156 [Norman copy with anonymous inscription].

Discovery of radioactivity 10. BECQUEREL, Antoine Henri. (1) Sur les radiations émises par phosphorescence. In: Comptes rendus des séances de l'Académie des Sciences 122, no. 8 (24. February), pp. 420-21. (2) Sur les radiations invisibles émises par les corps phosphorescents. In: ibid., no. 9 (2 March) pp. 501-2. (3) Sur quelques propriétés nouvelles des radiations invisibles émises par divers corps phosphorescents. In: ibid., no. 10 (9 March) pp. 559-64. (4) Sur les radiations invisibles émises par les sels d'uranium. In: ibid., no. 12 (23 March) pp. 689-94. (5) Sur les propriétés différents des radiations invisibles émises par les sels d'uranium, et du rayonnement de la paroi anticathodique d'un tube de Crookes. In: ibid., no. 13 (30 March) pp. 762-67. (6) Émission de radiations nouvelles par l'uranium métallique. In: ibid., no. 20 (18 May) pp. 1086-88. Paris: Gauthier-Villars, 1896. First edition. $11,500 An exceptional set of the six weekly issues of the Comptes Rendus in which Becquerel first announced his discovery of radioactivity (not to be confused with the later issued and common annual volumes as in the Norman and Plotnick collections). “On 24 February 1896, Becquerel announced to the French Academy of Sciences that fluorescent crystals of potassium uranyl sulfate had exposed a photographic plate wrapped in black paper after both had lain for several hours in direct sunlight, and on 3 March, he reported similar exposures after both crystals and plate had been kept together in total darkness. In the following two months, Becquerel determined that only crystals containing uranium emitted the penetrating rays, that nonluminescent compounds of uranium also produced radiation, and that the rays were capable of ionizing gases. On 18 May, he reported that a disc of pure uranium produced penetrating radiation three to four times stronger than that produced by the potassium uranyl sulfate crystals. In 1903 Becquerel shared the Nobel Prize for physics with the Curies, as his investigations had opened the way for the Curies’s discovery of radium and polonium.” (Norman).

❧Grolier/Medicine 84a; Norman 157. ‘The most spectacular event of the century in the history of British mathematics’ 11. BERKELEY, George. The Analyst; or, a discourse addressed to an infidel mathematician. London: J. Tonson, 1734. $20,000 First edition, first issue, of Berkeley’s famous attack on the new analysis of Newton and Leibniz, which “marks a turning-point in the history of mathematical thought in Great Britain” (Cajori), bound with Berkeley’s Theory of Vision (1733) - a work of “of major importance” (Keynes), and Defence of Free-Thinking in Mathematics (1735), and five more pamphlets. “Despite the great progress of analysis during the 18th century, foundational questions remained largely unsolved. … The most influential criticism of the new analysis was put forward by the famous English philosopher George Berkeley in 1734. The subtitle of his work The Analyst Or A Discourse Addressed to an Infidel Mathematician [referred to Newton’s friend and proponent of fluxions Edmund Halley]. … 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, History of Analysis).

❧Barchas 167; Stanitz 52a.

The calculus of probabilities 12. BERNOULLI, Jacob. Ars conjectandi. Basel: Impensis Thurnisiorum Fratum, 1713. $9,500 First edition of the “establishment of the fundamental principles of the calculus of probabilities” (Grolier/Horblit). Bernoulli’s posthumous treatise was edited by his nephew and is considered the first significant book on probability theory. The title refers to conjectandi, or ‘casting’ as in the casting of dice. The Ars conjectandi “was the first systematic attempt to place the theory of probability on a firm basis and is still the foundation of much modern practice in all fields where probability is concerned- insurance, statistics and mathematical heredity tables” (PMM). The work is divided into four parts: the first a commentary on Huygens’ De ratiociniis in aleae ludo (1657), the second a treatise on permutations and combinations (the former Bernoulli’s own term), the third an application of the theory of combination to various games of chance, and the final, and most important, part which contains Bernoulli’s philosophical thoughts on probability - as a measurable degree of certainty, necessity and chance, of moral versus mathematical expectation, and of a priori and a posteriori probability. It also contains his theorem, an application of probability to statistics.

❧PMM 179; Dibner 110; Evans 8; Grolier/Horblit 12; Sparrow 21. Bohr’s principle of complementarity, inscribed offprint 13. BOHR, Niels. Das Quantenpostulat und die neuere Entwicklung der Atomistik. Berlin: Julius Springer, 1928. First edition. $23,500 Very rare offprint issue, inscribed presentation copy, of this fundamental paper introducing Bohr’s statement of his ‘complementarity’ principle, the basis of what became known as the ‘Copenhagen interpretation’ of quantum mechanics. “From the epistemological point of view, the discovery of the new type of logical relationship that complementarity represents is a major advance that radically changes our whole view of the role and meaning of science. In contrast with the nineteenth-century ideal of a description of the phenomena from which every reference to their observation would be eliminated, we have the much wider and truer prospect of an account of the phenomena in which due regard is paid to the conditions under which they can actually be observed - thereby securing the full objectivity of the description” (DSB).

‘The most significant treatise between Kepler and Newton’ 14. BOULLIAU, Ismael. Astronomia philolaica. Paris: Simeonis Piget, 1645. $21,500 First edition, very rare, of “the first treatise after Kepler’s Rudolphine Tables to take elliptical orbits as a basis for calculating planetary tables” (The Cambridge Companion to Newton), and the first astronomy work to state that the planetary moving force “should vary inversely as the square of the distance—and not, as Kepler had held, inversely as the first power” (Boyer in DSB). “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, MacTutor History of Mathematics).

❧Sotheran’s I:500 (“This important work according to Newton first mentions the sun’s attraction, which decreases in inverse proportion to its distance”); Favaro, Bibliografia Galileiana #205. The first popular explanation of surveying by triangulation 15. BOURNE, William. A booke called the Treasure for traveilers, devided into five Bookes or partes, contaynyng very necessary matters, for all sortes of Traveilers, eyther by Sea or by Lande. London: Thomas Dawson, 1578. First edition. $33,000 A fine copy of the first popular explanation of surveying by triangulation, and of the importance of mathematics to seamen; the first English book to describe the volume, capacities and proportions of ships’ hulls, and the sizes and weights of cordage, with rules for their computation; and one of the first descriptions of the currents of the ocean. This copy is from the celebrated library of Boies Penrose (1902-1976), author of the esteemed book Travel and Discovery in the Renaissance, 1420-1620, whose small but important collection of early travel and navigation books was auctioned in 1971 by Sotheby’s. We have been able to find just three other similar copies auctioned since then: 1. The Harrison D. Horblit copy (Sotheby’s 1974); 2. The Robert B. Honeyman copy (Sotheby’s 1978); 3. The copy from the Pierre S. duPont Collection of Navigation. Frank S. Streeter had Bourne’s Regiment for the Sea but did not obtain a copy of the Treasure for travellers.

❧Horblit 160; Penrose 34; Honeyman 451.

The basis of Kepler’s laws 16. BRAHE, Tycho. Astronomiae Instauratae Mechanica. Nuremberg: Levinus Hulsius, 1602. $64,500 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 Rantzov’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 Herschel’s A General Catalogue of Nebulae and Clusters of Stars (London 1864), bookplate, signature dated 1875 and a few notes laid in; Francisco J.M. Duarte (owner’s signature).

❧Norman 320; Sparrow, Milestones of Science 29. The first recognition of electrical repulsion 17. CABEO, Niccolo. Philosophia Magnetica. Ferrara: Francesco Suzzi, 1629. First edition. $15,000 “The first Italian book on magnetism and electricity, and only the second to be published on these subjects, the De Magnate (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 of some … 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.

One of the earliest commercial arithmetics 18. CALANDRI, Filippo. Arithmetrice introductor. Florence: Bernardo Zuchetta, 1518. $60,000 Very rare second edition of the first illustrated Italian arithmetic, containing the first printed example of the modern method of long division, and the first printed use of the word ‘zero’. Calandri’s work was used to teach elementary mathematical techniques necessary for business, both for craftsmen and merchants. This edition follows the first of 1491, with the same illustrations. One of the earliest printed works to teach commercial arithmetic, it gives the leading rules for integers and for lire, soldi and denari. Calandri is the first to give long division in the modern form, known to the Italian writers by the name ‘a danda’. “Indeed Calandri gives only the ‘a danda’ method, omitting the galley forms, and is therefore fully a century ahead of his time” (Smith). Born in Florence in 1467, Filippo Calandri was, like his grandfather, father and brother, an abacist (a book-keeper or accountant in modern terms). Almost nothing else is known of his life. Apart from his Arithmetic, he also composed a work on probability and games of chance entitled Varie ragioni tratte de vari luogi; this was never published, but the manuscript survives in the Biblioteca Communale in Siena.

❧Sotheran 6673 (‘of excessive rarity... whereas 6 copies of the edition of 1491 have been sold in the last 10 years, no copy of the present one can be traced at all’); Honeyman 568; Smith 47. With an original contribution by Fermat 19. CASTELLI, Benedetto. Traicté de la mesure des eaux courantes. Castres: F. Barcouda, 1664. $33,500 Rare first edition in French of two works which founded the modern science of hydraulics, and including an original contribution by Fermat which appears here for the first time. Only one other scientific work of Fermat was published in his lifetime. The second work has a preface by the translator Saporta addressed to Fermat. Fermat had prompted Saporta to undertake the translation as a sequel to that of Castelli. The last four pages of the book contain the ‘Observation sur Synesius’ which in translation begins as follows: “The pages which remain empty in this quire made me think of filling them with the splendid observation which I learned some days ago from the incomparable M. Fermat, who does me the honor of being my friend and of frequently talking with me. It is in the fifteenth letter of Synesius, Bishop of Cyrene, which deals with something not understood by any of his commentators, not even by the learned Father Petau, as he himself avows in his notes on this author. I give this observation even more willingly as it has much in common with the treatises here printed.” The ailing Synesius (378-430 AD) wrote in 402 to his friend and teacher Hypatia asking for an instrument he called a hydroscopium or baryllion, and provided detailed instructions as to its construction. When the works of Synesius were published by the Jesuit theologian Denis Petau (1583- 1652) in 1640, Petau confessed that he was unable to understand Synesius’s letter. Castelli asked Fermat for his opinion, and the latter’s response was published as the ‘Observation sur Synesius’. Fermat showed that the instrument described by Synesius was a hydrometer, used to measure the specific gravities of liquids, and he gives a detailed description of its construction, with a diagram. The only other scientific work of Fermat to be published in his lifetime was De linearum curvarum, which appeared as an appendix to Antoine de Lalouvere’s Veterum geometrica promota (1660).

The blueprint for the Internet 20. CERF, Vinton G. & KAHN, Robert E. A Protocol for Packet Network Intercommunication. New York: IEEE Transactions on Communications, 1974. First edition. $10,500 A very fine and entirely unrestored copy of the most important article on the Internet’s development: Cerf and Kahn’s creation of the Transmission Control Program (TCP), the blueprint for the Internet. “In the early 1970s ARPANET, and other data networks that were beginning to be constructed around the word, were hampered by the fact that each operated according to different hardware and software protocols, thus making it impossible for them to communicate with one another … This problem was solved by Cerf and Kahn’s invention of the TCP/IP cross-network protocol that allowed the creation of an international network of computer networks; i.e., the Internet [a term the authors invented around 1973 as an abbreviation for ‘inter-networking of networks’. The authors laid out the architecture of such a network in the present paper: It describes gateways, which sit between networks to send and receive ‘datagrams.’ Datagrams, similar to envelopes, enclose messages and display destination addresses that are recognized by gateways. Datagrams can carry packets of various sizes. The messages within datagrams are called transmission control protocol (TCP) messages. TCP is the standard program, shared by each network, for loading and unloading datagrams; it is the only element of the international network that must be uniform among the small networks, and it is the crucial element that makes global networking possible.” (Norman).

❧Origins of Cyberspace 528. The copy of Athanasius Kircher 21. CEVA, Giovanni . De Lineis Rectis se invicem secantibus statica constructio. Milan: Lodovico Monza, 1678. First edition. $10,000 A fine copy, with distinguished provenance, of this rare and important work; “For most of his life Giovanni Ceva worked on geometry. He discovered one of the most important results on the synthetic geometry of the triangle between Greek times and the 19th Century. The theorem states that lines from the vertices of a triangle to the opposite sides are concurrent precisely when the product of the ratio the sides are divided is 1. He published this in De lineis rectis (1678), which he dedicated to the Duke of Mantua, a book in two parts together with an important appendix. Ceva also rediscovered and published Menelaus’s theorem in this work. That the book was not fully appreciated at the time of its publication is suggested by the fact that only one edition appeared and also by the fact that many of the results in the book were later rediscovered by others who were unaware of Ceva’s work. The importance of Ceva’s discoveries was only fully appreciated when pointed out by Michel Chasles in the 19th century.” (MacTutor History of Mathematics).

❧Roberts and Trent, Bibliotheca Mechanica 65.

The most exhaustive treatise on lens making in the seventeenth century 22.CHERUBIN d’Orléans, Capuchin. La dioptrique oculaire, ou la théorique, la positive, et la mechanique de l’oculaire dioptrique en toutes ses espèces. Paris: Jolly and Benard, 1671 [1670]. $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 Origins of the Telescope, pp. 289-291). The copy of Carl Friedrich Gauss 23.CHLADNI, Ernst Florens Friedrich. Entdeckungen über die Theorie des Klanges. Leipzig: Weidmanns Erben und Reich, 1787. First edition. $7,250 A fine copy, with the most distinguished possible provenance, of the book which established the scientific study of acoustics. “The production of sound from solid bodies was not clearly understood until Chladni devised the method of sand figures to illustrate the structure of vibrations in a solid body. He spread sand over glass and copper plates and drew a violin bow over their edges, causing the plates to vibrate; the sand, agitated by vibrations, collected over the nodal curves where no motion occurred. Chladni then classified the sand figures according to geometrical shape and noted for each the corresponding pitch, thus demonstrating that he patters and sounds of a vibrating plate are analogues to the shapes and tones of the modes in the harmonic series string. The strange and beautiful ‘Chladni figures,’ first described in the above work, attracted much scientific attention in the early nineteenth century, inspiring fruitful investigation of the mathematics of elastic vibration.” (Norman). This copy is from the personal library of Gauss. It was sold as a duplicate in 1951 by the Göttingen State and University Library, at which time it passed into private hands.

❧Dibner 150; PPM 233a; Sparrow 39; Norman 480.

A precursor to the calculus 24. CUNHA, José Anastácio da. Principios Mathematicos. Lisbon: Antonio Rodrigues Galhardo, 1790. $13,500

First edition, very rare, of this important but neglected work by “one of the main precursors of the reform of the foundations of infinitesimal calculus, initiated in the first decades of the nineteenth century” (DSB). Later commentators have found books IX and XV to be especially significant. Book IX of the Principios begins with the definition of a convergent series which is equivalent to what is now called the Cauchy convergence criterion … As a corollary, Cunha establishes the convergence of the exponential series, by term-by-term comparison with a geometric series. Using this result, Cunha is able to give a definition of ax by means of a convergent series; the logarithm is then defined as an inverse function. “What we have here is a perfectly rigorous and ‘modern’ approach to powers and logarithms, perhaps the first time that this was done this way and correctly. Cunha’s work on logarithms was praised by none other than C. F. Gauss, in a letter to Bessel, November 21, 1811” (Queiró). The foundation work of atomic theory 25. DALTON, John. A New System of Chemical Philosophy. Manchester: S. Russell for R. Bickerstaff; Russell & Allen for R. Bickerstaff; Executives of S. Russell for G. Wilson, 1808; 1810; 1827. First edition. $60,000 Very rare complete set with all half-titles, uncut in original boards. The rarity of complete sets of this work is well known. In 1921 Sotheran’s described a complete set as being ‘excessively scarce’, and during the past thirty years only a handful of copies have appeared on the market, all inferior to ours: Richard Green 2008 (a made-up set lacking the half-titles); Friedman 2001 (modern bindings); the Freilich-Norman copy 2001/1998 (non-uniform cloth-backed boards); Honeyman 1979 (rebacked and made-up). The copy which comes closest in condition to ours is the Freilich-Norman copy (Sotheby’s 2001, $43,875). However, that copy was bound in three different types of boards (plain grey, blue, and marbled), with the cloth laid over the boards, and the spine labels were hand-lettered. All three parts of our copy are bound in uniform cloth-backed plain grey boards, with the cloth laid under the paper of the boards, and have the original printed spine labels intact.

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

Exceptionally large copy in the original Dutch vellum 26.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. First edition. $190,000 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- Euclidean 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. The Dirac Equation 27. DIRAC, Paul Adrien Maurice. The Quantum Theory of the Electron. London: Harrison, 1928. $6,000 A fine copy in original wrappers of the discovery of the ‘Dirac equation’. “The relativistic wave equation of the electron ranks among the highest achievements of twentieth-century science” (Pais, Inward Bound, p. 290). “What is widely regarded as Dirac’s greatest contribution to physics came in 1928, when he found an equation which incorporates both quantum physics and the requirements of the special theory of relativity to give a complete description of the electron. One of the most remarkable features of this equation was that it had two sets of solutions, corresponding to positive energy electrons and negative energy electrons; the ‘negative energy electrons’ are now called positrons. Dirac had predicted the existence of antimatter, although even Dirac was not entirely clear what the equations meant until the positron was discovered by Carl Anderson in 1932. Because they incorporated relativistic effects, Dirac’s wave equations had accurately predicted the electron’s motion, spin, and magnetic and other properties. Moreover, these equations laid the foundations for the theory of quantum electrodynamics, which incorporates both quantum and relativity theory in its descriptions of the interactions of charged particles with the electromagnetic field” (Britannica).

❧Brandt, Harvest of a Century, Episode 43.

‘One of the most remarkable volumes in the whole scientific literature’ (Max Born) - offered together with his celebrated E=mc2 paper 28. 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 geforderte Bewegung von in ruhenden Flussigkeiten suspendierten Teilchen; 4) Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? Leipzig: Johann Ambrosius Barth, 1905. First edition. $25,000 Volumes 17 & 18 of the Annalen der Physik, bound in two uniform contemporary half-cloth bindings, fine unsophisticated copies without stamps or other markings. “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., 17] of the Annalen der Physik, the three papers having been submitted within a period of only three and half months.” (Wolff). Volume 18 contains Einstein’s famous paper in which he first announced his celebrated equation relating mass and energy E=mc2.

❧Dibner 167; Grolier/Horblit 26b; Norman 691a First German Euclid 29. EUCLID of Alexandria. Das sibend, acht vnd neünt Buch, des hochberühmbten Mathematici Euclidis Megarensis. Augsburg: Valentine Ottmar, 10 April 1555. $30,000 Very rare first appearance of any part of Euclid’s work in German, and one of the earliest vernacular editions (preceded only by Italian translations). This is a fine copy with distinguished provenance: Jakob Fugger (1542-98), member of the famous German family of merchant princes. Then the richest family in Europe, the Fuggers were generous patrons of the arts and learning and philanthropists, notably at Augsburg, their principal residence. Their fortune was largely built on a virtual monopoly in the mining and trading of silver, copper, and mercury. Very rare: No copies in the major collections of Macclesfield, Honeyman, Horblit, or De Vitry. The last collection included nearly 200 editions of Euclid. We can locate no auction records from the past 50 years. OCLC: Brown, Columbia, British Library, National Library of Wales.

❧Thomas-Stanford, Early editions of Euclid’s Elements, XVI (p. 54); Steck, M. Bib. Euclideana, III.54 (p. 65); Grässe, II, p. 513; Riccardi, P. Bib. Euclidea, p. 19, no. 1555. Not in Schweiger, STC German, or Adams.

Creation of the Calculus of Variations 30. EULER, Leonhard. Methodus inveniendi Lineas Curvas Maximi Minimive proprietate gaudentes, sive Solutio Problematis isoperimetrici latissimo sensu accepti. Lausanne & Geneve: Bosquet & Socios, 1744. First edition. $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. On the theory of light and colors 31. EULER, Leonhard. Opuscula Varii Argumenti, I-III. Berlin: A. Haude & J.C. Spener, 1746-50-51. First edition. $8,750 First edition of this collection of tracts which contains the first printing of Euler’s major treatise on the theory of light and colors Nova theoria lucis et colorum. According to Casper Hakfoort the wave- particle duality debate in optics really began with Euler’s publication of this work. “When Leonhard Euler published his treatise ‘Nova theoria lucis et colorum’ (A new theory of light and colours) in 1746, he made a contribution to the medium tradition in physical optics that was without parallel in the eighteenth century. The ‘Nova theoria’ constitutes the most lucid, comprehensive, and systematic medium theory of that century. The significance of Euler’s theory can be gauged partly from the fact that it was so widely discussed. No earlier attempts to provide an alternative to the theories developing within the emission tradition had stimulated pens to the same extent as Euler’s ‘Nova theoria’. It is remarkable that a relatively short treatise published as part of a collection of articles on a range of subjects created such resonances, and all the more so when we compare this reaction with the limited response to Huygens’ Traité - a complete book - and with the way in which Johann II Bernoulli’s prize essay was virtually ignored.” (Hakfoort, Optics in the Age of Euler, p. 72, Cambridge University Press, 1995). The ‘Nova theoria’ is pp. 169-244 of volume 1. There are twelve further tracts by Euler (on astronomy, magnetism, electricity, mathematics, and physics) in the three volumes all of which, except one, are published here for the first time. The Eneström numbers are 86-91; 151-154; 109,173-174.

❧Honeyman 1064; Wheeler Gift 366.

Euler’s earliest publication 32. EULER, Leonhard. Positiones Logicae Miscellaneae quas…pro vacante Cathedra Logica ad d. 30. Ian. M DCC XXII…publico eruditorum examini subjiciet M. Ioh. Rudolphus Battierius…respondente…Leonhardo Eulero. [Basel]: E. & J. R. Thurneisen, 1722. $10,000 First edition, extremely rare (OCLC locates the copy at Basel only), of the first publication of Leonhard Euler (1707-83). It records Euler’s role as respondent to the thesis of Johann Rudolf Battier (1693-1759), a candidate for the vacant Chair of Logic. Euler was then just fourteen years old. Euler entered the Philosophy Faculty of the University of Basel on 20 October 1720, aged thirteen. He studied a range of subjects, including mathematics, and received private tuition in this subject from Johann I Bernoulli, who in 1705 had followed his brother Jakob to the chair of mathematics at Basel. In January 1722, Euler acted as respondent to the logic thesis of Battier, and in November of the same year to a thesis on Roman ship-building. On 9 June 1722, Euler received his prima laurea, a degree corresponding to the bachelor of arts. In 1723, soon after receiving his master’s degree in philosophy, and according to his father’s wishes, Euler joined the Faculty of Theology, where he studied ancient Greek and Hebrew, among other subjects. However, mathematics remained his real interest, and on 8 June 1724 it is recorded that he delivered a lecture (in Latin) comparing the Newtonian and Cartesian philosophies (the text is now lost). From these beginnings, Euler’s career in mathematics continued for the next sixty years and established him as the greatest mathematician of the eighteenth century. Complete set of Faraday’s Electricity Papers 33. FARADAY, Michael. Experimental researches in electricity. 1st – 30th series, plus supplement to the 11th series. 31 extracts from the Philosophical Transactions (1832-56). London: 1832-56. $12,800 All First editions. A fine complete set of Faraday’s epochal papers on electricity, as they originally appeared in the Philosophical Transactions over 24 years. Between 1832 and 1856, Faraday published a series of 30 papers (or ‘series’) entitled ‘Experimental researches in electricity,’ in which his major discoveries relating to electricity and magnetism were first announced to the world. The first 29 of these papers were collected and published in three volumes between 1839 and 1855; the 30th paper, published in 1856, never appeared in book form. The wealth of material in these papers is impossible to summarize adequately in a few paragraphs, but we highlight some of the major contributions.

❧Dibner 64 (citing 29 parts); Evans 39 (1st paper); PMM 308 and Horblit 29 (both citing the later book-form edition).

Feynman Diagrams & the Feynman Rules of QED 34. FEYNMAN, Richard. Theory of Positrons; Space-Time Approach to Quantum Electrodynamics Lancaster, American Physical Society, 1919. First edition. $4,200 A fine copy, in unrestored original wrappers, of these two famous papers in which the author first announced the celebrated Feynman diagrams and the Feynman rules for quantum electrodynamics. “The greatest physicist of his generation, ranking with Isaac Newton and Albert Einstein, Feynman reformulated quantum mechanics to put it on a secure logical foundation in which classical mechanics is naturally incorporated (in a manner reminiscent of the way Newtonian gravitational theory is incorporated within the general theory of relativity) … He developed the path integral approach to quantum physics (using Feynman diagrams), from which he derived the clearest and most complete version of quantum electrodynamics (QED), which stands alongside the general theory of relativity as one of the two most successful and well-established theories in physics.” (Gribbin). “Feynman’s two papers on QED were completed in April and May 1949. In the first one, The Theory of Positrons, he carefully explains the meaning of his diagrams beginning with their application to the Schrödinger equation. Application to the Dirac equation yields an interpretation of the positron in which Dirac’s original hole theory is no longer needed. The second paper Space-Time Approach to Quantum Electrodynamics, contains the Feynman rules and explains their usage. By these rules, computations for specific problems are simplified so much that Schwinger, much later, said: ‘Like the silicon chip of more recent years, the Feynman diagram was bringing computation to the masses’.” (Brandt).

❧Brandt, Harvest of a Century, Episode 71. The speed of light 35. FOUCAULT, Jean Bernard Léon. Thèse présentée à la faculté des sciences de Paris... Sur les vitesses rélatives de la lumière dans l’air et dans l’eau. Paris: Bachelier, 1853. First edition. $24,000 An exceptionally fine copy, unopened in original wrappers, of Foucault’s rare doctoral thesis on the speed of light, in which he provides a convincing proof for the wave theory of light. In the 1840s Foucault undertook a series of optical experiments using an apparatus of rotating mirrors to determine the velocity of light. Originally developed by Charles Wheatstone to measure the velocity of electricity, the rotating mirror apparatus had been proposed as an instrument for the measurement of light in 1838 by Dominique-Francois Arago who failed in his own attempts to carry out the experiment. Foucault’s initial work was carried out in conjunction with the physicist Armand Hippolyte Louis Fizeau (1819- 1896); but a personal dispute broke up their partnership in 1847 and the two collaborators became rivals, working separately on the same problem using the same technique. Both reached the same conclusion, but while Fizeau was the first to obtain, in 1849, a precision measurement of the velocity of light, Foucault pre-empted him in announcing, on 30 April 1850, that light travels faster in air than in water, a decisive argument in favour of the wave theory of light, which by the mid-nineteenth century had become generally accepted. In his thesis Foucault gives a detailed account of his experiment, illustrating his apparatus; it was not until 1862 that he was able to determine a numerical value for the speed of light, of about 298,000 kilometers per second, a figure significantly smaller, and more accurate, than Fizeau’s.

❧Norman 820. Gauss’s own personal copy 36. GAUSS, Carl Friedrich Allgemeine Lehrsätze in Beziehung auf die im verkehrten Verhältnisse des Quadrats der Entfernung wirkenden Anziehungs- und Abstossungs-Kräfte. Leipzig: Weidmann, 1840. First edition. $40,000 Gauss’s own personal copy, of “the first systematic treatment of potential theory as a mathematical topic, [which] recognized the necessity of existence theorems in that field, and reached a standard of rigor that remained unsurpassed for more than a century” (DSB). In Allgemeine Theorie der Erdmagnetismus, his general theory of terrestrial magnetism, Gauss determined the magnetic force at the earth’s surface by expressing the magnetic potential as the sum of a converging series of spherical functions (Gauss retained only the first few terms as an approximation). “A year after the publication of his general theory of earth magnetism, Gauss published a systematic presentation of the mathematical tool he had used in that work, the potential. Here Gauss formally introduced the term ‘potential’ to designate the function from which the components of forces varying as the inverse square of the distance can be derived. He wrote the function as V = Σ µ/r, which expresses the action at any point of a collection of point ‘masses’ or, in general, ‘agents’, and he developed a collection of theorems concerning the behavior of this function. The significance of V is that its properties are the ‘key to the attracting or repelling forces’ of nature. Potential theory applies to the phenomena of nature described by inverse- square forces between particles, to the phenomena of gravitation, electricity and magnetism. Gauss even considered its application to electrodynamic phenomena, since Ampère’s force between current elements depends on the inverse square of the distance; but the action of this force is complicated by the directionality of currents, and Gauss did not treat it here and only spoke of discussing it in a later paper, which he never did. “Gauss showed that despite the striking differences of the observed phenomena of gravitation, electricity and magnetism, their mathematical description draws on a common body of theorems. Potential theory provided mathematical methods of impressive generality: by studying the behavior of one function, abstracted from any one domain of phenomena, physicists could learn at once the mathematical structures relating the phenomena belonging to several domains. The conservation of energy principle, enunciated soon after Gauss’s potential theory, made the potential an even more important aid in developing physical laws” (Jungnickel & McCormmach, pp. 68-9.

❧Norman 882. ‘The Copernicus of logic’ 37. GÖDEL, Kurt. Ergebnisse eines mathematischen Kolloquiums, unter Mitwirkung von Kurt Gödel und Georg Nöbeling. Herausgegeben von Karl Menger. Heft 1-7. Leipzig & Berlin: B.G. Teubner, 1931-1936. All first editions. $10,000 An absolutely mint set, in the original wrappers, of these rare proceedings to which Gödel contributed fifteen important papers and remarks on the foundations of logic and mathematics. “By invitation, in October 1929 Gödel began attending Menger’s mathematics colloquium, which was modeled on the Vienna Circle. There in May 1930 he presented his dissertation results, which he had discussed with Alfred Tarski three months earlier, during the latter’s visit to Vienna. From 1932 to 1936 he published numerous short articles in the proceedings of that colloquium (including his only collaborative work) and was coeditor of seven of its volumes. Gödel attended the colloquium quite regularly and participated actively in many discussions, confining his comments to brief remarks that were always stated with the greatest precision.” (DSB).

❧Dawson, Bibliography of the Published Works of Kurt Gödel.

‘The most important work on the science of navigation to be published in the seventeenth century’ 38. GUNTER, Edmund. De sectore et radio. The description and use of the sector in three bookes. The description and use of the Crosse-Staffe in other three bookes. For such as are studious of mathematicall practise. London: William Iones, 1623. $27,000 First edition of Gunter’s book on the sector and other mathematical instruments, which introduced logarithms into the science of navigation and led to the development of the slide-rule. “This book must be reckoned, by every standard, to be the most important work on the science of navigation to be published in the seventeenth century. It opened the whole subject of mathematical application to navigation and nautical astronomy to every mariner who was sufficiently interested in devoting time to the perfecting of his art” (Cotter). This book is justly renowned as a contribution to navigation, but it seems not to be widely known that it also contains (p. 60 of the second part) the first printed observation of the temporal variation of magnetic declination, the discovery of which is normally ascribed to Henry Gellibrand who published it 12 years later in A discourse mathematicall on the variation of the magneticall needle.

❧Macclesfield 959 (that copy lacking five text leaves and the volvelle); The Horblit copy (lacking the letterpress title) was offered by H. P. Kraus in Cat. 168 (1975) for $4200. Inscribed offprints of her Nobel papers 39. HODGKIN, Dorothy Mary Crowfoot. Structure of Vitamin B12; The X-ray Crystallographic Investigation of the Structure of Penicillin (together with six other offprints). 1945-65. $12,500 Exceptional collection of inscribed offprints, from the library of crystallographer Jack D. Dunitz, of Hodgkin’s most important papers, in which she solved the molecular structure of penicillin and vitamin B12, the last of which revealed the existence of a hitherto-unsuspected chemical grouping, the corrin nucleus. Lawrence Bragg compared these achievements with ‘breaking the sound barrier’, and in 1964 Hodgkin received the Nobel Prize in Chemistry for this work. Provenance: All items are from the library of Jack David Dunitz, British chemist and one of the greatest chemical crystallographers. Together with Sydney Brenner, Dorothy Hodgkin, Leslie Orgel, and Beryl M. Oughton he was one of the first people in April 1953 to see the model of the structure of DNA, constructed by Francis Crick and James Watson.

The wave theory of light 40. HUYGENS, Christian. Traité de la Lumière. Leyden: Pierre vander Aa, 1690. First edition. $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 contrasted markedly with Newton’s notion of a universal attractional force intrinsic to matter. Indeed, Huygens added to the original treatise of 1669 a review of Newton’s theory, rejecting it out of hand because of the impossibility of explaining it by any mechanical principle or law of motion. Huygens’s work fell into oblivion during the following century, but his theory of light was confirmed at the beginning of the 19th century by Thomas Young, who used it to explain optical interference, and by Jean-Augustin Fresnel a few years later. Modern physics has reconciled Newton’s and Huygens’s theories in discerning both corpuscular and wave characteristics in the properties of light.

❧Grolier/Horblit 54; Dibner 146; Evans 32; Sparrow 111. ‘The most influential book on probability and statistics ever written’ 41. LAPLACE, Pierre Simon. Théorie Analytique des Probabilités. Paris: Courcier, 1812. First edition. $30,000 “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 posterior probabilities. On the applied side, games of chance were still evidence, but they were dominated by problems of data analysis and Bayesian methods for combining probabilities of judgments, which replaced the earlier non-Bayesian methods of Hooper and Bernoulli.” (Grattan-Guinness: History and Philosophy of the Mathematical Sciences, p.1301). “It was the first full–scale study completely devoted to a new specialty, … [and came] to have the same sort of relation to the later development of probability that, for example, Newton’s Principia Mathematica had to the later science of mechanics.” (DSB).

❧Evans 12; Landmark Writings in Western Mathematics 24.

With the two unpublished plates 42. LAVOISIER, Antoine Laurent. Mémoires de chimie. [Paris: de l'imprimerie de Du Pont, 1792/1805]. $18,000 First edition of this very rare work; copy of the Lavoisier scholar and antiquarian Lucien Scheler, with prints of the two copper plates meant to illustrate the work but never issued, which Scheler and Duveen discovered and described together in the 1950’s (see below), finely bound by Lobstein with a three page manuscript letter by Scheler about the work, together with the original wrappers. We know of just one other copy accompanied by these two plates (Haskell F. Norman). “The collection contains thirty-nine memoirs, twenty-nine by Lavoisier, of which twelve appear here for the first time; the remaining memoirs are by Séguin, Meusnier, Brisson, Vauquelin, Macquart and Fourcroy. The fifth memoir in Vol. II contains Lavoisier’s claim to the discovery of the theory of oxidation” (Norman). The contents of this important and final work by Lavoisier are discussed in detail by Duveen and Klickstein. Provenance: This copy belonged to the Lavoisier scholar and famous antiquarian Lucien Scheler (1902-1999), and is accompanied by a three page letter by him about the work and the two plates bound in with this copy. There are references to illustrations in the Mémoires but no plates accompanied the work when Mme. Lavoisier distributed copies. In 1950 two copper plates were discovered in the addict of Mme P. de Chazelles. Scheler had prints taken of these plates and together with Denis Duveen he published an article describing these hitherto unknown illustrations for the Mémoires. The original copper plates are now, together with 108 prints, at the Lavoisier Archive in Cornell University.

❧Norman 1297; Duveen & Klickstein 186-200; Neville p.17; Thornton & Tully 168. PMM 238 – A new epoch in chemistry 43. LAVOISIER, Antoine-Laurent de Traité élémentaire de Chimie, présenté dans un ordre nouveau, et d'après les découvertes modernes. Paris: Chez Cuchet, 1789. First edition. $7,850 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.

Very rare complete set of his collected letters 44. LEEUWENHOEK, Anthony van. Ontledingen en Ontdekkingen... Brieven [Brieven seu Werken]. 6 vols. Leyden, Delft: Boutesteyn, Krooneveld, Beman, 1684-1718. First edition, first issue. $100,000 Extremely rare fully complete set with all 100 engraved plates and all the letters in their first state; we know of just one other similar copy - the Dobell/Honeyman copy. Dobell writes in his bibliography of Leeuwenhoek (1922) that his set was the only ‘perfect’ copy he had ever seen. The Norman and Horblit copies were highly incomplete and the Friedman set consisted of mixed issues. “Leeuwenhoek’s scientific communications consisted exclusively of letters to fellow scientists, the majority addressed to the Royal Society in London. 165 were published, in two chronological sequences, numbered 28-146 and I-XLIV (letters 1-27 were not published separately, although abstracts appeared in the Philosophical Transactions). 120 letters were abstracted in English or Latin in volumes VIII-XXXII of the Transactions (1673-1723).” (Norman). “Leeuwenhoek himself did not publish his work until 1684, when he brought out some of his letters in Dutch; from 1685 onward he also published Latin translations [not his own, as he had no knowledge of Latin]. He initially edited, reprinted, and reissued some of his letters separately or in groups of two or three, a practice that has resulted in some bibliographical confusion. From 1687 he adopted a more systematic course of publication...” (DSB).

❧Dobell 20; Medicine’s 10 Greatest Discoveries 3; Grolier/Horblit 65; Norman 1301-15. The most authoritative defense of Newton’s fluxions 45. MACLAURIN, Colin. A Treatise of Fluxions. In Two Books. Edinburgh: T.W. and T. Ruddimans, 1742. First edition. $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, foundational 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, Maclaurin 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.

PMM 260 – The metric system 46. MÉCHAIN; DELAMBRE; BIOT & ARAGO. Base du Système Mètrique Décimal. I-IV. Paris: Baudouin & Garnery, 1806-21. First edition. $40,000 Rare complete set (in four volumes) of the foundation work of the metric system. “In 1790, at the request of Talleyrand, the Academic 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 measures 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). ‘The paper that led to Einstein being awarded the Nobel Prize’ 47. MILLIKAN, Robert Andrews. A Direct Photoelectric Determination of Planck’s “h”. [Lancaster: American Physical Society], 1916. First edition. $5,400 Rare offprint issue of Millikan’s famous determination of Planck’s constant “that led to Einstein being awarded the Nobel Prize for his theory of the photoelectric effect (the citation of Einstein’s prize specifically mentions Millikan’s work), and to the notion of light quanta becoming firmly established as respectable physics.” (Gribbin). “In 1915, Millikan experimentally verified Einstein’s all-important photoelectric equation, and made the first direct photoelectric determination of Planck’s constant h. Einstein’s 1905 paper proposed the simple description of ‘light quanta,’ or photons, and showed how they explained the photoelectric effect. By assuming that light actually consisted of discrete energy packets, Einstein proposed a linear relationship between the maximum energy of electrons ejected from a surface, and the frequency of the incident light. The slope of the line was Planck’s constant, introduced 5 years earlier by Planck. Millikan was convinced that the equation had to be wrong, because of the vast body of evidence that had already shown that light was a wave. If Einstein was correct, his equation for the photoelectric effect suggested a completely different way to measure Planck’s constant. Millikan undertook a decade-long experimental program to test Einstein’s theory by careful measurement of the photoelectric effect, and even devised techniques for scraping clean the metal surfaces inside the vacuum tube needed for an uncontaminated experiment. For all his efforts Millikan found what to him were disappointing results: he confirmed Einstein’s predictions in every detail, measuring Planck’s constant to within 0.5% by his method. … [Millikan] received the Nobel Prize in part for this discovery.” (APS biography of Millikan).

‘The most important book on mechanics published in the sixteenth century’ (Drake) 48. MONTE, Guidobaldo, Marchese Del. Mechanicorum Liber. Pesaro: Hieronymus Concordia, 1577. First edition. $20,000 Monte’s theories were most influential for Galileo’s discoveries in the field of applied mechanics as expressly stated by Galileo in his Discorsi. According to Lagrange (Mécanique analytique, 1811) Monte was the first to apply the theory of momentum to simple machines, and to discover the principle of virtual velocities in the lever and the pulley. “From the time of its publication in 1577 [it was] the most authoritative treatise on statics to emerge since antiquity, and it remained pre- eminent until the appearance of Galileo’s Two New Sciences in 1638. It marks the high point of the Archimedean revival of the Renaissance.” (Rose). The Liber mechanicorum “was regarded by contemporaries as the greatest work on statics since the Greeks. It was intended as a return to classical Archimedean models of rigorous mathematical proof and as a rejection of the ‘barbaric’ medieval proofs of Jordanus de Nemore (revived by Tartaglia in his Quesiti of 1546), which mixed dynamic principles with mathematical analysis.” (DSB).

❧Bibliotheca Mechanica 229. ‘One of the most important landmark works on probability theory’ 49. MONTMORT, Pierre Rémond de. Essay d'Analyse sur les Jeux de Hazard. Seconde edition. Revue & augmentée de plusieurs Lettres. Paris: J. Quilau, 1713. $16,000 Author’s presentation copy of one of the most important landmark works on probability theory of the eighteenth century. This second edition is arguably more important than the first, as it contains the first publication of extensive correspondence between Montmort and Johann I and Nikolaus Bernoulli, in which many important discoveries are described. “The Essay [first published in 1708] is the first published comprehensive text on probability theory, and it represents a considerable advance compared with the treatises of Huygens (1657) and Pascal (1665). Montmort continues in a masterly way the work of Pascal on combinatorics and its application to the solution of problems on games of chance. He makes effective use of the methods of recursion and analysis to solve much more difficult problems than those discussed by Huygens. Finally, he uses the method of infinite series, as indicated by Bernoulli ... Montmort’s work had three pioneering features: (1) It demonstrated the four methods of solution mentioned above; (2) it gave the solutions of many important problems; and (3) it inspired Nicholas Bernoulli and de Moivre to generalize these problems and develop new methods of proof” (Hald).

❧David, Games, Gods and Gambling, Chap. 14; Todhunter, History of the Theory of Probability, Chap. 7; Hald, A History of Probability and Statistics and their Applications before 1750, Chapter 18.

First appearance of Halley’s lunar theory

50. MOORE; PERKINS; FLAMSTEED; HALLEY. A New Systeme of the Mathematicks. London: Godbid and Playford, for Robert Scott. 1681. $32,000 First edition of Moore’s principal work, incorporating one of the three main works of his protégé, John Flamsteed, and a treatise on geography by Edmund Halley illustrated with 61 maps including nine of America. Moore himself wrote the first section of volume I, which covers arithmetic and algebra, practical geometry, trigonometry and cosmology, including 6 finely engraved star charts. This is followed by a long chapter on navigation, which Moore had intended to write, but which could not be found at his death and so was contributed by his pupil Peter Perkins. Volume I also contains Perkins’s Arithmetick, with a title page dated 1680. This contains, with separate titles, ‘The first six books of Euclid’s elements’; ‘The eleventh and twelfth books of Euclid’s elements’; and ‘The doctrine of surds’. Then comes Flamsteed’s Doctrine of the sphere, grounded on the motion of the earth and the antient Pythagorean or Copernican system of the world, which has a separate title page dated 1680. It contains Flamsteed’s important lunar theory and his very accurate solar tables (see DSB). He introduces his method of calculating parallaxes invented in 1676. Halley himself contributed A New Geography, with maps to each country in Vol. II, with a title page dated 1681, in which several parts of America are described. The first part of Vol. II is an extensive set of astronomical, logarithmic, trigonometric and other tables, with instructions for their use. Left unfinished at Moore’s death in 1679, the work was completed by Flamsteed and Perkins and edited by his sons-in-law William Hanway and John Potenger. ‘Arguably the most important paper in the history of optics’ 51. NEWTON, Isaac. A Letter of Mr. Isaac Newton; containing his New Theory about Light and Colors. London: for John Martyn, 1671/72. First edition, first printing. $32,500 An exceptionally fine copy, in contemporary Cambridge-style paneled calf, of Newton’s letter announcing his theory of colors and light. “This was Newton’s first scientific publication and one of his most important, leading to his brilliant work in optics. In this he recounted how he placed a glass prism in the path of a ray of light entering his darkened chamber thru a window-slit. Instead of a circular pattern of light upon the opposite wall Newton saw an oblong spectrum. A second, inverted prism restored the refracted light into a white ray. He concluded that sunlight (or white light) was composed of a mixture of light of many colors, each having its own degree of refrangibility and that none could be converted into another. This paper led to extended controversies with Hooke, Huygens, Linuc, Lucas, Pardies, and others” (Dibner).

❧Dibner 144; Grolier/Horblit 79a; Evans 29.

A fine copy the Tournes edition 52. PARACELSUS, Theophrastus. Opera Omnia Medico-Chemico-Chirurgica, tribus voluminibus comprehensa. Editio novissima et emendatissima ad Germanica & Latina exemplaria accuratissime collata. Geneva: Sumptibus Joan. Antonii, & Samuelis De Tournes. 1658. First Tournes edition. $20,000 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 compendium 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. The beginning of quantum theory 53. PLANCK, Max. Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum. Leipzig: Johann Ambrosius Barth, 1900. First edition, first printing. $22,000 A fine copy of the founding document of quantum theory, “marking the dividing line between classical and modern physics” (Norman). In this celebrated first announcement of quantum theory, Planck derived his radiation law based upon the assumption that energy is emitted and absorbed in discrete quanta. “In this important paper he stated that energy flowed not in continuous, indefinitely divisible currents, but in pulses or bursts of action [or quanta]” (Dibner). Planck determined a unit of energy in a system showing a natural frequency in definite quanta and proposed a constant of angular momentum, the value of which is known as ‘Planck's constant.’ This unit of energy enabled the explanation of wave- length, specific heat of solids, photo-chemical effects of light, the orbits of electrons in the atom, the wave lengths of the lines of the spectrum, or Röntgen rays, the velocity of rotating gas molecules, and the distances between the particles of a crystal. “It contradicted the mechanics of Newton and the electromagnetics of Faraday and Maxwell. Moreover it challenged the notion of the continuity of nature” (PMM). Published by the Berlin Physics Society, the first appearance of Planck’s revolutionary work is very rare. (It was later published, in 1901, in the more widely distributed Annalen der Physik).

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

‘As rare as beautiful’ 54. PORTA, Giovanni Battista della. De Distillatione Lib. IX. Rome: Ex Typographia Reu, Camerae Apostolicae, 1608. First edition. $13,500 A very fine copy of “the most comprehensive view of the applications of distillation of the period” (Norman). “This book is as rare as beautiful. Ferguson, speaking of the reimpression (Strassburg, 1609), says that ‘the Roman edition is a much finer book.’ (Duveen). “Porta published in 1608 at Rome a work on distillation, its methods, apparatus and applications, which is of interest as giving a more comprehensive view of the application of distillation in the sixteenth century than is found in any other work of the period.” (Stillman). “The first and longest, and the most fully illustrated, of the nine books deals with different forms of stills. Porta describes various forms of distilling apparatus for various uses including the preparation of essential oils, on which Forbes says he is a very good authority having had occasion to observe the industry in Naples. Porta was the first to give yields from different materials. He also deals with various stills designed to produce different strengths of alcohol, all with air cooled condensers; one still is heated by the sun. In the same spirit as his Physiognomonia and Phytognomonica, in one section he compares the stills and their functions with animals. Hot things require a still with a short thick neck, just as nature has given ‘angry and furious creatures’ like the bear and the lion short strong necks. After this preliminary treatise on stills, the other 8 books give more specific details of the preparation of perfumes and the distillation of essential oils; resins; and woods; and the extraction of virtues of substances, such as aqua vita essential, that is alcohol.

❧Norman 1725; Honeyman 2521; Neville 323. Only one other complete copy known 55. RECORD, Robert. The Grounde of Artes ... And now of late diligently ouerseene and augmented with new and necessarie 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 Library 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.

Published the same year as Copernicus’s De Revolutionibus 56. REGIOMONTANUS, Johannes; PEURBACH, Georg. Epitome, in Cl. Ptolemaei magnam compositionem. Basel: Heinrich Petri, August 1543. $16,800 A beautiful copy, entirely untouched in the publisher’s boards, of the second printed edition (first 1496) of this epochal text. The date of publication of this edition of the Epitome coincides, of course, with that of the first edition of Copernicus’s De revolutionibus (printed at Nuremberg by Petreius). In his annotated Census of Copernicus’s great work, Owen Gingerich notes that the 1543 Epitome is the work most commonly bound up with copies of De revolutionibus (it is found with 12 copies of the first edition and four of the second), and comments that this is appropriate not just because of the timing but also the subject matter. But in his review of the Census (Journal for the History of Astronomy 34 (2003), pp. 97-111), Adam Mosley suggests that there may be another explanation. Petreius studied at Basel, after which he worked as a corrector in the printing office of Heinrich Petri’s father Adam. Mosley suggests that the two printer- publishers, Petreius and Petri, may have been co-distributors of the first edition of De revolutionibus, and the close relationship between them is further suggested by the fact that Petri published the second edition of Copernicus in 1566. Creation of wave mechanics 57. SCHRÖDINGER, Erwin. Quantisierung als Eigenwertproblem, I-IV. [with:] Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen. Leipzig: Johann Ambrosius Barth, 1926. First edition. $11,000 An exceptional set in original wrappers of Schrödinger’s creation of wave mechanics and his announcement of the Schrödinger equation. In January 1926, Schrödinger published in Annalen der Physik the paper ‘Quantisierung als Eigenwertproblem’ [tr. Quantization as an Eigenvalue Problem] on wave mechanics and presented what is now known as the Schrödinger equation. In this paper he gave a derivation of the wave equation for time independent systems, and showed that it gave the correct energy eigenvalues for a hydrogen-like atom. This paper has been universally celebrated as one of the most important achievements of the twentieth century, and created a revolution in quantum mechanics and indeed of all physics and chemistry. A second paper was submitted just four weeks later that solved the quantum harmonic oscillator, the rigid rotor and the diatomic molecule, and gave a new derivation of the Schrödinger equation. A third paper in May showed the equivalence of his approach to that of Heisenberg and gave the treatment of the Stark effect. A fourth paper in this most remarkable series showed how to treat problems in which the system changes with time, as in scattering problems. These papers were the central achievement of his career and were at once recognized as having great significance by the physics community.

❧Brandt, Harvest of a Century, no. 39.

A classic work on optical instruments 58. SELVA, Lorenzo. Sei Dialoghi Ottici Teorico-Pratici. Venice: Simone Occhi, 1787. $4,000 Rare first edition of this classic work on optics and optical instruments, illustrated with 4 finely engraved plates. Lorenzo Selva was the second in line of a family of opticians and instrument-makers working in Venice during the secondi half of the seventeenth century. Both father and son were the most active opticians in Italy at the time and enjoyed an international reputation for the quality of their various optical instruments. Boscovich, who experimented with optics and published on the subject, considered Lorenzo - and not Dolland - as the inventor of the achromatic lens; and around the time the Dialoghi was published the great scientist was, in fact, collaborating with Lorenzo on perfecting lenses made of flintglass. The dialogues contained in this work cover all aspects of optics and glass-making which were of concern to the opticians of the latter part of the eighteenth century: eyeglasses and their corrective function; the various kinds of telescopes - terrestrial & celestial; post-Newtonian lenses, Herschel’s telescope; various experiments with achromatic lenses by Boscovich and the author; microscopes; burning mirrors and other optical and mechanical devices including magic lanterns, cameras obscura, drawing instruments, prisms, and electrical machines, etc. Perhaps the most interesting aspect of this work is the fact that the Sei Dialoghi was written not just by a theoretician but a maker in Venice (the center of glass manufacturing in Italy). Very rare pre-publication of this hugely influential book 59. SIMON, Herbert A. Administrative Behavior: A Study of Decision-Making Processes in Administrative Organization. Preliminary Edition. Chicago: Illinois Institute of Technology, 1945. $4,800 Preliminary edition of this classic which the Royal Swedish Academy cited as “epoch-making” in awarding the 1978 Nobel Prize in Economics to Simon “for his pioneering research into the decision- making process within economic organizations”. OCLC locates just one copy of this edition (Yale). “Simon’s theories and observations about decision-making in organizations apply very well to the systems and techniques of planning, budgeting and control that are used in modern business and public administration. These theories are less elegant and less suited to overall economic analysis than is the classic profit-maximizing theory, but they provide greater possibilities for understanding and predictions in a number of areas. They have been used successfully to explain and predict such diverse activities as the distribution of access to information and decision-making within companies, market adjustment to limited competition, choosing investment portfolios and choosing a country in which to establish a foreign investment. Modern business economics and administrative research are largely based on Simon’s ideas.” (Nobel Press Release). The first edition was published by Macmillan in 1947; the second, in 1957; the third, in 1976; and the fourth, in 1997. A 1990 article in Public Administration Review named it the “public administration book of the half century” (1940- 1990). It was voted the fifth most influential management book of the 20th century in a poll of the Fellows of the Academy of Management.

Offprint of the original Polish edition 60. SMOLUCHOWSKI, Marian. Zarys teoryi kinetycznej ruchów Browna i roztworów metnych. Kraków: Akademia Umiejetnosci, 1906. First edition, offprint issue. $7,250 Very rare first and original edition of this famous paper on Brownian motion (more commonly known in the form of its German translation Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen published two months later in the Annalen der Physik 21: 756–80). “If Marian Ritter von Smolan-Smoluchowski had been only an outstanding theoretical physicist and not a fine experimentalist as well, he would probably have been the first to publish a quantitative theory on Brownian motion.” (Pais). “From about 1900 Smoluchowski worked on Brownian movement. He wished to use experimental data to verify the theory he had obtained, a desire complicated by the confused situation of experimental research. In the meantime Einstein, in papers of 1905 and 1906, had presented a solution to the problem. Smoluchowski then decided to publish his results in ‘Zarys kinetycznej teorii ruchow Browna’ [the offered paper], which presented his different method.” (DSB). “Smoluchowski is probably best known to the aerosol community for equations which now carry his name – the Smoluchowski Equations. Derived within the theory of Brownian motion, they also form the foundations of stochastic processes and modern statistical physics. In 1906 Smoluchowski published his mathematical model of Brownian motion … The main point in the Smoluchowski theory of Brownian motion is the finding that the proper measure of the motion is not the mean velocity of the particle in the suspension, but the mean square of its shift from an initial position. This quantity was published by Einstein (1905) from general laws of diffusion and statistical mechanics and, on the other hand, by Smoluchowski (1906) by detailed analysis of the mechanism of particle motion. In his work, Smoluchowski acknowledged Einstein’s approach, but emphasized that his ‘method is more direct and hence more convincing than Einstein’s’. This was also later stated by Einstein who said that ‘Smoluchowski delivered a particularly beautiful and descriptive theory of Brownian motion’, a piece of work of great relevance to aerosol science. Smoluchowski’s work on Brownian motion marks indeed the start of the study of stochastic processes … Chandrasekhar recognized ‘Marian Smoluchowski as the Founder of the Physics of Stochastic Phenomena’.” (Szymanski, Marian Wilhelm Theofil von Smoluchowski). One of the rarest and most important books on distillery 61. ULSTADT, Philipp. Coelum philosophorum seu De secretis naturae liber. Denuo reuisus & castigatus. [Fribourg: 1525]. $26,000 First edition, extremely rare, of this work which served as “a standard authority on the preparation and use of distillates for nearly a century” (DSB). OCLC locates just one copy in America and three in Europe (of which one is incomplete). “Despite his use of alchemical terminology, Ulstad clearly dissociated himself from the enigmatic aspects of the alchemical tradition in offering his concise and rational account of the preparation of distilled remedies. Concerned with culling from the mediaeval alchemical corpus those techniques and ideas of practical utility, he ensured that they were made available to as large an audience as possible, including all apothecaries, surgeons, and medical doctors. The lucidity of his technical directions was a major reason for the influence exerted by Ulstad. His discussion of apparatus and manipulative procedures afforded the sixteenth-century investigator an accurate summary of the best distilling theory then available”. (DSB). OCLC lists copies at Madison Wisconsin, Sheffield, Oxford (incomplete), and the Museum of Natural History, Paris. We have been unable to locate any copy in auction records.

First printing of the ‘Ad logisticem speciosam notae priores’ 62.VIÈTE, François. In artem analyticum isagoge: eiusdem, Ad logisticem speciosam notae priores. Francisci Vieta Fontenaeensis ; recensuit, scholiisq; illustravit I.D.B[eaugrand]. Paris: Guillaume Baudry, 1631. First edition. $53,500 First printing of Viète’s Ad logisticem speciosam notae priores (one of his main works), together with the second edition of his In artem analyticum isagoge, “the earliest work on symbolic algebra [by] the greatest French mathematician of the sixteenth century” (PMM). The first edition of the Isagoge, published at Tours in 1591, is, together with the Lobachevsky, the rarest mathematical work in PMM, and this second edition is in fact rarer than the first in institutional collections [OCLC lists only copies in France and UK]. “The ‘Introduction to the Art of Analysis’ is the earliest work on symbolic algebra. Viète’s greatest innovation in mathematics was the denoting of general or indefinite quantities by letters of the alphabet instead of abbreviations of words as used hitherto. Known quantities were represented by consonants, unknown ones by vowels; squares, cubes, etc., were not represented by new letters but by adding the words quadratus, cubus, etc. Viète also brought the + and – signs into general use. This algebraic symbolism made possible the development of analysis, with its complicated processes, a fundamental element in modern mathematics” (PMM). “This innovation, considered one of the most significant advances in the history of mathematics, prepared the way for the development of algebra” (DSB). “To the treatises of the Isagoge belong Ad logisticen speciosam notae priores and Ad logisticen speciosam notae posteriores, the latter now lost. The first was not published during his lifetime, because Viète believed that the manuscript was not yet suitable for publication. (It was published by Jean Beaugrand in 1631 [offered here].) It represents a collection of elementary general algebraic formulas that correspond to the arithmetical propositions of the second and ninth books of Euclid’s Elements, as well as some interesting propositions that combine algebra with geometry. In propositions 48-51 Viète derives the formulas for sin 2x; cos 2x; sin 3x; cos 3x; sin 4x; cos 4x; sin 5x; cos 5x expressed in terms of sin x and cos x by applying proposition 46... He remarks that the coefficients are equal to those in the [binomial] expansion..., that the various terms must be ‘homogeneous’ and that the signs are alternately + and –” (DSB). ❧OCLC: BNF and Glasgow only; COPAC adds Oxford, UCL and University of London Senate House. The founding paper of mathematical game theory 63.VON NEUMANN, John. Zur Theorie der Gesellschaftsspiele. Berlin: Julius Springer, 1928. $20,000 Very rare offprint issue of the foundational work on mathematical game theory. “John von Neumann single-handedly invented game theory, introducing the general mathematical concept of ‘strategy’ in a paper on games of chance (Mathematische Annalen 100 [1928]: 295-320). This contained the proof of his ‘minimax’ theorem that says ‘a strategy exists that guarantees, for each player, a maximum payoff assuming that the adversary acts so as to minimize that payoff’.” (Hook & Norman: Origins of Cyberspace, p.473, under the 1944 monograph co-authored with Morgenstern). “Our considerations will lead to the application of the mathematical theory of ‘games of strategy’ developed by one of us in several successive stages in 1928 and 1940-1951. The first phases of this work were published: J. von Neumann, ‘Zur Theorie der Gesellschaftsspiele,’ … The subsequent completion of the theory, as well as the more detailed elaboration of the considerations of loc. cit. above, are published here for the first time.” (Von Neumann & Morgenstern: The Theory of Games and Economic Behavior, 1944, p.1). Von Neumann’s 1928 paper “contained a long and difficult existence proof for the equilibrium of the two- person, discrete game. … Twenty-five years later, George B. Dantzig showed how linear programming provides a constructive proof for finding the solution to any two-person matrix game.” (Gass & Assad: Annotated Timeline of Operations Research, p.36).

The ‘Yellow Peril’ 64.WIENER, Norbert. The Extrapolation, Interpretation and Smoothing of Stationary Time Series with Engineering Applications. [Washington, DC: National Defense Research Council], 1942. $22,000 Very rare first appearance of this classic in modern communication theory. “It has been the opinion of many that Wiener will be remembered for his Extrapolation long after Cybernetics is forgotten. Indeed few computer-science students would know today what cybernetics is all about, while every communication student knows what Wiener’s filter is. The work was circulated as a classified memorandum in 1942, as it was connected with sensitive war-time efforts to improve radar communication. This book became the basis for modern communication theory, by a scientist considered one of the founders of the field of artificial intelligence. Combining ideas from statistics and time-series analysis, Wiener used Gauss’s method of shaping the characteristic of a detector to allow for the maximal recognition of signals in the presence of noise. This method came to be known as the ‘Wiener filter’.” (MIT Press). “Working with the Fire Control Division of the National Defense Research Committee during World War II, Wiener was assigned the critical problem of anti-aircraft control, specifically the task of designing a gun that could accurately and automatically aim at a high-speed moving target guided by human intelligence. Wiener and his assistant, Julian Bigelow, developed a system whereby they would treat the airplane’s path as a stationary time series and use probability theory to extrapolate the airplane’s future path from its past actions. The theory Wiener developed and explained in this classified document for internal government use only became a milestone in communication theory. Claude Shannon, in his Mathematical Theory of Communication (pp.626-7) notes: ‘Communication theory is heavily indebted to Wiener for much of its basic philosophy and theory. His classic NDRC report The Interpolation, Extrapolation, and Smoothing of Stationary Time Series, to appear soon in book form, contains the first clear-cut formulation of communication theory as a statistical problem, the study of operations on time series.’ Wiener’s famous report did indeed appear in book form in 1949, seven years after this classified report. Wiener’s report was extremely difficult to read, and thus was known to generations of students after the war as the ‘yellow peril’ after its plain yellow wrappers.” (Norman).

❧Origins of Cyberspace 990.