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JEVONS (William Stanley): Pure Logic and Other Minor Works.., edited by Robert Adamson and Harriet A. Jevons, with a Preface by Professor Adamson,
First Edition, xxiii, 299pp., complete with 4 plates, tall 8vo, a fine copy in original orange/red cloth, London, Macmillan, 1890.* One of Jevons's rarest works despite being late in the canon. It includes four chapters on the Theory of Logic one of which is Jevons's 1870 article on his "logical piano - a logic machine - a sort of motional form of the later diagrammatic scheme of John Venn. Jevons' 'logical piano' .. was built for him by a Salford clockmaker. It resembled a small upright piano, with twenty-one keys for classes and operations in an equational logic. Four terms, A, B, C, and D, with their negations, in binary combinations, were displayed in slots in front and in back of the piano; and the mechanism allowed for classification, retention, or rejection, depending upon what the player fed in via the keyboard. The keyboard was arranged in an equational form, with all eight terms on both left and right and a 'copula' key between them. The remaining four keys were, on the extreme left, 'finis' (clearance) and the inclusive 'or', and, on the extreme right, 'full stop' (output) and the inclusive 'or again.' In all 216 (65,536) logical selections were possible. "The machine earned much acclaim. .. Although its principal value was as an aid to the teaching of the new logic of classes and propositions, it actually solved problems with superhuman speed and accuracy, and some of its features can be traced in modern computer designs" (DSB. 7: 105). Five further essays are grouped under the general title of "John Stuart Mill's Philosophy Tested." Of the latter, the editors note that Jevons "attached much weight to his critical examination of J.S. Mill's doctrines, and the labour bestowed on it played a large part in the last ten or twelve years of his life." Includes the 1864 book 'Pure Logic, or the Logic of Quality Apart from Quantity: with Remarks on Boole's System and on the Relation of Logic and Mathematics', which is one of Jevons's rarest publications and one to which he himself attached high importance. The principle of sameness forms the basis of this, his first book on logic which he described in the following terms: "The original principle of this theory is that sameness is the one great relation which the mind deals in when constructing science". Of the need for simplification in logic Jevons was convinced: he found the subject in as confused a state as political economy before he set out to "re-establish the science on a sensible basis". He therefore aimed to simplify logical theory as far as possible, and his important modifications on Boole's system (which are still accepted today) were to this end. He showed, for example, that the Boolean operations for subtraction and division were superfluous: he redefined the symbol + to mean 'either one, or the other, or both'. Jevons went on to champion the principles of Boole's system against that of Mill, writing three articles against Mill's system. (Book ref. 20520)   £620.00
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BABBAGE (Charles); DAVIES (Gilbert); ROYAL SOCIETY:: Two pamphlets bound in one volume relating to the Royal Society controversy.
PHOTOGRAPHS AND FULL DETAILS SENT ON REQUEST. Comprising: 1. [DAVIES Gilbert (formerly Gilbert Giddy)] A Statement of Circumstances Connected with the Late Election for the Presidency of The Royal Society, First Edition, 47pp., octavo, a very good copy. [London, by Taylor for Author], 1831. BOUND WITH: 2. ROYAL SOCIETY: The Morality of its Members, [newly collected and reset extracts] Reprinted from [issues 1484, 1485, 1596, 1603, 1604 of] the Mechanics Magazine by the Permission of the Editor, [in support of Charles Babbage], 15pp., octavo, in small typeface, title slightly soiled, with neat early disposal stamp of H.M. Stationery Office, London, by Tyler, 1854. Yale and McGill Universities in OCLC. Not in BLIC or NSTC. Two items bound together in early russia-backed green cloth with leather label, with the bookplate of John Davies Enys [1837-1912, the first author's grandson and notable New Zealand naturalist] and later stamp of Cornwall County Record Office on first free endpaper and neat disposal stamp on Contents leaf. * Two pamphlets relating to the controversy surrounding corruption at the Royal Society and the future of science in the 1830s. The first by Davies Gilbert explains his position and the second expounds Babbage's attack and extensively quotes from him and from the reviewers of his books. Davies Gilbert was an early supporter of Babbage's work on the Difference Engine but by 1830 he had become the focus of Babbage's campaign to reform science in England which culminated in his book Reflection on the Decline of Science and Some of its Causes, 1830. All Babbage's books contain a campaigning element but the Decline of Science is by far the most polemical. It had three principal objectives: to remove Davies Gilbert from the Presidency of the Royal Society; to secure reform of the Society and more generally to promote the reform of science in England. "While Babbage was abroad during 1827, Davies became temporary president. Previously he had supported reform.. [but], surrounding himself with a coterie and hopelessly lost in the habits of political intrigue, instead of turning for support to the active members, he attempted to follow Humphry Davy's high-handed methods of running the Society. Lacking Davy's prestige and scientific ability he soon alienated Babbage, Herschel and the leading scientific men." Hyman, Charles Babbage, p.88ff. Although Babbage recognised that Davies Gilbert was a most amiable and kind-hearted man he was unforgiving of the damage, as he saw it, that he done to the cause of science. Babbage accused the leadership of the Royal Society of corruption, nepotism, stifling open discussion, malpractice and for failing the true scientific community. In reaction, there was talk of an establishment attempt to expel Babbage but this fizzled out in June 1830 as to have done so by the votes of a coterie of mediocrities would have made the Royal Society the laughing stock of scientific Europe. Instead, by November, Davies Gilbert himself resigned but with great political adroitness proposed the (unscientific) Duke of Sussex (third son of George II) as his successor against Hershel who was supported by Babbage and the radicals. When the Duke actually won the vote, Babbage and his National Science Reform Movement was broken and Babbage, the leading radical scientific figure of his day, was permanently removed from the centre of power. One positive result, however, was that the controversy directly lead to the establishment in 1831 of the democratic British Association for the Advancement of Science to which Babbage and other radical scientists contributed. According to DNB "Davies Gilbert's importance to the development of science in the early nineteenth century lay in his faith that science provided the best means to tackle practical problems and in his facility as a parliamentary promoter of scientific ventures." (Book ref. 20513)   £550.00
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BABBAGE (Charles): The Exposition of 1851; or, Views of the Industry, the Science,
and the Government of England, second edition, with additions, xvi, 289, 4pp plus 16pp bookseller's catalogue bound in, tall 8vo, a very good copy in original cloth green cloth gilt lettered on spine and front board, small repair to top of front hinge, very slight occasional spotting but a fresh copy, uncut and unopened, London, Murray, 1851. Van Sinderen 61. On 1st May 1851, Queen Victoria opened the Great Exhibition. The event took place in Joseph Paxton's magnificent Crystal Palace in Hyde Park, London, and it was the first of the great international exhibitions held to celebrate progress in the world's arts and manufactures. Having been a source of aggravation to the scientific establishment for many years, Babbage was not invited to take part in the organization of the exhibition. This did not, of course, prevent him from putting forward his views, but they were ignored. In consequence he wrote this vitriolic book, The Exposition of 1851, which appeared shortly after the opening of the exhibition. In addition to a critique of the policies and the organization of the exhibition, Babbage also took the opportunity to address the corrupt state of science in England in general. Babbage was also angered by the fact that he was refused permission to display his pioneer computer, the model Difference Engine at the exhibition. He therefore bound in with the book copies of an earlier (1849) pamphlet the eleventh chapter of the History of the Royal Society, by C. R. Weld, which included a review from the Athenaeum written by Augustus De Morgan. Both of these dealt with the history of Babbage's work on calculating Engines and they were factually correct, the comments of both Weld and De Morgan being basically objective and providing a useful insight into Babbage's work as viewed by some of his contemporaries. Babbage himself provides a fascinating chapter on Calculating Engines (chapter 13, p.173-188) in which he explains the history of his project. In this edition Babbage added significant new material to Chapters 8 and 11, and the Weld chapter was brought into the book as a formal appendix. There is a 4 page bibliography of Babbage's own writings at the end of the printed text. This important book is very rare in any edition; we have only seen two copies in 30 years. Photograph available on request. (Book ref. 11970)   £2500.00
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BOOLE (George): An Investigation of the Laws of Thought: on which are Founded the Mathematical Theories of Logic and Probabilities,
First Edition, probable third issue, iv, errata leaf, 424pp, tall royal octavo, original publisher's green pebble grained cloth, blind ruled on boards, gilt lettered, spine extremities neatly restored and with new endpapers, a very good copy, London, Macmillan, 1854. PHOTOGRAPHS AVAILABLE ON REQUEST. "Boole invented the first practical system of logic in algebraic form, which enabled more advances in logic to be made in the decades of the nineteenth century than in the twenty-two centuries preceding. Boole's work led to the creation of set theory and probability theory in mathematics, to the philosophical work of Peirce, Russell, Whitehead and Wittgenstein, and to computer technology via the master's thesis of C. E. Shannon (1937), who recognized that the true/false values in Boole's two-valued algebra were analgous to the open and closed states of electric circuits. Since Boole showed that logics can be reduced to very simple algebraic systems - known today as Boolean Algebras - it was possible for Babbage and his sucessors to design organs for a computer that could perform the necessary logical tasks. Thus our debt to this simple, quiet man, george Boole, is extraordinarily great." "This invention of the binary digit or "bit" made possible the development of the digital computer" (Norman). Today nearly everyone who uses a computer is familiar with Boolean Logic but the book that launched the theory is scarce. Norman 266; Origins of Cyberspace 224. (Book ref. 20484)   £2500.00
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NAPIER (John); KNOTT (Cargill Gilston, editor): Napier Tercentenary Memorial Volume.
comprising addresses and essays delivered before the "International Congress which met in Edinburgh towards the end of July, 1914, to commemorate the Tercentenary of the publication of John Napier's 'Mirifici Logarithmorum Canonis Descriptio'." First Edition, xi, 442pp., quarto, colour portrait frontispiece and 15 plates, including several which reproduce Napier's original manuscripts; text illustrations. A very fine copy, uncut and unopened in original cream-colored cloth with front cover with Napier's coat of arms stamped in gilt, top edge gilt. London: Longmans, Green, for the Royal Society of Edinburgh, 1915. *Essential text on Napier, with historical and bibliographical articles by authorities including Cajori, D. Eugene Smith, and two by d'Ocagne. Includes a detailed bibliography of the books exhibited at the Tercentenary including some that were from Babbage's library. Hook and Norman; Origins of Cyberspace, 331: "An elegantly printed collection of addresses and essays at the Napier tercentennial celebration… The essays concerned either Napier's life and work or developments in calculating since Napier. The essays include two by Ocagne "Numerical tables and nomograms" and "On the origin of machines of direct multiplication" - as well as J. R. Milne's "Arrangement of mathematical Tables… J. W. L. Glaisher contributed a chapter on "Logarithms and Computation" covering the history and then-current use of logarithms." Randall 1982a, 482 (Book ref. 20424)   £285.00
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GOLDING (Henry A.): Horse Power Computer for Steam, Gas & Oil Engines,
First Edition, comprising; card calculator volvelle with three moving circular pieces fastened with a brass rivet on a back-board (this measuring 6.5 inches square), with an accompanying text of 12 pages, stitched as issued, all in excellent order, in original slim cardboard box with protective tissue paper, London, Griffin, 1908. 'The computer is an ingenious form of mechanical calculator for solving the numerous problems connected with the power, size and speed of steam engines of all kinds. Its action is based upon the well-known principle of logarithmic calculation, the operations of multiplication and long division being effected mechanically by the addition and subtraction of distances proportional to the logarithms of the quantities represented...' -introduction. (Book ref. 19995)   £28.00
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COMPUTER MACHINE: Horse Power Computer for Steam, Gas & Oil Engines by Henry A.GOLDING
First Edition, comprising; calculator on varnished thick card with three moving circular pieces of graduating size fastened at the centre with a brass rivet on a back-board (this measuring 6.5 inches square), with an accompanying text of 12 pages, stitched as issued, all in excellent order, in original slim cardboard box with the original protective tissue paper, London, Griffin, 1908. 'The computer is an ingenious form of mechanical calculator for solving the numerous problems connected with the power, size and speed of steam engines of all kinds. Its action is based upon the well-known principle of logarithmic calculation, the operations of multiplication and long division being effected mechanically by the addition and subtraction of distances proportional to the logarithms of the quantities represented...' -introduction. An unusual survival of a comparatively early computing machine - pioneering hardware! (Book ref. 19994)   £28.00
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KLIR (George J.): Trends in General Systems Theory,
First Edition, 462pp large octavo, a few library marks but a very good copy in original cloth, with dust-wrapper, Wiley-Interscience, NY, 1972. Contents: I: History and basic aspects and role of computers; II: Discusses some important contemporary system problems - mainly in social sciences; III: Describes the Mesarovic and Wymore theories, as well as the authors; IV: Studies of some aspects of formal systems theories. (Book ref. 19753)   £12.00
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BABBAGE: [JACQUARD, Joseph Marie]; POSSELT (Emanuel Anthony): New and Revised Edition of The Jacquard Machine Analyzed and Explained: the Preparation of Jacquard Cards,
and Practical Hints to Learners of Jacquard Designing, fourth edition, 120pp plus 22pp advertisements at end, portrait (of Jacquard) and numerous large wood-engraved illustrations, a fine copy in original gilt lettered cloth, forming vol 4 in the series Posselt's Textile Library, Philadelphia:, Posselt, undated but c.1900. Photograph available on request. Babbage got the idea of the computer programme from Joseph Jacquard's looms. These avoided the use of skilled weavers by using a string of cards punched with holes that were attached to a rotating block over the looms. Where there were holes, threads could be picked up by hooks to be woven automatically into the patterns. The insight was marvellous - "the Engine eating its own tail" were Babbage's words for his application of the idea. With this start, and with the further ideas that he had, Babbage had established the basic principles on which today's computers work. See; Origins of Cyberspace, 355 for the first edition of 1888 (which made $6,000 at Christie's NY, 23rd February, 2005, lot 134): "This extensively illustrated work is the most detailed published account of the design and operation of the Jacquard loom, on which Jacquard himself appears to have never published any details. It includes an excellent description of the punched cards. The book includes a brief history of the Jacquard loom, a detailed description of its mechanism and an appendix on the preparation and stamping of Jacquard cards, illustrated with pictures of the stamping machines. The punched card method of storing and processing data evolved from methods developed by textile manufacturers in the 18th and 19th centuries for weaving complex patterns in cloth." "Born into a Lyonnese family of weavers, Jacquard was inspired by Vaucanson's punched-card loom to invent the Jacquard attachment, which caused any loom that used it to be called a Jacquard loom. The attachment was an automatic device that for the first time allowed a single operator to control from the loom all the movements involved in the production of complex woven patterns. The Jacquard loom reduced the amount of redundant manual labor that had previously been required in weaving, lowering labor and manufacturing costs and reducing physical hardship for the textile workers. It served as the catalyst for the technological revolution of the textile industry in the nineteenth century.Jacquard developed the idea for his invention in 1790, but because of the French Revolution did not exhibit it until 1801. Jacquard was granted a patent for his invention in 1803; in 1806 his loom was declared public property, and Jacquard was awarded a pension and royalties on each machine sold. Under the terms of Jacquard's pension he was required to introduce his technology to the textile industry of Lyons. During his first efforts, workers rioted out of fear of losing their jobs to the new technology, and at one point Jacquard had to flee for his life. However, he persevered and by the year 1812 there were eleven thousand Jacquard looms operating in France. By the time of Jacquard's death in 1834, twenty thousand Jacquard looms were installed in the Lyons region alone. Jacquard's invention made use of a punched-card system for storing and generating patterns. In the production of designs different cards were tied together by ribbons and hundreds of cards could be used in elaborate designs. Charles Babbage later incorporated punched-card technology as a method of data and program input in the design of his Analytical Engine. Even though the Analytical Engine was never constructed, Babbage's application of Jacquard punched card technology connected the Jacquard loom in the history of computing. The technology of punched cards was applied in data processing many years later, for use in the United States Census of 1890, when Herman Hollerith developed electrical machines for tabulating data stored on punched cards. Hollerith's company eventually evolved into IBM. Punched-card tabulation remained a primary means of data processing until it was phased out around 1960." (Origins of Cyberspace, 328). (Book ref. 19196)   £700.00
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BABBAGE [SMITHSONIAN INSTITUTION];: Charles Babbage,
[original article] compiled for the Smithsonian Institution, in: Annual Report of the Board of Regents of the Smithsonian Institution.. for the year 1873, First Edition, pp.162-197 in the complete volume, 452pp large octavo, a very good copy in original purple cloth, Washington, Government Printing Office, 1874. This original essay is essentially an extended obituary. Of great interest because it demonstrates great American enthusiasm for Babbage and obvious appreciation of his work - at a time when, in Britain, he had been largely ignored by the scientific establishment. Photograph available on request. (Book ref. 19198)   £70.00
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BABBAGE (Charles) with: HERSCHEL (J. F. W.): Barometrical Observations made at the Fall of the Staubbach,
First Edition, in: The Edinburgh Philosophical Journal.., conducted by Dr Brewster and Professor Jameson, p.224-227, in the complete volume, 412pp tall octavo, some spotting but a very good copy in contemporary half calf, rebacked retaining original red leather label, a few neat early library stamps, Edinburgh, Constable, 1822. Van Sinderen 16. Origins of Cyberspace, 28. Barometrical observations taken at a waterfall in Germany. Photograph available on request. (Book ref. 19178)   £150.00
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BABBAGE (Charles): On Some New Methods of Investigating the Sums of Several Classes of Infinite Series,
First Edition, extracted from Transactions of the Royal Society, 34pp quarto, bound in boards with paper label on the front, an excellent copy, with very wide margins, [London, Bulmer], 1819. See Van Sinderen 11. Origins of Cybernetics, 24. First Journal Edition, preceded only by the rare offprint, of which probably only 50 copies were printed. "Babbage brings his great powers of inventiveness to this subject [i.e., infinite series] but like many of his contemporaries, appeared insensitive to problems arising out of convergence, and accepted unquestioningly several absurd results" (Dubbey 1978, 135-36). Photograph available on request. (Book ref. 19175)   £220.00
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BABBAGE (Charles): On Machinery for Calculating and Printing Mechanical Tables,
First Edition, pp.274-281, in: The Edinburgh Philosophical Journal, Vol. 7, complete volume, (iv, iv, 415pp) tall octavo, a very good copy in old style quarter leather with marbled boards, a few early library stamps but a very good copy, Edinburgh, Archibald Constable, 1822. Photograph available on request. Van Sinderen no. 18 (n). Origins of Cyberspace, 30. This paper is an abstract of Babbage's Letter to Sir Humphrey Davy of the same year proposing construction of his Difference Engine No. 1. "In the early 1820s Babbage, frustrated by "the intolerable labour and fatiguing monotony of a continued repetition of similar arithmetical calculations", came up with the plan of designing a machine capable of performing various mathematical functions. By 1822 Babbage had constructed a model of his Difference Engine Number One, a special-purpose calculating machine far more complex than any that had previously been conceived, designed to compute mathematical tables by the method of finite differences and to print the results. In the design of his machine Babbage was influenced by the division of labor employed in the celebrated manuscript tables of de Prony which Babbage had seen in 1819. The division of labor, both physical and mental, became central themes of Babbage's economic thought later developed in his Economy of Machinery and Manufactures.Babbage was convinced of the "great utility" of his machine, but knew that constructing a larger version would entail "very considerable expense," and would also leave him no time to pursue his studies in pure mathematics. On July 3, 1822, as a means of testing the waters, Babbage wrote an open letter to Sir Humphry Davy, president of the Royal Society, in which he presented a detailed description of his Difference Engine. This was his first public statement of his plans for his calculating engine, and his first publication on his project for developing calculating engines, on which he would devote most of his creative energy for the remainder of his life. A copy of this letter published as a pamphlet reached the Lords of the Treasury, who referred it back to the Royal Society on April 1, 1823, with a letter requesting the Society's opinion of Babbage's machine. One month later, on May 1, the Royal Society responded to the Treasury as follows: "That it appears to the Committee, that Mr. Babbage has displayed great talents and ingenuity in the construction of his machine for computation, which the Committee think fully adequate to the attainment of the objects proposed by the Inventor, and that they consider Mr. Babbage as highly deserving of public encouragement in the prosecution of his arduous undertaking" (Great Britain. Parliament. House of Commons. Sessional Papers [1823], p. 6).This favourable report gained Babbage his first national funding of £1000 toward his construction of the Difference Engine. The project tested the limits of precision obtainable by machine tool makers at the time; it also ended up being far more costly than expected, claiming £17,000 of the government's money over the next decade before foundering in 1833, largely due to contractual disputes between Babbage and Joseph Clement, the engineer hired to construct Babbage's machine. By this time Babbage had begun to turn his attention to the Analytical Engine, a far more complex and powerful calculating machine whose design would occupy Babbage for most of the rest of his scientific career."- Origins of Cyberspace p.29. (Book ref. 19179)   £380.00
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BABBAGE (Charles): On Electrical and Magnetic Rotations,
First Edition, extracted from The Proceedings of the Royal Society, volume 116, pp.394-428, quarto, with the 1 large engraved plate, modern boards with label on front, small paper repair on final leaf but an excellent copy, London, The Royal Society, 1826. Photograph available on request. Van Sinderen 28. Not in Origins of Cyberspace. First Journal Edition, preceded only by the rare offprint, of which probably only 50 copies were printed. Here Babbage continued alone research he had begun with John Herschel on Arago's rotating discs. The experiments initiated by Arago, and carried on in England by Herschel and Babbage, led finally in 1831 to the discovery of electromagnetic induction by their friend Faraday, and thence to the generation of our electrical power. In the course of this investigation Babbage and Herschel came very close to discovering electromagnetic induction, seven years before Faraday. Hyman 58. (Book ref. 19182)   £350.00
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BABBAGE (Charles): On A Method of Expressing by Signs the Action of Machinery,
First Edition, extracted from The Proceedings of the Royal Society, volume 116, pp.250-65, quarto, modern paper boards with label on front cover, with the 4 large engraved plates illustrating mechanical notation, an excellent copy, London, The Royal Society, 1826. Photograph available on request. Van Sinderen 27. Origins of Cyberspace 37. First journal edition, preceded only by the rare offprint, of which probably only 50 copies were printed. This was Babbage's first formulation and explanation of his mechanical notation system, which was fundamental to all design work on his Difference Engine and Analytical Engine. "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 in following in detail succeeding stages of a machine's action. This led him to develop a mechanical notation which provided a systematic method for labelling 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 . . . the most powerful formal method for describing switching systems until Boolean algebra was applied to the problem in the middle of the twentieth century" (Hyman 58).Thus this crucial paper publishes, for the first time, Babbage's system of mechanical notation which enabled him to describe the logic and operation of his machines on paper as they would be fabricated in metal. 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 of some other equivalent language. The Difference Engine No. 2 ... is entirely described by its aid" (Babbage 1864, 104).Thus here Babbage demonstrated for the first time his new mechanical notation system, a system which would be essential for all the design work for his famous Difference Engine, the first machine to mechanically perform mathematical calculations, and his later Analytical Engine. Babbage's system, when combined with the discoveries in logic by Boole (1847 and 1854) and the application to modern circuitry by Claude Shannon (1938), became an essential developmental step in the conception of the modern computer.Babbage considered his mechanical notation system to be one of his finest inventions, and thought it should be widely implemented. It was a source of frustration to him that no other machine designer adopted it (probably because no other engineer during Babbage's time attempted to build machines as logically and mechanically complex as Babbage's). More than one hundred years later, in the 1930s, when developments in logic were applied to switching systems Claude Shannon demonstrated in his famous master's thesis that Boolean algebra could be applied to the same types of problems for which Babbage had designed his mechanical notation system.With its four plates, this paper was also one of the most extensively illustrated that Babbage published. (Book ref. 19181)   £850.00
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BABBAGE (Charles): Observations on the Analogy which Subsists between the Calculus of Functions and other Branches of Analysis,
First Edition, extracted from Transactions of the Royal Society, 20pp quarto, bound in modern boards with label on front, an excellent copy, with very wide margins, [London, Bulmer], 1817. Van Sinderen 7. Origins of Cybernetics, 21. The first paper read by Babbage to The Royal Society after his selection as a member. The paper is highly innovative and brought from Cauchy, the French mathematician, the remark that it proved that "in the land of Newton there were still generations of geometricians who worked for the progress of analysis" - the note of surprise is not hidden in this somewhat back-handed compliment. First journal edition, preceded only by the rare offprint, of which probably only 50 copies were printed. "It can be said with some assurance that no mathematician prior to Babbage had treated the calculus of functions in such a systematic way... Babbage must be given full credit as the inventor of a distinct and important branch of mathematics" (Dubbey 1978, 90). Elsewhere Dubbey states that "Babbage believed that his new scheme would serve as a generalized calculus to include all problems capable of analytical formulation, and it is possible to see here a hint of the inspiration for his concept of the Analytical Engine. While the work on the engines and his other scientific, social and political activities caused him virtually to abandon mathematical research at the age of thirty, the calculus of functions was the area he often yearned to continue. In fact the calculus of functions was not taken up by other workers, and it is the aspect of Babbage's mathematical work that modern mathematicians find the most fascinating" (Dubbey 1989, 18-19). Many years later, in his Passages from the Life of a Philosopher, Babbage referred to the calculus of functions as his "earliest step" and "one to which I would willingly recur if other demands on my time permitted" (Babbage 1864, p.435). Photograph available on request. (Book ref. 19172)   £420.00
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BABBAGE (Charles): An Examination of some Questions connected with Games of Chance,
First Edition, extracted from Transactions of the Royal Society of Edinburgh, 25pp quarto, modern boards with paper label on front, an excellent copy, partially unopened and with very wide margins, Read March 21, 1820, [Edinburgh, Royal Society Edinburgh], 1821. Van Sinderen 14. Not in Origins of Cybernetics. Babbage's only paper on probability. Photograph available on request. (Book ref. 19177)   £300.00
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BABBAGE (Charles): On the Application of Analysis to the Discovery of Logical Theorems and Porisms,
First Edition, extracted from Transactions of the Royal Society of Edinburgh, 16pp quarto with full-page engraved plate, read May 1st, 1820, modern boards, an excellent copy, partially unopened and with very wide margins, [Edinburgh, Royal Society Edinburgh], 1823. Van Sinderen 21. Not in Origins of Cyberspace. One of Babbage's few papers on geometry. Photograph available on request. (Book ref. 19180)   £345.00
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BABBAGE (Charles): Observations on the Discovery in Various Localities of the Remains of Human Art mixed with the Bones of Extinct Races of Animals,
First Edition, in: The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, pp.297-308, in the complete monthly issue for October 1859, a fine copy in original printed wrappers, London, by Taylor and Francis, 1859. See Van Sinderen 75 for the second printing in the Royal Society of London Proceedings, 1860, only - the current edition unlisted. See Origins of Cyberspace, 78 - which similarly misses this edition of 1859. "Babbage's contribution to the then-current controversy surrounding the dating of human artifacts found in the same geological strata as the remains of extinct animals. Babbage pointed out the imprecise nature of the evidence and concluded that "whilst we ought to be quite prepared to examine any evidence which tends to prove the great antiquity of our race, yet that if facts adduced can be explained and accounted for by the operation of a few simple and natural causes, it is unphilosophical to infer the co-existence of man with those races of extinct animals.".." Babbage goes on to explain at great length how the dating evidence of the time is unclear, given that the events surrounding the flooding of caves are not predictable. He based his evidence from his own experience and observations made when he visited the caverns of Michelstown in Ireland. The long paper is an interesting light on Babbage's consistently enquiring scientific mind – a mind unrestricted to its own natural sphere and always interested in the controversies current at the time. Photograph available on request. (Book ref. 19190)   £150.00
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BABBAGE (Charles): Demonstration of a Theorem relating to Prime Numbers,
First Edition, in: The Edinburgh Philosophical Journal.., conducted by Dr Brewster and Professor Jameson, p.46-49, in the complete volume, 436pp plus 9 engraved plates, some spotting but a very good copy in contemporary half calf, rebacked retaining original red leather label, a few neat early library stamps, Edinburgh, Constable, 1819. Van Sinderen, 12. Origins of Cyberspace, 25: "Babbage's only published work on number theory, concerned with an extension of Wilson's theorem (first published in 1776) that the number (n-1)! + 1 is divisible by n if n is a prime number, otherwise it is not divisible by n. "Babbage's aim was to provide a function of the integer n which had similar property with respect to n2... The proof is not complete for Babbage says nothing about the "otherwise it is not" part of the theorem." (Dubbey, 1978, 139-40)." Photograph available on request. (Book ref. 19176)   £120.00
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