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  • Seller image for Leibniz on the Parallel Postulate and the Foundations of Geometry: The Unpublished Manuscripts (Science Networks. Historical Studies, 51, Band 51). for sale by ANTIQUARIAT Franke BRUDDENBOOKS
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    Gebundene Ausgabe, Gr.-8°. Condition: Gut. 1st ed. 2016. 203 S. Das Buch ist in gutem, sauberen Zustand. Ecken und Kanten leicht bestossen. Sonst sauberes und wohlerhaltenes Exemplar. -----Inhalt:. This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz's work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the seventeenth-century studies on the foundations of geometry. It also provides a detailed mathematical and philosophical commentary on his writings on the theory of parallels, and discusses how they were received in the eighteenth century as well as their relevance for the non-Euclidean revolution in mathematics. The second part offers a collection of Leibniz's essays on the theory of parallels and an English translation of them. While a few of these papers have already been published (in Latin) in the standard Leibniz editions, most of them are transcribed from Leibniz's manuscripts written in Hannover, and published here for the first time. The book provides new material on the history of non-Euclidean geometry, stressing the previously neglected role of Leibniz in these developments. This volume will be of interest to historians in mathematics, philosophy or logic, as well as mathematicians interested in non-Euclidean geometry. 1.Introduction.- 2.The Theory of Parallel Lines in the Age of Leibniz.- 3.Leibniz' Epistemology of Geometry and the Parallel Postulate.- 4.Leibniz' Attempts to prove the Parallel Postulate.- 5.Reception and Legacy.- Leibniz' Texts on Parallel Lines.- Bibliography. ISBN: 9783319198620 Wir senden umgehend mit beiliegender MwSt.Rechnung. Sprache: Englisch Gewicht in Gramm: 522.

  • HOFMANN, Joseph E.:

    Published by Cambridge: Cambridge University Press, 1974., 1974

    ISBN 10: 0521202582 ISBN 13: 9780521202589

    Language: English

    Seller: Ted Kottler, Bookseller, Redondo Beach, CA, U.S.A.

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    Hardcover. Condition: Very Good. No Jacket. 1st Edition. Revised English translation of Die Entwicklungsgeschichte der Leibnizschen Mathematik während des Aufenthalts in Paris (1672-1676) (1st German ed., 1949). Frontispiece, xi, 372 pp; 30 figs. Original cloth. Very Good, without dust jacket. In print in paperback only at US$50.00. 'When Gottfried Wilhelm Leibniz first arrived in Paris in 1672 he was a well-educated, sophisticated young diplomat who had yet to show any real sign of his latent mathematical abilities. Over his next four crowded, formative years, which Professor Hofmann analyses in detail, he grew to be one of the outstanding mathematicians of the age and to found the modern differential calculus. In Paris, Leibniz rapidly absorbed the advanced exact science of the day. During a short visit to London in 1673 he made a fruitful contact with Henry Oldenburg, the secretary of the Royal Society, who provided him with a wide miscellany of information regarding current British scientific activities. Returning to Paris, Leibniz achieved his own first creative discoveries, developing a method of integral 'transmutation' through which lie derived the 'arithmetical' quadrature of the circle by an infinite series. He also explored the theory of algebraic equations. Later, by codifying existing tangent and quadrature methods and expressing their algorithmic structure in a 'universal' notation, lie laid the foundation of formal 'Leibnizian' calculus' (Cambridge University Press Web site). Contents: 1. Introduction; 2. The 'Accessio ad Arithmeticam Infinitorum'; 3. The first visit to London; 4. Oldenburg's communication of 6 (16) April 1673; 5. The great discoveries of the year 1673; 6. Readings in contemporary mathematical literature; 7. First communication about the new results; 8. The quarrel over rectification; 9. Disputes about clocks; 10. Leibniz receives first details of Gregory's and Newton's work; 11. Studies in algebra; 12. The meeting with Tschirnhaus; 13. The invention of the calculus; 14. Dispute about Descartes' method; 15. The report on Gregory's results and Pell's methods; 16. Newton's first letter for Leibniz; 17. Leibniz' reply; 18. Tschirnhaus' reaction; 19. Newton's second letter for Leibniz; 20. The second visit to London; 21. Conclusion.

  • Franz Durst

    Published by Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, DE, 2010

    ISBN 10: 3642090486 ISBN 13: 9783642090486

    Language: English

    Seller: Rarewaves.com USA, London, LONDO, United Kingdom

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    Paperback. Condition: New. 1st ed. Softcover of orig. ed. 2008. Fluid mechanics is a field that spreads widely and to all fields of engineering, science and medicine. The book takes this into account and provides a sound basis.This is a modern book on fluid mechanics that is written in a way needed these days to teach the subject to students in engineering and science at higher educational institutes. The book is well structured for this purpose and is arranged in a logical teaching sequence of chapters. It is starting with an introductory chapter that contains also the summary of the history of fluid mechanics. In two chapters the basic knowledge in mathematics and physics is summarized to provide the background information needed by the students to enter the fluid mechanics. Kinematics of fluid motion is briefly described followed by the complete derivations of the differential form of the continuity and momentum equations, as well as the mechanical and thermal form of the energy equation. Subjects like hydrostatics, similarity theory,potential flows, gas dynamics etc. are treated in an introductory way to lead the students into fluid mechanics. The t_ij terms are introduced to describe the molecular momentum transport and their complete derivation is given by looking at the basis of molecular motions like that in an ideal gas. Subjects like one-dimensional viscous flows, stationary and in stationary, are treated to give the students an introduction into laminar flows. Wave motions in fluids, low Reynolds number flows, high Reynolds number flows and flows with heat transfer are treated to permit the students to get introductory treatments of important parts of fluid mechanics. Introductions are also provided into numerical computations of flows, into turbulence, as well as into measuring techniques as applied in fluid mechanics. In this way, the entire theory and practise of fluid mechanics is treated in the book, providing the student with information needed for more advanced books in specialized subjects of fluidflow treatments.Advancements of fluid flow measuring techniques and of computational methods have led to new ways to treat laminar and turbulent flows. These methods are extensively used these days in research and engineering practise. This also requires new ways to teach the subject to students at higher educational institutions in an introductory manner. The book provides the knowledge to students in engineering and natural science they need to enter fluid mechanics applications in various fields. Analytical treatments are provided based on the Navier-Stokes equations. Introductions are also given into numerical and experimental methods applied to flows.The main benefit the reader will derive from the book is a sound introduction into fluid mechanics with introductions into subfields that are of interest to engineering and science.TWM Brief Market Research ReportAdvanced Fluid Mechanics Market Size Estimate 5,100Market Leaders: 1) White - Viscous Flow 2/e, '06 (McGraw-Hill) 1,300 25%2) Kundu/Coh.


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    Hardcover. Condition: Very Good+. Dust Jacket Condition: No Dust Jacket. Scholar's bookplate to inner cover (G. P. Goold). Light soiling to rear board of vol. 2 else books have very minor shelfwear. ; The seventh book of Pappus's Collection, his commentary on the Domain (or Treasury) of Analysis, figures prominently in the history of both ancient and modern mathematics: as our chief source of information concerning several lost works of the Greek geometers Euclid and Apollonius, and as a book that inspired later mathematicians, among them Viete, Newton, and Chasles, to original discoveries in their pursuit of the lost science of antiquity. This presentation of it is concerned solely with recovering what can be learned from Pappus about Greek mathematics. The main part of it comprises a new edition of Book 7; a literal translation; and a commentary on textual, historical, and mathematical aspects of the book. It proved to be convenient to divide the commentary into two parts, the notes to the text and translation, and essays about the lost works that Pappus discusses. The first function of an edition of this kind is, not to expose new discoveries, but to present a reliable text and organize the accumulated knowledge about it for the reader's convenience. Nevertheless there are novelties here. The text is based on a fresh transcription of Vat. Gr. 218, the archetype of all extant manuscripts, and in it I have adopted numerous readings, on manuscript authority or by emendation, that differ from those of the old edition of Hultsch. Moreover, many difficult parts of the work have received little or no commentary hitherto. ; 749 pages.

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    Hardcover. Condition: Very Good. Dust Jacket Condition: Very Good. 1st Edition. English translation of Traité d'optique sur la gradation de la lumière (1st French ed., 1760). Frontispiece, xiv, 1 leaf, 248 pp; 48 figs.; 7 tables. Original cloth. Very Good, in very good dust jacket. Bookplate of Robert E. Schofield, who reviewed the book for Technology and Culture (Vol. 3, No. 2, Spring, 1962, pp. 183-184). 'In the latter part of the Essai [1729], Bouguer published the second of his great optical discoveries, often called Bouguer's law: In a medium of uniform transparency the light remaining in a collimated beam is an exponential function of the length of its path in the medium. This law was restated by J. H. Lambert in his Photometria (1760) and, perhaps because of the great rarity of copies of Bouguer's Essai, is sometimes unjustifiably referred to as Lambert's law. Just before he died, Bouguer completed a much larger book on photometry, the Traité d'optique sur la gradation de la lumière, published posthumously (1760) by his friend the Abbé Nicolas Louis de la Caille. The Traité goes far beyond the Essai, describing a number of ingenious kinds of photometers, including a method of goniophotometry, and even attempting an elaborate theory of the reflection of light from rough surfaces, although this was not successful. The third and last part of the book, however, gives a valid elementary theory of the horizontal visual range through an obscuring atmosphere, arriving at a law, usually credited to H. Koschmieder, considered to belong to the twentieth century. It is fair to consider Pierre Bouguer not only the inventor of the photometer but also the founder of an important branch of atmospheric optics. The eighteenth century is not an outstanding epoch in the history of optics, but Bouguer's contribution to that science is notable by any standard' (Middleton in D.S.B. II: 343-4; he notes a Latin translation appeared in 1762 and a Russin one in 1950). [441].

  • Seller image for Noções geraes das dormideiras, da sua cultura, e da extracção do verdadeiro opio, que ellas contem. for sale by Richard C. Ramer Old and Rare Books

    BROTERO, Felix de Avelar.

    Published by Lisbon, Na Impressão Regia, 1824., 1824

    Seller: Richard C. Ramer Old and Rare Books, New York, NY, U.S.A.

    Association Member: ABA ABAA ILAB

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    11 titles bound in 1 volume. Small 8°, contemporary quarter morocco over marbled boards (minor wear), smooth spine gilt in romantic fashion with "miscellanea // medica" lettered in gilt at cener, pink endleaves. Woodcut Portuguese-Brazilian royal arms on title page. In very good condition. 30 pp., (1 blank l.). *** FIRST and ONLY EDITION of this work on the cultivation of poppies and the extraction of opium.Avellar Brotero (1744-1828) fled to France in 1788 to escape persecution by the Inquisition, and there published his Compendio de botanica in order to earn his living. It immediately established his reputation as a botanist, and upon his return to Portugal in 1790 he was given the chair of botany and agriculture at Coimbra. His two best known works, Flora lusitanica, 1804, and Phytographia Lusitaniae selectior, 1816-1827, were the first lengthy descriptions of native Portuguese plants. As director of the botanical gardens at Coimbra and Ajuda, he was responsible for their reorganization and enlargement.Provenance: The entire volume was owned by Francisco António Rodrigues de Gusmão (1815-1888), physician and author, perhaps the most significant collaborator of Innocêncio Francisco da Silva in the course of the writing of the still indispensable Dicionário bibliographico portuguez. He presumably commissioned the binding. It was purchased in the auction of books owned by Rodrigues de Gusmão and Mário Tomás da Costa Roque (1932-1983), distinguished physician, the author of books on the history of medicine and on printing history, an important auction catalogue with 1,320 lots, sold 1 and 2 April, 1998. See Silva's and Pedro de Azevedo, Biblioteca de Francisco António Rodrigues de Gusmão e Mário Tomás da Costa Roque, Lisbon: Silva's, 1998. The introduction to the catalogue contains an extract from the Dicionário bibliographico about Rodrigues de Gusmão, and an essay by Joaquim Veríssimo Serrão about Costa Roque. For Rodrigues de Gusmão see Grande enciclopédia, XII, 929.*** Innocêncio II, 259-64. Lisbon, Faculdade de Medicina, Catálogo da coleção portuguesa I, 53-54. Not in Pires de Lima, Catálogo da Bibliotheca da Escola Medico-Cirurgica do Porto. Not in Wellcome. NUC: ViU, ICN.*** BOUND WITH: PINTO, Agostinho Albano da Silveira, ed. Noções sobre a colera-morbus Indiana extrahidas principalmente da obba [sic] de James Kennedy e d'outas coordinadas . Lisbon: Na Impressão Regia, 1832. Small 8º, xii, 113 pp., (1 l. errata). Woodcut Portuguese royal arms on title page. In very good to fine condition. FIRST and ONLY EDITION. There is much information specific to India. Silveira Pinto (1785-1852), a native of Porto, earned degrees in philosophy, medicine and mathematics from Coimbra University. He fought with the Batalhão Academico during the Peninsular War. A member of the Academia Real das Sciencias de Lisboa, as well as numerous other learned societies both foreign and domestic, he was a deputy to the Côrtes in every legislature from 1838 to 1852, and was responsible for a number of other publications.* Innocêncio I, 13. Gonçalves Rodrigues, A tradução em Portugal 4252. Lisbon, Faculdade de Medicina, Catálogo da coleção portuguesa II, 321. Not in Pires de Lima, Catálogo da Bibliotheca da Escola Medico-Cirurgica do Porto. Not located in OCLC. Porbase locates a single copy, in the Biblioteca Nacional de Portugal. Not located in Jisc. KVK (51 databases searched) locates only the copy cited by Porbase. AND BOUND WITH:PEREIRA, J.[oao] F.[elix]. Breves e claras instrucções contra a cholera-morbus ordenadas em beneficio da familias e a ellas dedicadas. Lisbon: Na Impressão Regia, 1833. Small 8º, 16 pp. Woodcut Portuguese royal arms on title page. In very good condition. We were not able to find any other author with last name Pereira and initials J.F.FIRST and ONLY EDITION. According to the catalogue of the Lisbon Faculdade de Medicina, the initials J.F. on the title page stand for João Felix. However, João Felix Pereira appears to have.

  • Guilhou, Nadine (ed.)

    Published by Archaeopress, Oxford, 2016

    ISBN 10: 178491522X ISBN 13: 9781784915223

    Language: Multiple languages

    Seller: Archiv Fuenfgiebelhaus, Rostock, Germany

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    Softcover. Condition: Sehr gut. 1. Auflage. XXVI + 374 pages, very good condition. - - Contents: Foreword, Introductions. - - Part 1: Nut and the Realm of the Stars: Nils Billing: The Dialogue of Geb and Nut in Relation to the Royal Sarcophagus in the Pyramid of King Pepy I. - - Nadine Guilhou: Le Soleil dans les Bras de Nut dans les Tombes Thébaines. - - Mykola Tarasenko: The "Children of Nut" and their Rebellion in Chapter 175A of the Book of the Dead. - - Bernard Arquier: L' Astérisme du Bélier dans l' Ancienne Egypte. - - Azza Ezzat: Staircases in Ancient Egyptian Pools: Iconographic Attestations and Ouranographic Connotations. - - Brigitte Vallée: Les Hypocéphales et la Déesse Céleste Nut. - - Kurt Locher: Gods Coming from the Left : Possible Astronomical Origins of Religious Processions. - - Sabine Stemmler-Harding: Devil in Disguise - On the Stellar Mythology of Apophis and its Potential Connection to the Constellation Htp-Rdwy. - - Frank Goddio: Un Récit de la Création ressurgit des Profondeurs. - - Anne-Sophie von Bomhard: The Genesis of the Stars in Ancient Egypt, according to the Naos of the Decades. - - Massimiliano Franci: Defining Time. - - Gaëlle Chantrain: Une Journée dans le Temps et l'Espace - Remarques Lexicales au Sujet de hrw et grh. - - Themis G. Dallas: The Ancient Skyscape Over the Sanctuary of Egyptian Gods in Marathon. - - Mona Haggag: The Tazza Farnese: An Alexandrian Vision of the Cosmos. - - Jean-Pierre Levet: Les Constellations Anthropomorphes de l' Hémisphère Nord et l' Astrosophie chez Ptolémée. - - Part 2: Ancient Egyptian Religon, Art, History and Their Celestial Undertones: Jean-Pierre Pätznick: La Déesse d'Eléphantine à l'Epoque Thinite : Tabouisation Locale du Nom Divin. - -Tatjana A. Sherkova: Sacral Numbers in Ancient Egypt : Historical and Psychological Study. - - Azzazy/Ezzat: The Sycamore in Ancient Egypt - Textual, Iconographic & Archaeopalynological Thoughts. - - Ahmed Mansour: Notes on the role of Htm(w)/Htmty-Ntr in Turquoise Mining Expeditions. - - Dina 'El-Gabry: A Fragmentary Dyad of Penwah and of his Wife Meryt : Cairo Museum JE 27955, CG 1003. - - Hamdy Ahmed 'El-Sorogy: The Flea Insect as a New Symbol for God Seth. - - Hedvig Györy: On the History of Feline Amulets - A Preliminary Study of Cat Amulets. - - Detlev Quintern: The Lion and the Mouse - Travelling Ethics. - - Sophia Tsourinaki: Between Dionysos and Christ : Cosmological Images on a Hellenistic Fulnerary Textile. - - Ashraf-Alexandre Sadek: De la Spiritualité des Anciens Egyptiens à la Spiritualité Chrétienne. - - Youhanna N. Youssef: The Date of Consecration of the Sanctuary of Patriarch Benjamin. - - Manto Papaioannou: Psychostasia in Byzantine Art through the Iconography of Archangel Michael. - - Part III: Egyptian Mathematics, Medicine, Archaeoanthropology and Egyptomania: Irem Aslan-Seyhan: Considerations on the Study of Ancient Egyptian Mathematics in Modern Turkey. - - Stephanos Geroulanos: An Introduction to Alexandrian Medicine and Surgery. - - Constantinos Triantaphyllidis: The Genetic History of Hellas, Egypt and of the Near East and the DNA Study of King Tut'ankhamun. - - Adam Lukaszewicz. One more Hand that rocked the Cradle of Egyptology - Count Jan Potocki. - - Mladen Tomorad: Aegyptiaca and Various Forms of Egyptomania in Croatia. - - Antigoni Maniati: Brief CV and list of Publication of Prof. Dr Dr Alicia Maravelia. - - Evi Batra: Epilogue - Dr Dr Alicia Maravelia and the Association of Greek Women Scientists.

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    Rilegato. Condition: nuovo. Paul Hullmeine (ed). Pages: 479 p. Illustrations:10 b/w, 4 tables b/w. Language(s):English, Arabic. Publication Year:2024. Brepols. ISBN: 978-2-503-60717-7. Hardback -- Summary Ptolemy's Almagest (2nd century AD) is the most influential work of ancient and medieval astronomy. This work, however, does not tell us the full story about its author's views of the heavens. After completing the Almagest, Ptolemy turned his attention to a physical investigation of celestial motions. The result is the Planetary Hypotheses, a bold attempt to provide a celestial physics that coheres with the mathematical account of astronomical observations in his Almagest. This book provides the first complete critical edition and English translation of the Arabic version of the Planetary Hypotheses, which is lost for the most part in its original Greek. It furthermore provides an extensive commentary on the whole work, which situates the Planetary Hypotheses within the context of its time and investigates philosophical ideas central to the work. These include the epistemic value of mathematics relative to natural philosophy, and the shape, number, and dynamics of the celestial bodies. The book also investigates the influence of the Planetary Hypotheses on a wide range of medieval Arabic astronomical and philosophical works from the 9th to the 13th century AD. The upshot is to establish the Planetary Hypotheses as a crucial text for understanding the history of philosophy and science from Greek antiquity to the Arabic Middle Ages TABLE OF CONTENTS I Introduction II Astronomy, Natural Philosophy, and the Physical Reality of the Celestial Bodies III The Dynamics of Celestial Motions IV Conclusion V The Arabic Version of the Planetary Hypotheses: Edition and Translation VI Commentary Glossary Bibliography Index.

  • Seller image for Arithmeticorum libri sex, et de numeris multangulis liber unus. Cum commentariis C.G. Bacheti V.C. & observationibus D.P. de Fermat senatoris Tolosani Accessit doctrinae analyticae inventum novum, collectum [by J. de Billy] ex varijs . Fermat epistolis [ed. Samuel de Fermat] for sale by SOPHIA RARE BOOKS

    First edition. LARGE PAPER COPY WITH THE PORTRAIT - INSCRIBED BY FERMAT'S SON TO HIS BROTHER-IN-LAW. First edition, presentation copy inscribed by Fermat's son Clement-Samuel to his brother-in-law, printed on large and thick paper and with the engraved frontispiece portrait of Fermat (intended only for the few large paper copies), of Fermat's annotated edition of Diophantus' Arithmetica. This is the first printing of Fermat's contributions to the theory of numbers, of which he is the undisputed founder, including his famous statement of 'Fermat's last theorem.' This is the only inscribed presentation copy we have ever seen or heard of. Since most of Fermat's work in number theory remained unpublished in his lifetime, "it was neither understood nor appreciated until Euler revived it and initiated the line of continuous research that culminated in the work of Gauss and Kummer in the early nineteenth century" (DSB). Fermat showed little interest in publishing his work, which remained confined to his correspondence, personal notes, and to marginal jottings in his copy of the 1621 editio princeps, edited by Claude Bachet, of Diophantus' Arithmetica. Fermat's marginalia included not only arguments against some of Bachet's conclusions, but also new problems inspired by Diophantus. After his death, Fermat's eldest son Clement-Samuel published his father's marginalia in this new edition. Most famous of the 48 observations by Fermat included here is the tantalizing note that appears on fol. H3r "regarding the impossibility of finding a positive integer n > 2 for which the equation xn + yn = zn holds true for the positive integers x, y, and z" (Norman). Fermat noted that he had discovered a "truly marvellous demonstration" of this proposition, but that the margin was too narrow to transcribe it. This simple statement became known as the single most difficult problem in mathematics, and for over 300 years no mathematician succeeded in either proving or disproving it. In 1995 Andrew Wiles, professor of mathematics at Princeton, who had been obsessed with Fermat's last theorem since the age of 10, completed a 130-page proof (first presented in 1993, with a flaw that required revision), using the most advanced techniques of modern mathematics. His achievement was described by fellow mathematicians as the mathematical equivalent "of splitting the atom or finding the structure of DNA" (Singh, Fermat's Enigma (1997), p. 279). Although Fermat's marginal jottings in Diophantus hold a special place in the history of mathematics, much of what we know of Fermat's methods of proof is found in his letters to the French Jesuit Jacques de Billy, a pupil of Bachet, printed for the first time in the present work as Doctrinae Analyticae Inventum Novum. RBH lists no presentation copies, and only two other large paper copies, the Macclesfield copy and one offered by Goldschmidt in 1927. The large paper copies are printed on paper with a different watermark from ordinary paper copies, and the text block is about 30% thicker. This copy is slightly taller than the Macclesfield copy. Provenance: 1. Inscription by Clement-Samuel de Fermat on title page, 'de Molières ex dono authoris'. Louis-Armand de Molières (1610-1687), President Treasurer of France in Montauban, was married in 1646 to Louise de Fermat, Clement-Samuel's sister. 2. Autograph correction to the result of a calculation by Fermat on p. 135, and two inserted slips of paper with contemporary but more elementary annotations at pp. 61 and 197 (the former is where Fermat's last theorem is stated). (These corrections are not present in the Macclesfield copy.) The correction on p. 135 relates to the problem of finding numbers that can be expressed as a difference of two cubes in more than one way, i.e., finding rational numbers (fractions) a, b, c, d such that a3 b3 = c3 d3. Fermat gives the solution a = 2024284625/6128487, b = 1981385216/6128487, c = 1265/183, d = 1256/183; the denominators have been changed in manuscript to 226981 and 61. This correction could only have been made by, or under the direction of, an expert in Diophantine equations, most likely de Billy before the copy was sent to its recipient. 3. Lucien Scheler (his code on p. 9). Almost nothing is known about the life of Diophantus. His place of birth is unknown and his arrival in Alexandria could have been at any time within a five-century period. In his writings Diophantus quotes Hyspicles and therefore must have lived after 150 BC; on the other hand his own work is quoted by Theon of Alexandria and therefore he must have lived before AD 364. A date around AD 250 is generally accepted. "The Arithmetica is essentially a logistical work, but with the difference that Diophantus' problems are purely numerical with the single exception of problem V, 30. In his solutions Diophantus showed himself a master in the field of indeterminate analysis, and apart from Pappus he was the only great mathematician during the decline of Hellenism" (DSB). "The Arithmetica begins with an introduction addressed to Dionysiusarguably St. Dionysius of Alexandria. After some generalities about numbers, Diophantus explains his symbolismhe uses symbols for the unknown (corresponding to our x) and its powers, positive or negative, as well as for some arithmetic operationsmost of these symbols are clearly scribal abbreviations. This is the first and only occurrence of algebraic symbolism before the 15th century. After teaching multiplication of the powers of the unknown, Diophantus explains the multiplication of positive and negative terms and then how to reduce an equation to one with only positive terms (the standard form preferred in antiquity). With these preliminaries out of the way, Diophantus proceeds to the problems. Indeed, the Arithmetica is essentially a collection of problems with solutions, about 260 in the part still extant. The introduction also states that the work is divided into 13 books. Six of these books were known.

  • Seller image for JAPAN DESCRIBED AND ILLUSTRATED BY THE JAPANESE. Written By Eminent Japanese Aut for sale by RARE ORIENTAL BOOK CO., ABAA, ILAB
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    Boston [1897], Millet. Red cloth spines over stiff wrappers, 15 vol. set, 382p.,29 of 30 hand colored albumen photos +215 b.w. collotype photos by Tamamura,15 color flower collotypes by K. Ogawa. folio size:32 x 39.5 cm .*FIRST & ONLY EDITION* . *** **** *** . . .A STUNNINGLY EXCELLENT ILLUSTRATED DESCRIPTION OF OLD JAPAN . . WITH . . 29 HAND-COLORED 8 X 10" ORIGINAL ALBUMEN PHOTOGRAPHS . . & 215 BLACK & WHITE COLLOTYPE TEXT PHOTOS . . BY THE EMINENT JAPANESE PHOTOGRAPHER K. TAMAMURA . . . PLUS . . 30 FULL-PAGE COLOR COLLOTYPE PHOTOGRAPHS . . BY JAPAN'S MOST CELEBRATED PHOTOGRAPHER, K. OGAWA . . . INCLUDING . . . 15 FULL-PAGE TEXTILE PATTERNS IN COLOR . . * THE TEXT AUTHOR: CAPTAIN FRANCIS [Frank] BRINKLEY 1841-1912; . He was an Anglo-Irish newspaper owner, editor, scholar, Military advisor & journalist who resided in Meiji period [1968-1912] Japan for over 40 years. . In 1867 Captain Brinkley returned to Japan, never again to return home. Attached to the British-Japanese Legation and still an officer in the Royal Artillery, he was assistant military attaché to the Japanese Embassy. . He resigned his commission in 1871 to take up the post of foreign advisor to the new Meiji government and taught artillery techniques to the new Imperial Japanese Navy at the Naval Gunnery School. . Brinkley was one of a very few westerners who actually mastered the Japanese language soon after his arrival, and both spoke and wrote it well. This may account for the Japanese naval success over Russia in 1904! . In 1878 he was invited to teach mathematics at the Imperial College of Engineering, which later became part of Tokyo Imperial University, remaining in this post for two and a half years. . In the same year he married Yasuko Tanaka, the daughter of a former Samurai from the Mito clan. They were the parents of two daughters and a son named Jack Ronald Brinkley [1887 - 1964]. . In 1881 until his death he owned and edited the JAPAN MAIL, Mail a newspaper, receiving financial support from the Japanese government and consequently maintaining a pro-Japanese stance. The newspaper was perhaps the most influential and widely read English language newspaper in the Far East. . He was an eminent author of numerous books on Japanese culture, art and architecture and an English-Japanese Dictionary. See below for more details. . *** RARITY: This set is highly collectable, seldom found, among his RAREST sets, most of his works consist of 10 volumes, this being a 15 volume set was issued in a small edition. With excellent photos & illustrations of Japan. . *** SUBJECTS & CONTENTS: An eclectic work, covering all of aspects of Japan, Japanese life, people, costumes, famous scenery, Mt. Fuji, costume, customs, trades, textiles, tattooed men, rice culture, Ikebana Zen flower arrangement, tea, musical instruments, dancers, women, gardens & many Yokohama views. . Additionally includes silk culture & weaving, arms, armor & Samurai, flowers in color, theatre, actors, Sumo, landscape, Kimono & other garments, Kyoto, Tokyo, Kobe, Nagasaki, architecture, bronzes and too many to list. . Views of famous places, daily activities, toil, work, trades, farming, commerce, household activities and much more. . A keen insight to the Japanese with essays by their scholars in English. . *** LAVISHLY ILLUSTRATED BY TWO EMINENT JAPANESE PHOTOGRAPHERS: . K. OGAWA IMAGES: Each volume begins with 15 beautiful full-page color collotype photo of a flowers. . T. TAMAMURA IMAGES: Followed by followed by 2 hand-tinted albumen large size photos per volume [29 of 30] present, each is large size: 8 x 10 inches, each with separate caption sheet. . They show portraits, famous scenic spots, famous people, sights and much more. . Followed by 215 black and white text collotype photographs. . These photos show interiors of homes, art works, country scenery, activities of daily life, and a host of other views on Japan in the late 19th century. . * This work is a fascinating insight to the Japanese and their way of life, culture and the results of western influences from abroad. . An excellent primary visual source for Japan prior to her modernization and huge leap into the western--influenced new world. . A superb photographic essay capturing stunning images of old Meiji period [1968-1912] Japan, by her two most iconic photographers. . *** CONTENTS OF THE 15 SECTION/VOLUME SET: . This title was edited by Captain Francis Brinkley. . The table of contents is found on the last page of volume 15. Volume 1 begins with page 1, and each volume continues the pagination to the end on volume 15 as page 382, the set is complete. . Introduction by Arthur J. Mundy . Chapter.1: THE EMPIRE, ITS SIZE, BUILDINGS, CITIES & SCENERY . Edited by Captain Francis Brinkley. . Chapter 2. THE EARLY JAPANESE AND THEIR HISTORY. . Chapter 3. ditto above, concluded. Lacking 1 of 2 color . albumen photos. . Chapter 4: ESTABLISHMENT OF THE TOKUGAWA DYNASTY AND . JAPAN'S RELATIONS WITH THE ORIENT IN THE EARLY . AGES OF THE CHRISTIAN ERA. . Chapter.5: JAPAN'S DEBT TO CONTINENTAL NEIGHBORS IN EARLY . ERAS. . Chapter 6: MEDIAEVAL JAPAN . Chapter 7: YOSHITSUNE, GENGHIS AND THE MONGOL INVASION . Chapter 7: ditto above, concluded. . Chapter 8: CREEDS AND CASTES . Chapter 9: RELIGION AND RITES . Chapter 10: SUPERSTITIONS AND DIVINATION . Chapter 11: FESTIVALS . Chapter 12. OBSERVANCES AND PASTIMES . Chapter 12. ditto concluded . Chapter 13: JAPAN'S COMMERCIAL AND POLITICAL INTERCOURSE . WITH FOREIGN COUNTRIES. . Chapter 13. ditto above, concluded . Chapter 14. THE ATTITUDE OF JAPAN TOWARD FOREIGN RESIDENTS, . JAPANESE FINANCE. . Chapter 14. ditto above, concluded . Chapter 15: MODERN JAPAN IN BRIEF. . *** Color photos are posted to our website. . *** PROFUSELY ILLUSTRATED BY TWO ICONIC JAPANESE PHOTOGRAPHERS: . TAMAMURA KOZABURO [1856-1923?] & OGAWA Kazumasa [1860-1929]: . He worked in his Yokohama studio & provided images, albums and photographic service to both Japanese and mostly his foreign clie.