Download or read book The Ancient Tradition of Geometric Problems written by Wilbur Richard Knorr and published by Courier Corporation. This book was released on 1993-01-01 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illustrated study focuses on attempts by ancient Greeks to solve three classical problems: cube duplication, angle trisection, and circle quadrature. Origins of the study of conics, introduction of special mechanical curves, more. 1986 edition.
Download or read book The Ancient Tradition of Geometric Problems PT 1 written by Knorr and published by . This book was released on 1987-01-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Evolution of the Euclidean Elements written by W.R. Knorr and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incommensurable magnitudes beginning from the first discoveries by fifth-century Pythago reans, advancing through the achievements of Theodorus of Cyrene, Theaetetus, Archytas and Eudoxus, and culminating in the formal theory of Elements X; (2) to correlate the stages of this developing theory with the evolution of the Elements as a whole; and (3) to establish that the high standards of rigor characteristic of this evolution were intrinsic to the mathematicians' work. In this third point, we wish to counterbalance a prevalent thesis that the impulse toward mathematical rigor was purely a response to the dialecticians' critique of foundations; on the contrary, we shall see that not until Eudoxus does there appear work which may be described as purely foundational in its intent. Through the examination of these problems, the present work will either alter or set in a new light virtually every standard thesis about the fourth-century Greek geometry. I. THE PRE-EUCLIDEAN THEORY OF INCOMMENSURABLE MAGNITUDES The Euclidean theory of incommensurable magnitudes, as preserved in Book X of the Elements, is a synthetic masterwork. Yet there are detect able seams in its structure, seams revealed both through terminology and through the historical clues provided by the neo-Platonist commentator Proclus.
Download or read book Textual Studies in Ancient and Medieval Geometry written by W.R. Knorr and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: For textual studies relating to the ancient mathematical corpus the efforts by the Danish philologist, 1. L. Heiberg (1854-1928), are especially significant. Beginning with his doctoral dissertation, Quaestiones Archimedeae (Copen hagen, 1879), Heiberg produced an astonishing series of editions and critical studies that remain the foundation of scholarship on Greek mathematical 4 science. For comprehensiveness and accuracy, his editions are exemplary. In his textual studies, as also in the prolegomena to his editions, he carefully described the extant evidence, organized the manuscripts into stemmata, and drew out the implications for the state of the text. 5 With regard to his Archimedean work, Heiberg sometimes betrayed signs of the philologist's occupational disease - the tendency to rewrite a text deemed on subjective grounds to be unworthy. 6 But he did so less often than his prominent 7 contemporaries, and not as to detract appreciably from the value of his editions. In examining textual questions bearing on the Archimedean corpus, he attempted to exploit as much as possible evidence from the ancient commentators, and in some instances from the medieval translations. It is here that opportunities abound for new work, extending, and in some instances superseding, Heiberg's findings. For at his time the availability of the medieval materials was limited. In recent years Marshall Clagett has completed a mammoth critical edition of the medieval Latin tradition of Archimedes,8 while the bibliographical instruments for the Arabic tradition are in good order thanks to the work of Fuat Sezgin.
Download or read book A History of Analysis written by Hans Niels Jahnke and published by American Mathematical Soc.. This book was released on 2003 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis as an independent subject was created as part of the scientific revolution in the seventeenth century. Kepler, Galileo, Descartes, Fermat, Huygens, Newton, and Leibniz, to name but a few, contributed to its genesis. Since the end of the seventeenth century, the historical progress of mathematical analysis has displayed unique vitality and momentum. No other mathematical field has so profoundly influenced the development of modern scientific thinking. Describing this multidimensional historical development requires an in-depth discussion which includes a reconstruction of general trends and an examination of the specific problems. This volume is designed as a collective work of authors who are proven experts in the history of mathematics. It clarifies the conceptual change that analysis underwent during its development while elucidating the influence of specific applications and describing the relevance of biographical and philosophical backgrounds. The first ten chapters of the book outline chronological development and the last three chapters survey the history of differential equations, the calculus of variations, and functional analysis. Special features are a separate chapter on the development of the theory of complex functions in the nineteenth century and two chapters on the influence of physics on analysis. One is about the origins of analytical mechanics, and one treats the development of boundary-value problems of mathematical physics (especially potential theory) in the nineteenth century. The book presents an accurate and very readable account of the history of analysis. Each chapter provides a comprehensive bibliography. Mathematical examples have been carefully chosen so that readers with a modest background in mathematics can follow them. It is suitable for mathematical historians and a general mathematical audience.
Download or read book Apollonius of Perga s Conica written by Michael Fried and published by BRILL. This book was released on 2017-09-18 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a historically sensitive analysis and interpretation of Apollonius of Perga's Conica, one of the greatest works of Hellenistic mathematics. It provides a long overdue alternative to H. G. Zeuthen's Die Lehre von den Kogelschnitten im Altertum.
Download or read book Using the Mathematics Literature written by Kristine K. Fowler and published by CRC Press. This book was released on 2004-05-25 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.
Download or read book The History of Mathematical Proof in Ancient Traditions written by Karine Chemla and published by Cambridge University Press. This book was released on 2012-07-05 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.
Download or read book Exploring Classical Greek Construction Problems with Interactive Geometry Software written by Ad Meskens and published by Birkhäuser. This book was released on 2017-02-02 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the classical Greek construction problems are explored in a didactical, enquiry based fashion using Interactive Geometry Software (IGS). The book traces the history of these problems, stating them in modern terminology. By focusing on constructions and the use of IGS the reader is confronted with the same problems that ancient mathematicians once faced. The reader can step into the footsteps of Euclid, Viète and Cusanus amongst others and then by experimenting and discovering geometric relationships far exceed their accomplishments. Exploring these problems with the neusis-method lets him discover a class of interesting curves. By experimenting he will gain a deeper understanding of how mathematics is created. More than 100 exercises guide him through methods which were developed to try and solve the problems. The exercises are at the level of undergraduate students and only require knowledge of elementary Euclidean geometry and pre-calculus algebra. It is especially well-suited for those students who are thinking of becoming a mathematics teacher and for mathematics teachers.
Download or read book Classics in the History of Greek Mathematics written by Jean Christianidis and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: The twentieth century is the period during which the history of Greek mathematics reached its greatest acme. Indeed, it is by no means exaggerated to say that Greek mathematics represents the unique field from the wider domain of the general history of science which was included in the research agenda of so many and so distinguished scholars, from so varied scientific communities (historians of science, historians of philosophy, mathematicians, philologists, philosophers of science, archeologists etc. ), while new scholarship of the highest quality continues to be produced. This volume includes 19 classic papers on the history of Greek mathematics that were published during the entire 20th century and affected significantly the state of the art of this field. It is divided into six self-contained sections, each one with its own editor, who had the responsibility for the selection of the papers that are republished in the section, and who wrote the introduction of the section. It constitutes a kind of a Reader book which is today, one century after the first publications of Tannery, Zeuthen, Heath and the other outstanding figures of the end of the 19th and the beg- ning of 20th century, rather timely in many respects.
Download or read book The Cambridge History of Science Volume 3 Early Modern Science written by David C. Lindberg and published by Cambridge University Press. This book was released on 2003 with total page 833 pages. Available in PDF, EPUB and Kindle. Book excerpt: An account of European knowledge of the natural world, c.1500-1700.
Download or read book The Analytic Turn written by Michael Beaney and published by Routledge. This book was released on 2010-12-22 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection, with contributions from leading philosophers, places analytic philosophy in a broader context comparing it with the methodology of its most important rival tradition in twentieth-century philosophy--phenomenology, whose development parallels the development of analytic philosophy in many ways. The Analytic Turn will be of great interest to historians of philosophy generally, analytic philosophers, and phenomenologists.
Download or read book History of Mathematics written by Craig Smorynski and published by Springer Science & Business Media. This book was released on 2007-12-03 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: General textbooks, attempting to cover three thousand or so years of mathematical history, must necessarily oversimplify just about everything, the practice of which can scarcely promote a critical approach to the subject. To counter this, History of Mathematics offers deeper coverage of key select topics, providing students with material that could encourage more critical thinking. It also includes the proofs of important results which are typically neglected in the modern history of mathematics curriculum.
Download or read book Reader s Guide to the History of Science written by Arne Hessenbruch and published by Routledge. This book was released on 2013-12-16 with total page 965 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Reader's Guide to the History of Science looks at the literature of science in some 550 entries on individuals (Einstein), institutions and disciplines (Mathematics), general themes (Romantic Science) and central concepts (Paradigm and Fact). The history of science is construed widely to include the history of medicine and technology as is reflected in the range of disciplines from which the international team of 200 contributors are drawn.
Download or read book Oxford Studies in Ancient Philosophy Volume 53 written by Victor Caston and published by Oxford University Press. This book was released on 2017-12-08 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Oxford Studies in Ancient Philosophy is a volume of original articles on all aspects of ancient philosophy. The articles may be of substantial length, and include critical notices of major books. OSAP is now published twice yearly, in both hardback and paperback. "'Have you seen the latest OSAP?' is what scholars of ancient philosophy say to each other when they meet in corridors or on coffee breaks. Whether you work on Plato or Aristotle, on Presocratics or sophists, on Stoics, Epicureans, or Sceptics, on Roman philosophers or Greek Neoplatonists, you are liable to find OSAP articles now dominant in the bibliography of much serious published work in your particular subject: not safe to miss." - Malcolm Schofield, Cambridge University "OSAP was founded to provide a place for long pieces on major issues in ancient philosophy. In the years since, it has fulfilled this role with great success, over and over again publishing groundbreaking papers on what seemed to be familiar topics and others surveying new ground to break. It represents brilliantly the vigour - and the increasingly broad scope - of scholarship in ancient philosophy, and shows us all how the subject should flourish." - M.M. McCabe, King's College London
Download or read book Using History to Teach Mathematics written by Victor J. Katz and published by Cambridge University Press. This book was released on 2000-09-21 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines how the history of mathematics can find application in the teaching of mathematics itself.
Download or read book The History of Mathematics A Source Based Approach written by June Barrow-Green and published by American Mathematical Society. This book was released on 2021-12-17 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the first volume of the two-volume set, takes readers from the beginning of counting in prehistory to 1600 and the threshold of the discovery of calculus. It is notable for the extensive engagement with original—primary and secondary—source material. The coverage is worldwide, and embraces developments, including education, in Egypt, Mesopotamia, Greece, China, India, the Islamic world and Europe. The emphasis on astronomy and its historical relationship to mathematics is new, and the presentation of every topic is informed by the most recent scholarship in the field. The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.
