L Irrationalit Dans Les Math Matiques Grecques Jusqu Euclide Volume 3
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L Irrationalit Dans Les Math Matiques Grecques Jusqu Euclide Volume 3
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Author : Maurice Caveing
language : fr
Publisher: Presses Univ. Septentrion
Release Date : 1998
L Irrationalit Dans Les Math Matiques Grecques Jusqu Euclide Volume 3 written by Maurice Caveing and has been published by Presses Univ. Septentrion this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
La découverte des grandeurs géométriques dites "incommensurables", que nous devons aux anciens Grecs, a été de grande conséquence dans l'histoire de la pensée. D'une part, elle a eu pour effet de détacher la notion de grandeur géométrique de ses modèles physiques, de l'autre elle a engagé la notion de nombre sur la voie d'un évolution qui aboutit, bien plus tard, à l'idée de nombre "sourds" ou "irrationels". Le fait, entouré de mystère, a passionné les historiens des sciences qui ont cru y voir - sans doute avec quelque excès - la première "crise" de l'histoire des mathématiques. Dès l'Antiquité cependant, il a entraîné une refonte de la notion de proportionnalité dont les Eléments d'Euclide donnent un exposé célèbre. Que s'est'il passé en réalité? C'est en quelque sorte l'archéologie de cette théorie à laquelle s'est livré l'auteur, à partir de textes antérieurs comme ceux de Platon, mais aussi des contextes scientifiques variés, à travers lesquels les mathématiciens ont été progressivement conduits à la certitude que la mesure des grandeurs ne peut se limiter à l'usage des nombres entiers ou fractionnaires. C'est la complexité de l'histoire du savoir qui ressort de l'étude ici présentée. Les philosophes furent ainsi amenés à prendre en compte ces bouleversements et à placer l'objet des mathématiques dans de pures idéalités, ou en tout cas dans des abstractions concevables par l'intellect seul, pour lesquelles le donné sensoriel enveloppait toujours le risque d'erreur. Le rationalisme philosophique trouvait là un de ses motifs majeurs. Cet ouvrage offre ainsi, sur un exemple précis et avec une vaste documentation, une analyse novatrice des relations à la fois fortes et subtiles unissant science et philosophie.
From China To Paris
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Author : Yvonne Dold-Samplonius
language : en
Publisher: Franz Steiner Verlag
Release Date : 2002
From China To Paris written by Yvonne Dold-Samplonius and has been published by Franz Steiner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
The reports of a conference of 11 scholars who began the task of examing together primary sources that might shed som elight on exactly how and in what fomrs mathematical problems, concepts, and techniques may have been transmitted between various civilizations, from antiquity down to the European Renaissance following more or less the legendary silk routes between China and Western Europe.
The Mathematical Writings Of Variste Galois
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Author : Évariste Galois
language : en
Publisher: European Mathematical Society
Release Date : 2011
The Mathematical Writings Of Variste Galois written by Évariste Galois and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Galois theory categories.
Before he died at the age of twenty, shot in a mysterious early-morning duel at the end of May 1832, Evariste Galois created mathematics that changed the direction of algebra. This book contains English translations of almost all the Galois material. The translations are presented alongside a new transcription of the original French and are enhanced by three levels of commentary. An introduction explains the context of Galois' work, the various publications in which it appears, and the vagaries of his manuscripts. Then there is a chapter in which the five mathematical articles published in his lifetime are reprinted. After that come the testamentary letter and the first memoir (in which Galois expounded on the ideas that led to Galois Theory), which are the most famous of the manuscripts. These are followed by the second memoir and other lesser known manuscripts. This book makes available to a wide mathematical and historical readership some of the most exciting mathematics of the first half of the nineteenth century, presented in its original form. The primary aim is to establish a text of what Galois wrote. The details of what he did, the proper evidence of his genius, deserve to be well understood and appreciated by mathematicians as well as historians of mathematics.
Diophantus Of Alexandria
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Author : Thomas L. Heath
language : en
Publisher: CUP Archive
Release Date : 1910
Diophantus Of Alexandria written by Thomas L. Heath and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1910 with Algebra categories.
Nonstandard Analysis
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Author : R. Lutz
language : en
Publisher: Springer
Release Date : 2006-11-14
Nonstandard Analysis written by R. Lutz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
From Cardano S Great Art To Lagrange S Reflections
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Author : Jacqueline A. Stedall
language : en
Publisher: European Mathematical Society
Release Date : 2011
From Cardano S Great Art To Lagrange S Reflections written by Jacqueline A. Stedall and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Algebra categories.
This book is an exploration of a claim made by Lagrange in the autumn of 1771 as he embarked upon his lengthy ``Reflexions sur la resolution algebrique des equations'': that there had been few advances in the algebraic solution of equations since the time of Cardano in the mid sixteenth century. That opinion has been shared by many later historians. The present study attempts to redress that view and to examine the intertwined developments in the theory of equations from Cardano to Lagrange. A similar historical exploration led Lagrange himself to insights that were to transform the entire nature and scope of algebra. Progress was not confined to any one country: at different times mathematicians in Italy, France, the Netherlands, England, Scotland, Russia, and Germany contributed to the discussion and to a gradual deepening of understanding. In particular, the national Academies of Berlin, St. Petersburg, and Paris in the eighteenth century were crucial in supporting informed mathematical communities and encouraging the wider dissemination of key ideas. This study therefore truly highlights the existence of a European mathematical heritage. The book is written in three parts. Part I offers an overview of the period from Cardano to Newton (1545 to 1707) and is arranged chronologically. Part II covers the period from Newton to Lagrange (1707 to 1771) and treats the material according to key themes. Part III is a brief account of the aftermath of the discoveries made in the 1770s. The book attempts throughout to capture the reality of mathematical discovery by inviting the reader to follow in the footsteps of the authors themselves, with as few changes as possible to the original notation and style of presentation.
Pangeometry
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Author : Nikolaĭ Ivanovich Lobachevskiĭ
language : en
Publisher: European Mathematical Society
Release Date : 2010
Pangeometry written by Nikolaĭ Ivanovich Lobachevskiĭ and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Geometry, Non-Euclidean categories.
Lobachevsky wrote Pangeometry in 1855, the year before his death. This memoir is a resume of his work on non-Euclidean geometry and its applications and can be considered his clearest account on the subject. It is also the conclusion of his life's work and the last attempt he made to acquire recognition. The treatise contains basic ideas of hyperbolic geometry, including the trigonometric formulae, the techniques of computation of arc length, of area and of volume, with concrete examples. It also deals with the applications of hyperbolic geometry to the computation of new definite integrals. The techniques are different from those found in most modern books on hyperbolic geometry since they do not use models. Besides its historical importance, Lobachevsky's Pangeometry is a beautiful work, written in a simple and condensed style. The material that it contains is still very alive, and reading this book will be most useful for researchers and for students in geometry and in the history of science. It can be used as a textbook, as a sourcebook, and as a repository of inspiration. The present edition provides the first complete English translation of Pangeometry available in print. It contains facsimiles of both the Russian and the French original versions. The translation is accompanied by notes, followed by a biography of Lobachevky and an extensive commentary.
Thomas Harriot S Doctrine Of Triangular Numbers
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Author : Janet Beery
language : en
Publisher: European Mathematical Society
Release Date : 2009
Thomas Harriot S Doctrine Of Triangular Numbers written by Janet Beery and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with History categories.
Thomas Harriot (1560-1621) was a mathematician and astronomer who founded the English school of algebra. He is known not only for his work in algebra and geometry but also as a prolific writer with wide-ranging interests in ballistics, navigation, and optics. (He discovered the sine law of refraction now known as Snell's law.) By about 1614, Harriot had developed finite difference interpolation methods for navigational tables. In 1618 (or slightly later) he composed a treatise entitled `De numeris triangularibus et inde de progressionibus arithmeticis, Magisteria magna', in which he derived symbolic interpolation formulae and showed how to use them. This treatise was never published and is here reproduced for the first time. Commentary has been added to help the reader follow Harriot's beautiful but almost completely nonverbal presentation. The introductory essay preceding the treatise gives an overview of the contents of the `Magisteria' and describes its influence on Harriot's contemporaries and successors over the next sixty years. Harriot's method was not superseded until Newton, apparently independently, made a similar discovery in the 1660s. The ideas in the `Magisteria' were spread primarily through personal communication and unpublished manuscripts, and so, quite apart from their intrinsic mathematical interest, their survival in England during the seventeenth century provides an important case study in the dissemination of mathematics through informal networks of friends and acquaintances.
The Development Of Greek Biography
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Author : Arnaldo Momigliano
language : en
Publisher: Harvard University Press
Release Date : 1993
The Development Of Greek Biography written by Arnaldo Momigliano and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Biography & Autobiography categories.
Arnaldo Momigliano traces the growth of ancient biography from the fifth century to the first century B.C. He asks new questions about the origins and development of Greek biography, and makes full use of new evidence uncovered in recent decades from papyri and other sources. By clarifying the social and intellectual implication of the fact that the Greeks kept biography and autobiography distinct from historiography, he contributes to an understanding of a basic dichotomy in the Western tradition of historical writing. The Development of Greek Biography is fully annotated, and includes a bibliography designed to serve as an introduction to the study of biography in general.
Selecta Diophantine Problems And Polynomials
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Author : Andrzej Schinzel
language : en
Publisher: European Mathematical Society
Release Date : 2007
Selecta Diophantine Problems And Polynomials written by Andrzej Schinzel and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Analyse diophantienne categories.