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Author: Alexander Jones
Publisher: Springer Science & Business Media
ISBN: 1461249082
Category : Mathematics
Languages : en
Pages : 764
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Book Description
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.
Author: Alexander Jones
Publisher: Springer Science & Business Media
ISBN: 1461249082
Category : Mathematics
Languages : en
Pages : 764
Get Book Here
Book Description
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.
Author: Serafina Cuomo
Publisher: Cambridge University Press
ISBN: 9780521036894
Category : Mathematics
Languages : en
Pages : 252
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Book Description
This book is at once an analytical study of one of the most important mathematical texts of antiquity, the Mathematical Collection of the fourth-century AD mathematician Pappus of Alexandria, and also an examination of the work's wider cultural setting. An important first chapter looks at the mathematicians of the period and how mathematics was perceived by people at large. The central chapters of the book analyse sections of the Collection, identifying features typical of Pappus's mathematical practice. The final chapter draws together the various threads and presents a fuller description of Pappus's mathematical 'agenda'. This is one of few books to deal extensively with the mathematics of Late Antiquity. It sees Pappus's text as part of a wider context and relates it to other contemporary cultural practices and opens avenues to research into the public understanding of mathematics and mathematical disciplines in antiquity.
Author: Heike Sefrin-Weis
Publisher: Springer Science & Business Media
ISBN: 1849960054
Category : Mathematics
Languages : en
Pages : 347
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Book Description
Although not so well known today, Book 4 of Pappus’ Collection is one of the most important and influential mathematical texts from antiquity. The mathematical vignettes form a portrait of mathematics during the Hellenistic "Golden Age", illustrating central problems – for example, squaring the circle; doubling the cube; and trisecting an angle – varying solution strategies, and the different mathematical styles within ancient geometry. This volume provides an English translation of Collection 4, in full, for the first time, including: a new edition of the Greek text, based on a fresh transcription from the main manuscript and offering an alternative to Hultsch’s standard edition, notes to facilitate understanding of the steps in the mathematical argument, a commentary highlighting aspects of the work that have so far been neglected, and supporting the reconstruction of a coherent plan and vision within the work, bibliographical references for further study.
Author: Victor J. Katz
Publisher: Princeton University Press
ISBN: 0691202818
Category : Mathematics
Languages : en
Pages : 720
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Book Description
"In recent decades, there has been extensive research on Greek mathematics that has considerably enlarged the scope of this area of inquiry. Traditionally, "Greek mathematics" has referred to the axiomatic work of Archimedes, Apollonius, and others in the first three centuries BCE. However, there is a wide body of mathematical work that appeared in the eastern Mediterranean during the time it was under Greek influence (from approximately 400 BCE to 600 CE), which remains under-explored in the existing scholarship. This sourcebook provides an updated look at Greek mathematics, bringing together classic Greek texts with material from lesser-known authors, as well as newly uncovered texts that have been omitted in previous scholarship. The book adopts a broad scope in defining mathematical practice, and as such, includes fields such as music, optics, and architecture. It includes important sources written in languages other than Greek in the eastern Mediterranean area during the period from 400 BCE to 600 CE, which show some influence from Greek culture. It also includes passages that highlight the important role mathematics played in philosophy, pedagogy, and popular culture. The book is organized topically; chapters include arithmetic, plane geometry, astronomy, and philosophy, literature, and education. Within each chapter, the (translated) texts are organized chronologically. The book weaves together ancient commentary on classic Greek works with the works themselves to show how the understanding of mathematical ideas changed over the centuries"--
Author: Juval Portugali
Publisher: Springer Science & Business Media
ISBN: 0585334854
Category : Computers
Languages : en
Pages : 365
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Book Description
and processes which are exclusive to humans in their encoding, storing, decoding and retrieving spatial knowledge for various tasks. The authors present and discuss connectionist models of cognitive maps which are based on local representation, versus models which are based on distributed representation, as well as connectionist models concerning language and spatial relations. As is well known, Gibson's (1979) ecological approach suggests a view on cognition which is diametrically different from the classical main stream view: perception (and thus cognition) is direct, immediate and needs no internal information processing, and is thus essentially an external process of interaction between an organism and its external environment. The chapter by Harry Heft introduces J. J. Gibson's ecological approach and its implication to the construction of cognitive maps in general and to the issue of wayfinding in particular. According to Heft, main stream cognitive sciences are essentially Cartesian in nature and have not as yet internalized the implications of Darwin's theory of evolution. Gibson, in his ecological approach, has tried to do exactly this. The author introduces the basic terminology of the ecological approach and relates its various notions, in particular optic flow, nested hierarchy and affordances, to navigation and the way routes and places in the environment are learned.
Author: Gerald J. Toomer
Publisher: Springer Science & Business Media
ISBN: 1461389852
Category : Mathematics
Languages : en
Pages : 978
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Book Description
With the publication of this book I discharge a debt which our era has long owed to the memory of a great mathematician of antiquity: to pub lish the /llost books" of the Conics of Apollonius in the form which is the closest we have to the original, the Arabic version of the Banu Musil. Un til now this has been accessible only in Halley's Latin translation of 1710 (and translations into other languages entirely dependent on that). While I yield to none in my admiration for Halley's edition of the Conics, it is far from satisfying the requirements of modern scholarship. In particular, it does not contain the Arabic text. I hope that the present edition will not only remedy those deficiencies, but will also serve as a foundation for the study of the influence of the Conics in the medieval Islamic world. I acknowledge with gratitude the help of a number of institutions and people. The John Simon Guggenheim Memorial Foundation, by the award of one of its Fellowships for 1985-86, enabled me to devote an unbroken year to this project, and to consult essential material in the Bodleian Li brary, Oxford, and the Bibliotheque Nationale, Paris. Corpus Christi Col lege, Cambridge, appointed me to a Visiting Fellowship in Trinity Term, 1988, which allowed me to make good use of the rich resources of both the University Library, Cambridge, and the Bodleian Library.
Author: Paul Keyser
Publisher: Oxford University Press
ISBN: 0190878835
Category : Literary Collections
Languages : en
Pages : 1200
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Book Description
With a focus on science in the ancient societies of Greece and Rome, including glimpses into Egypt, Mesopotamia, India and China, The Oxford Handbook of Science and Medicine in the Classical World offers an in depth synthesis of science and medicine circa 650 BCE to 650 CE. The Handbook comprises five sections, each with a specific focus on ancient science and medicine. The second section covers the early Greek era, up through Plato and the mid-fourth century bce. The third section covers the long Hellenistic era, from Aristotle through the end of the Roman Republic, acknowledging that the political shift does not mark a sharp intellectual break. The fourth section covers the Roman era from the late Republic through the transition to Late Antiquity. The final section covers the era of Late Antiquity, including the early Byzantine centuries. The Handbook provides through each of its approximately four dozen essays, a synthesis and synopsis of the concepts and models of the various ancient natural sciences, covering the early Greek era through the fall of the Roman Republic, including essays that explore topics such as music theory, ancient philosophers, astrology, and alchemy. The Oxford Handbook of Science and Medicine in the Classical World guides the reader to further exploration of the concepts and models of the ancient sciences, how they evolved and changed over time, and how they relate to one another and to their antecedents. There are a total of four dozen or so topical essays in the five sections, each of which takes as its focus the primary texts, explaining what is now known as well as indicating what future generations of scholars may come to know. Contributors suggest the ranges of scholarly disagreements and have been free to advocate their own positions. Readers are led into further literature (both primary and secondary) through the comprehensive and extensive bibliographies provided with each chapter.
Author: Joyce van Leeuwen
Publisher: Springer
ISBN: 3319259253
Category : Literary Criticism
Languages : en
Pages : 259
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Book Description
This book examines the transmission processes of the Aristotelian Mechanics. It does so to enable readers to appreciate the value of the treatise based on solid knowledge of the principles of the text. In addition, the book’s critical examination helps clear up many of the current misunderstandings about the transmission of the text and the diagrams. The first part of the book sets out the Greek manuscript tradition of the Mechanics, resulting in a newly established stemma codicum that illustrates the affiliations of the manuscripts. This research has led to new insights into the transmission of the treatise, most importantly, it also demonstrates an urgent need for a new text. A first critical edition of the diagrams contained in the Greek manuscripts of the treatise is also presented. These diagrams are not only significant for a reconstruction of the text but can also be considered as a commentary on the text. Diagrams are thus revealed to be a powerful tool in studying processes of the transfer and transformation of knowledge. This becomes especially relevant when the manuscript diagrams are compared with those in the printed editions and in commentaries from the early modern period. The final part of the book shows that these early modern diagrams and images reflect the altered scope of the mechanical discipline in the sixteenth century.
Author: J.R. Brown
Publisher: Springer Science & Business Media
ISBN: 9400923279
Category : Science
Languages : en
Pages : 654
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Book Description
The best philosophy of science during the last generation has been highly historical; and the best history of science, highly philosophical. No one has better exemplified this intimate relationship between history and philosophy than has Robert E. Butts in his work. Through out his numerous writings, science, its philosophy, and its history have been treated as a seamless web. The result has been a body of work that is sensitive in its conception, ambitious in its scope, and illuminat ing in its execution. Not only has his work opened new paths of inquiry, but his enthusiasm for the discipline, his encouragement of others (particularly students and younger colleagues), and his tireless efforts to build an international community of scholars, have stimulated the growth of HPS throughout Europe and North America. Many of the essays in this volume reflect that influence. Our title, of course, is deliberately ambiguous. The essays herein are by colleagues and former students, all of us wishing to honour an intimate friend. Happy Birthday, Bob! IX INTRODUCTION The essays herein cover a variety of concerns: from Descartes to reduction, from Galileo to gambling, from Freud's psychoanalysis to Kant's thing-in-itself. But under this diversity there is an approach common to them all. Things are largely done with a concern for and a sensitivity to historical matters (including contemporary history, of course).
Author: Edward J. Watts
Publisher: Oxford University Press
ISBN: 0190659149
Category : History
Languages : en
Pages : 225
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Book Description
A philosopher, mathematician, and martyr, Hypatia is one of antiquity's best known female intellectuals. During the sixteen centuries following her murder, by a mob of Christians, Hypatia has been remembered in books, poems, plays, paintings, and films as a victim of religious intolerance whose death symbolized the end of the Classical world. But Hypatia was a person before she was a symbol. Her great skill in mathematics and philosophy redefined the intellectual life of her home city of Alexandria. Her talent as a teacher enabled her to assemble a circle of dedicated male students. Her devotion to public service made her a force for peace and good government in a city that struggled to maintain trust and cooperation between pagans and Christians. Despite these successes, Hypatia fought countless small battles to live the public and intellectual life that she wanted. This book rediscovers the life Hypatia led, the unique challenges she faced as a woman who succeeded spectacularly in a man's world, and the tragic story of the events that led to her tragic murder.
