Pappus of Alexandria: Book 4 of the Collection
Pappus of Alexandria: Book 4 of the Collection

Author: Heike Sefrin-Weis

Publisher: Springer Science & Business Media

Published: 2010-04-06

Total Pages: 347

ISBN-13: 1849960054

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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.

Pappus of Alexandria Book 7 of the Collection
Pappus of Alexandria Book 7 of the Collection

Author: Alexander Jones

Publisher: Springer Science & Business Media

Published: 2013-11-09

Total Pages: 764

ISBN-13: 1461249082

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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.

Pappus of Alexandria and the Mathematics of Late Antiquity
Pappus of Alexandria and the Mathematics of Late Antiquity

Author: Serafina Cuomo

Publisher: Cambridge University Press

Published: 2007-06-21

Total Pages: 252

ISBN-13: 9780521036894

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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.

Making up Numbers: A History of Invention in Mathematics
Making up Numbers: A History of Invention in Mathematics

Author: Ekkehard Kopp

Publisher: Open Book Publishers

Published: 2020-10-23

Total Pages: 280

ISBN-13: 1800640978

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Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.

Ptolemy's Almagest
Ptolemy's Almagest

Author: Ptolemy

Publisher: Princeton University Press

Published: 1998-11-08

Total Pages: 712

ISBN-13: 0691002606

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Ptolemy's Almagest is one of the most influential scientific works in history. A masterpiece of technical exposition, it was the basic textbook of astronomy for more than a thousand years, and still is the main source for our knowledge of ancient astronomy. This translation, based on the standard Greek text of Heiberg, makes the work accessible to English readers in an intelligible and reliable form. It contains numerous corrections derived from medieval Arabic translations and extensive footnotes that take account of the great progress in understanding the work made in this century, due to the discovery of Babylonian records and other researches. It is designed to stand by itself as an interpretation of the original, but it will also be useful as an aid to reading the Greek text.

Ancient Mathematics
Ancient Mathematics

Author: Serafina Cuomo

Publisher: Routledge

Published: 2005-08-19

Total Pages: 519

ISBN-13: 1134710186

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The theorem of Pythagoras, Euclid's "Elements", Archimedes' method to find the volume of a sphere: all parts of the invaluable legacy of ancient mathematics. But ancient mathematics was also about counting and measuring, surveying land and attributing mystical significance to the number six. This volume offers the first accessible survey of the discipline in all its variety and diversity of practices. The period covered ranges from the fifth century BC to the sixth century AD, with the focus on the Mediterranean region. Topics include: * mathematics and politics in classical Greece * the formation of mathematical traditions * the self-image of mathematicians in the Graeco-Roman period * mathematics and Christianity * and the use of the mathematical past in late antiquity.

Geometry
Geometry

Author: John Tabak

Publisher: Infobase Publishing

Published: 2014-05-14

Total Pages: 241

ISBN-13: 0816068763

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Greek ideas about geometry, straight-edge and compass constructions, and the nature of mathematical proof dominated mathematical thought for about 2,000 years.

Sourcebook in the Mathematics of Ancient Greece and the Eastern Mediterranean
Sourcebook in the Mathematics of Ancient Greece and the Eastern Mediterranean

Author: Victor J. Katz

Publisher: Princeton University Press

Published: 2024-09-17

Total Pages: 720

ISBN-13: 0691202818

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"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"--