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This book contains a translation and study of ""Euclid's Phaenomena"", a work which once formed part of the mathematical training of astronomers from Central Asia to Western Europe. Included is an introduction that sets Euclid's geometry of the celestial sphere, and its application to the astronomy of his day, into its historical context for readers not already familiar with it. So no knowledge of astronomy or advanced mathematics is necessary for an understanding of the work. The book shows mathematical astronomy shortly before the invention of trigonometry, which allowed the calculation of exact results and the subsequent composition of ""Ptolemy's Almagest"".""The Phaenomena"" itself begins with an introduction (possibly not by Euclid) followed by eighteen propositions set out in geometrical style about how arcs of the zodiacal circle move across the sky. The astronomical application is to the small arc of that circle occupied by the Sun, but the Sun is not mentioned. This work and the (roughly) contemporaneous treatises of Autolycus and Aristarchos form a corpus of the oldest extant works on mathematical astronomy. Together with ""Euclid's Optics"", one has the beginnings of the history of science as an application of mathematics.
Biography of Greek mathematician Euclid describing the lasting influence he has had on the field of geometry.
"There does not seem to have been a book-length history of trigonometry in English before this fine book. Van Brummelen takes us from the unnamed Egyptians and Babylonians who created trigonometry to the subject's first few centuries in Europe. In between, he deftly traces how it was studied by the astronomers Hipparchus and Ptolemy in classical Greece, and later by a host of scholars in India and the Islamic world."--John H. Conway, coauthor of "The Book of Numbers" "This book is the first detailed history of trigonometry in more than half a century, and it far surpasses any earlier attempts. "The Mathematics of the Heavens and the Earth" is an extremely important contribution to scholarship. It will be the definitive history of trigonometry for years to come. There is nothing like this out there."--Victor J. Katz, professor emeritus, University of the District of Columbia "A pleasure to read. "The Mathematics of the Heavens and the Earth" is destined to become the standard reference on the history of trigonometry for the foreseeable future. Although other authors have attempted to tell the story, I know of no other book that has either the breadth or the depth of this one. Van Brummelen is one of the leading experts in the world on this subject."--Dennis Duke, Florida State University "Van Brummelen presents a history of trigonometry from the earliest times to the end of the sixteenth century. He has produced a work that rises to the highest standards of scholarship but never strays into pedantry. His extensive bibliography cites every work of consequence for the history of trigonometry, copious footnotes and diagrams illuminate the text, and reproductions from old printed works add interest and texture to the narrative."--J. Lennart Berggren, professor emeritus, Simon Fraser University "This book presents, for the first time in more than a century, a concise history of plane and spherical trigonometry, an important field within applied mathematics. It will appeal to a wide audience thanks to the pleasant style in which it is written, but at the same time it adheres to a very high scholarly standard."--Benno van Dalen, Ludwig Maximilians University, Munich
This book honors the career of historian of mathematics J.L. Berggren, his scholarship, and service to the broader community. The first part, of value to scholars, graduate students, and interested readers, is a survey of scholarship in the mathematical sciences in ancient Greece and medieval Islam. It consists of six articles (three by Berggren himself) covering research from the middle of the 20th century to the present. The remainder of the book contains studies by eminent scholars of the ancient and medieval mathematical sciences. They serve both as examples of the breadth of current approaches and topics, and as tributes to Berggren's interests by his friends and colleagues.
Der zweite Band des Handbuchs der griechischen Literatur der Antike umfaßt die Periode von 400 v. Chr. bis zur Zeitenwende. Er schließt in zweifacher Hinsicht eine wichtige Lücke im Handbuch der Altertumswissenschaften: Zum einen ist jener Band von Wilhelm Schmids und Otto Stählins Geschichte der griechischen Literatur, der die Literatur des größten Teils des 4. Jahrhunderts v. Chr. – Platon, Aristoteles, die klassische Rhetorik sowie die Geschichtsschreibung nach Thukydides und die Mittlere Komödie – enthalten sollte, nie erschienen, und zum anderen ist Band VII 2,1, der mit 320 v. Chr. einsetzt, in vielerlei Hinsicht überholt. Zahlreiche Papyrusfunde aus dem Sand Ägyptens haben zudem in den letzten 100 Jahren das Bild dieser Epoche entscheidend bereichert: Komödien Menanders, große Bruchstücke aus den Werken des Kallimachos oder auch – erst vor kurzem – Poseidipps Epigramme. Außerdem hat in der Forschung eine neue, methodisch und theoretisch begründete Betrachtung weiter Bereiche der Literatur nach 400 v. Chr. stattgefunden. Dies betrifft vor allem die hellenistische Dichtung und die Komödie nach Aristophanes, die auf der Basis neuer Ausgaben nun erst in ihrer Stellung in der Geschichte der griechischen Literatur angemessen gewürdigt werden können. Die Neubewertung kommt insbesondere der Fachliteratur zugute, die in diesem Band in einem umfassenden Kapitel in all ihren verschiedenen Aspekten dargestellt wird. Wie Band 1 des Handbuchs der griechischen Literatur ist auch Band 2 nach Gattungen und literarischen Formen gegliedert.

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