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Based on a series of lectures delivered at Cornell University in the fall of 1949, and since revised, this is the standard non-technical coverage of Egyptian and Babylonian mathematics and astronomy, and their transmission to the Hellenistic world. Entirely modern in its data and conclusions, it reveals the surprising sophistication of certain areas of early science, particularly Babylonian mathematics. After a discussion of the number systems used in the ancient Near East (contrasting the Egyptian method of additive computations with unit fractions and Babylonian place values), Dr. Neugebauer covers Babylonian tables for numerical computation, approximations of the square root of 2 (with implications that the Pythagorean Theorem was known more than a thousand years before Pythagoras), Pythagorean numbers, quadratic equations with two unknowns, special cases of logarithms and various other algebraic and geometric cases. Babylonian strength in algebraic and numerical work reveals a level of mathematical development in many aspects comparable to the mathematics of the early Renaissance in Europe. This is in contrast to the relatively primitive Egyptian mathematics. In the realm of astronomy, too, Dr. Neugebauer describes an unexpected sophistication, which is interpreted less as the result of millennia of observations (as used to be the interpretation) than as a competent mathematical apparatus. The transmission of this early science and its further development in Hellenistic times is also described. An Appendix discusses certain aspects of Greek astronomy and the indebtedness of the Copernican system to Ptolemaic and Islamic methods. Dr. Neugebauer has long enjoyed an international reputation as one of the foremost workers in the area of premodern science. Many of his discoveries have revolutionized earlier understandings. In this volume he presents a non-technical survey, with much material unique on this level, which can be read with great profit by all interested in the history of science or history of culture. 14 plates. 52 figures.
The Middle East is the birthplace of astronomy and the centre for its development during the medieval period. In this brief introduction John Steele offers an intriguing insight into Middle Eastern achievements in astronomy and their profound influence on the rest of the world. Amongst other things, the book traces the Late Babylonians' ingenious schemes for modelling planetary motion. It also reveals how medieval Islamic advances in the study of the heavens, and the design of precise astronomical instruments, led to breakthroughs by Renaissance practitioners such as Copernicus and Kepler. An invaluable introduction to one of the oldest sciences in the world.
Setting Aside All Authority is an important account and analysis of seventeenth-century scientific arguments against the Copernican system. Christopher M. Graney challenges the long-standing ideas that opponents of the heliocentric ideas of Copernicus and Galileo were primarily motivated by religion or devotion to an outdated intellectual tradition, and that they were in continual retreat in the face of telescopic discoveries. Graney calls on newly translated works by anti-Copernican writers of the time to demonstrate that science, not religion, played an important, and arguably predominant, role in the opposition to the Copernican system. Anti-Copernicans, building on the work of the Danish astronomer Tycho Brahe, were in fact able to build an increasingly strong scientific case against the heliocentric system at least through the middle of the seventeenth century, several decades after the advent of the telescope. The scientific case reached its apogee, Graney argues, in the 1651 New Almagest of the Italian Jesuit astronomer Giovanni Battista Riccioli, who used detailed telescopic observations of stars to construct a powerful scientific argument against Copernicus. Setting Aside All Authority includes the first English translation of Monsignor Francesco Ingoli’s essay to Galileo (disputing the Copernican system on the eve of the Inquisition’s condemnation of it in 1616) and excerpts from Riccioli's reports regarding his experiments with falling bodies.
This monumental book traces the origins and development of mathematics in the ancient Middle East, from its earliest beginnings in the fourth millennium BCE to the end of indigenous intellectual culture in the second century BCE when cuneiform writing was gradually abandoned. Eleanor Robson offers a history like no other, examining ancient mathematics within its broader social, political, economic, and religious contexts, and showing that mathematics was not just an abstract discipline for elites but a key component in ordering society and understanding the world. The region of modern-day Iraq is uniquely rich in evidence for ancient mathematics because its prehistoric inhabitants wrote on clay tablets, many hundreds of thousands of which have been archaeologically excavated, deciphered, and translated. Drawing from these and a wealth of other textual and archaeological evidence, Robson gives an extraordinarily detailed picture of how mathematical ideas and practices were conceived, used, and taught during this period. She challenges the prevailing view that they were merely the simplistic precursors of classical Greek mathematics, and explains how the prevailing view came to be. Robson reveals the true sophistication and beauty of ancient Middle Eastern mathematics as it evolved over three thousand years, from the earliest beginnings of recorded accounting to complex mathematical astronomy. Every chapter provides detailed information on sources, and the book includes an appendix on all mathematical cuneiform tablets published before 2007.
Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This sourcebook presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time. Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments proving results on the conchoid—a curve previously unknown in medieval Europe; Levi ben Gershon’s use of mathematical induction in combinatorial proofs; Al-Mu’taman Ibn Hūd’s extensive survey of mathematics, which included proofs of Heron’s Theorem and Ceva’s Theorem; and Muhyī al-Dīn al-Maghribī’s interesting proof of Euclid’s parallel postulate. The book includes a general introduction, section introductions, footnotes, and references. The Sourcebook in the Mathematics of Medieval Europe and North Africa will be indispensable to anyone seeking out the important historical sources of premodern mathematics.
Was Western civilization founded by ancient Egyptians and Phoenicians? Can the ancient Egyptians usefully be called black? Did the ancient Greeks borrow religion, science, and philosophy from the Egyptians and Phoenicians? Have scholars ignored the Afroasiatic roots of Western civilization as a result of racism and anti-Semitism? In this collection of twenty essays, leading scholars in a broad range of disciplines confront the claims made by Martin Bernal in Black Athena: The Afroasiatic Roots of Classical Civilization. In that work, Bernal proposed a radical reinterpretation of the roots of classical civilization, contending that ancient Greek culture derived from Egypt and Phoenicia and that European scholars have been biased against the notion of Egyptian and Phoenician influence on Western civilization. The contributors to this volume argue that Bernal's claims are exaggerated and in many cases unjustified. Topics covered include race and physical anthropology; the question of an Egyptian invasion of Greece; the origins of Greek language, philosophy, and science; and racism and anti-Semitism in classical scholarship. In the conclusion to the volume, the editors propose an entirely new scholarly framework for understanding the relationship between the cultures of the ancient Near East and Greece and the origins of Western civilization. The contributors are: John Baines, professor of Egyptology, University of Oxford Kathryn A. Bard, assistant professor of archaeology, Boston University C. Loring Brace, professor of anthropology and curator of biological anthropology in the Museum of Anthropology, University of Michigan John E. Coleman, professor of classics, Cornell University Edith Hall, lecturer in classics, University of Reading, England Jay H. Jasanoff, Jacob Gould Schurman Professor of Linguistics, Cornell University Richard Jenkyns, fellow and tutor, Lady Margaret Hall, Oxford, and university lecturer in classics, University of Oxford Mary R. Lefkowitz, Andrew W. Mellon Professor in the Humanities, Wellesley College Mario Liverani, professor of ancient near eastern history, Universita di Roma, 'La Sapienza' Sarah P. Morris, professor of classics, University of California at Los Angeles Robert E. Norton, associate professor of German, Vassar College Alan Nussbaum, associate professor of classics, Cornell University David O'Connor, professor of Egyptology and curator in charge of the Egyptian section of the University Museum, University of Pennsylvania Robert Palter, Dana Professor Emeritus of the History of Science, Trinity College, Connecticut Guy MacLean Rogers, associate professor of Greek and Latin and history, Wellesley College Frank M. Snowden, Jr., professor of classics emeritus, Howard University Lawrence A. Tritle, associate professor of history, Loyola Marymount University Emily T. Vermeule, Samuel E. Zemurray, Jr., and Doris Zemurray Stone-Radcliffe Professor Emerita, Harvard University Frank J. Yurco, Egyptologist, Field Museum of Natural History and the University of Chicago
More than 200 rare scientific manuscripts, books, maps, amulets, and magical texts have been brought together from renowned collections in Europe, Canada, Israel, Great Britain, and the United States specifically for this exhibition. The most famous among these is a fragment from the Dead Sea Scrolls containing chapters 81 to 85 from the Book of Psalms: fragments from the scrolls have been in Canada on only two other occasions. The exhibition will have an Assyrian cuneiform tablet from the seventh century BCE that describes treatments for eye ailments, a first edition Copernicus, and several texts by Maimonides, including one with marginal notes by Martin Luther. Also featured, in a rare Latin translation, is an Arabic medical book written by a Jew, demonstrating the international and inter-faith nature of the medieval scientific endeavour.