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.

Mathematics has stood as a bridge between the Humanities and the Sciences since the days of classical antiquity. For Plato, mathematics was evidence of Being in the midst of Becoming, garden variety evidence apparent even to small children and the unphilosophical, and therefore of the highest educational significance. In the great central similes of The Republic it is the touchstone ofintelligibility for discourse, and in the Timaeus it provides in an oddly literal sense the framework of nature, insuring the intelligibility ofthe material world. For Descartes, mathematical ideas had a clarity and distinctness akin to the idea of God, as the fifth of the Meditations makes especially clear. Cartesian mathematicals are constructions as well as objects envisioned by the soul; in the Principles, the work ofthe physicist who provides a quantified account ofthe machines of nature hovers between description and constitution. For Kant, mathematics reveals the possibility of universal and necessary knowledge that is neither the logical unpacking ofconcepts nor the record of perceptual experience. In the Critique ofPure Reason, mathematics is one of the transcendental instruments the human mind uses to apprehend nature, and by apprehending to construct it under the universal and necessary lawsofNewtonian mechanics.

Explores the lifestyles of ancient Mesopotamia, including the civilization, rulers and leaders, economics, and more.

In antiquity, the expertise of the Babylonians in matters of the heavens was legendary and the roots of both western astronomy and astrology are traceable in cuneiform tablets going back to the second and first millennia BC. The Heavenly Writing, first publsiehd in 2004, discusses the place of Babylonian celestial divination, horoscopy, and astronomy in Mesopotamian intellectual culture. Focusing chiefly on celestial divination and horoscopes, it traces the emergence of personal astrology from the tradition of celestial divination and the use of astronomical methods in horoscopes. It further takes up the historiographical and philosophical issue of the nature of these Mesopotamian 'celestial sciences' by examining elements traditionally of concern to the philosophy of science, without sacrificing the ancient methods, goals, and interests to a modern image of science. This book will be of particular interest to those concerned with the early history of science.

Presents the emerging field of ethnomathematics from a critical perspective, challenging particular ways in which Eurocentrism permeates mathematics education and mathematics in general.

When it was first published in 1992, The Beginnings of Western Science was lauded as the first successful attempt ever to present a unified account of both ancient and medieval science in a single volume. Chronicling the development of scientific ideas, practices, and institutions from pre-Socratic Greek philosophy to late-Medieval scholasticism, David C. Lindberg surveyed all the most important themes in the history of science, including developments in cosmology, astronomy, mechanics, optics, alchemy, natural history, and medicine. In addition, he offered an illuminating account of the transmission of Greek science to medieval Islam and subsequently to medieval Europe. The Beginnings of Western Science was, and remains, a landmark in the history of science, shaping the way students and scholars understand these critically formative periods of scientific development. It reemerges here in a second edition that includes revisions on nearly every page, as well as several sections that have been completely rewritten. For example, the section on Islamic science has been thoroughly retooled to reveal the magnitude and sophistication of medieval Muslim scientific achievement. And the book now reflects a sharper awareness of the importance of Mesopotamian science for the development of Greek astronomy. In all, the second edition of The Beginnings of Western Science captures the current state of our understanding of more than two millennia of science and promises to continue to inspire both students and general readers.

Discover a different way to see classical civilization in this collection of ancient Greek and Roman texts on magic and the occult. Magic, miracles, daemonology, divination, astrology, and alchemy were the arcana mundi, the “secrets of the universe,” of the ancient Greeks and Romans. In this path-breaking collection of Greek and Roman writings on magic and the occult, Georg Luck provides a comprehensive sourcebook and introduction to magic as it was practiced by witches and sorcerers, magi and astrologers, in the Greek and Roman worlds. In this new edition, Luck has gathered and translated 130 ancient texts dating from the eighth century BCE through the fourth century CE. Thoroughly revised, this volume offers several new elements: a comprehensive general introduction, an epilogue discussing the persistence of ancient magic into the early Christian and Byzantine eras, and an appendix on the use of mind-altering substances in occult practices. Also added is an extensive glossary of Greek and Latin magical terms. In Arcana Mundi Georg Luck presents a fascinating?and at times startling?alternative vision of the ancient world. “For a long time it was fashionable to ignore the darker and, to us, perhaps, uncomfortable aspects of everyday life in Greece and Rome,” Luck has written. “But we can no longer idealize the Greeks with their “artistic genius” and the Romans with their “sober realism.” Magic and witchcraft, the fear of daemons and ghosts, the wish to manipulate invisible powers?all of this was very much a part of their lives.” “An excellent translation of ancient texts on the subject, but it’s a lot more than that. It’s a glimpse into the minds of the everyday people of the times and what made them turn, what made them stop, what made them look over their shoulders.” —Courier-Gazette,(Rockland, Maine) “No one currently at work in ancient magic or related fields can remotely compare with Luck for the breadth and profundity of his knowledge of the literary texts . . . or for the humility and lightness of touch with which he conveys his scholarship.” —Daniel Ogden, author of Magic, Witchcraft, and Ghosts in the Greek and Roman Worlds