An invaluable reference book on the mathematics of Greek antiquity Euclid, Archimedes, and Apollonius are familiar names to many of us, and their contributions have shaped mathematical practice up to modern times. Yet the mathematical activity of Greek antiquity extended far beyond their achievements and was furthered by diverse individuals in different contexts. Sourcebook in the Mathematics of Ancient Greece and the Eastern Mediterranean brings together an extensive collection of primary source materials that document the extraordinary breadth of mathematical ideas developed in the Eastern Mediterranean from 500 BCE to 500 CE, a millennium in which Greek cultural influence spanned the ancient world. Weaving together ancient commentaries with the works themselves, Victor Katz and Clemency Montelle present a wealth of newly translated texts along with sources difficult to find elsewhere, from writings by the great mathematical thinkers of Greek antiquity to those by practitioners who used mathematics in everyday life. This comprehensive and wide-ranging sourcebook includes lesser-known authors who made critical contributions, sometimes in languages other than Greek, as well as accounts of technical instrumentation, papyri by anonymous authors designed for teaching purposes, and evidence of hand computations and numerical tables. An essential resource for anyone interested in the mathematical achievements of this remarkable intellectual culture, Sourcebook in the Mathematics of Ancient Greece and the Eastern Mediterranean encompasses disciplines that illustrate the important role of mathematics in ancient Greek society more broadly, from astronomy, music, and optics to philosophy, literature, and theater.

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.

Greek civilization and identity crystallized not when Greeks were close together but when they came to be far apart. This book looks at how Greek the network shaped a small Greek world where separation is measured by degrees of contact rather than by physical dimensions.

New research that transforms how to understand food and eating in literature Meredith J. C. Warren identifies and defines a new genre in ancient texts that she terms hierophagy, a specific type of transformational eating where otherworldly things are consumed. Multiple ancient Mediterranean, Jewish, and Christian texts represent the ramifications of consuming otherworldly food, ramifications that were understood across religious boundaries. Reading ancient texts through the lens of hierophagy helps scholars and students interpret difficult passages in Joseph and Aseneth, 4 Ezra, Revelation 10, and the Persephone myths, among others. Features: Exploration of how ancient literature relies on bending, challenging, inverting, and parodying cultural norms in order to make meaning out of genres Analysis of hierophagy as social action that articulates how patterns of communication across texts and cultures emerge and diverge A new understanding of previously confounding scenes of literary eating

In recent decades it has become obvious that mathematics has always been a worldwide activity. But this is the first book to provide a substantial collection of English translations of key mathematical texts from the five most important ancient and medieval non-Western mathematical cultures, and to put them into full historical and mathematical context. The Mathematics of Egypt, Mesopotamia, China, India, and Islam gives English readers a firsthand understanding and appreciation of these cultures' important contributions to world mathematics. The five section authors--Annette Imhausen (Egypt), Eleanor Robson (Mesopotamia), Joseph Dauben (China), Kim Plofker (India), and J. Lennart Berggren (Islam)--are experts in their fields. Each author has selected key texts and in many cases provided new translations. The authors have also written substantial section introductions that give an overview of each mathematical culture and explanatory notes that put each selection into context. This authoritative commentary allows readers to understand the sometimes unfamiliar mathematics of these civilizations and the purpose and significance of each text. Addressing a critical gap in the mathematics literature in English, this book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom.

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.

A survey of ancient Egyptian mathematics across three thousand years Mathematics in Ancient Egypt traces the development of Egyptian mathematics, from the end of the fourth millennium BC—and the earliest hints of writing and number notation—to the end of the pharaonic period in Greco-Roman times. Drawing from mathematical texts, architectural drawings, administrative documents, and other sources, Annette Imhausen surveys three thousand years of Egyptian history to present an integrated picture of theoretical mathematics in relation to the daily practices of Egyptian life and social structures. Imhausen shows that from the earliest beginnings, pharaonic civilization used numerical techniques to efficiently control and use their material resources and labor. Even during the Old Kingdom, a variety of metrological systems had already been devised. By the Middle Kingdom, procedures had been established to teach mathematical techniques to scribes in order to make them proficient administrators for their king. Imhausen looks at counterparts to the notation of zero, suggests an explanation for the evolution of unit fractions, and analyzes concepts of arithmetic techniques. She draws connections and comparisons to Mesopotamian mathematics, examines which individuals in Egyptian society held mathematical knowledge, and considers which scribes were trained in mathematical ideas and why. Of interest to historians of mathematics, mathematicians, Egyptologists, and all those curious about Egyptian culture, Mathematics in Ancient Egypt sheds new light on a civilization's unique mathematical evolution.

The metaphor of the palimpsest has been increasingly invoked to conceptualize cities with deep, living pasts. This volume seeks to think through, and beyond, the logic of the palimpsest, asking whether this fashionable trope slyly forces us to see contradiction where local inhabitants saw (and see) none, to impose distinctions that satisfy our own assumptions about historical periodization and cultural practice, but which bear little relation to the experience of ancient, medieval or early modern persons. Spanning the period from Constantine’s foundation of a New Rome in the fourth century to the contemporary aftermath of the Lebanese civil war, this book integrates perspectives from scholars typically separated by the disciplinary boundaries of late antique, Islamic, medieval, Byzantine, Ottoman and modern Middle Eastern studies, but whose work is united by their study of a region characterized by resilience rather than rupture. The volume includes an introduction and eighteen contributions from historians, archaeologists and art historians who explore the historical and cultural complexity of eastern Mediterranean cities. The authors highlight the effects of the multiple antiquities imagined and experienced by persons and groups who for generations made these cities home, and also by travelers and other observers who passed through them. The independent case studies are bound together by a shared concern to understand the many ways in which the cities’ pasts live on in their presents.

The triangle described in this book hardly exists in reality. Tripartite relations among Greece, Turkey and Israel, if discernible at all, revolve around the crises which constantly beset the Middle East and the East Mediterranean. Even then, it is not a triangle per se: the three states seldom pursue a common policy. This book describes the various bones of contention among the three in all possible spheres—political, economic, religious, etc.—as well as the areas and periods of understanding among them. What emerges quite clearly is the fact that any show of unanimity among Ankara, Athens and Jerusalem was, in the past, likely to rest more on some temporary community of interest than on any inherent belief in the need for unanimity.