The ancient Greeks played a fundamental role in the history of mathematics and their ideas were reused and developed in subsequent periods all the way down to the scientific revolution and beyond. In this, the first complete history for a century. Reviel Netz offers a panoramic view of the rise and influence of Greek mathematics and its significance in world history. He explores the Near Eastern antecedents and the social and intellectual developments underlying the subject's beginnings in Greece in the fifth century BCE. He leads the reader through the proofs and arguments of key figures like Archytas, Euclid and Archimedes, and considers the totality of the Greek mathematical achievement which also includes, in addition to pure mathematics, such applied fields as optics, music, mechanics and, above all, astronomy. This is the story not only of a major historical development, but of some of the finest mathematics ever created.

This book represents a new departure in science studies: an analysis of a scientific style of writing, situating it within the context of the contemporary style of literature. Its philosophical significance is that it provides a novel way of making sense of the notion of a scientific style. For the first time, the Hellenistic mathematical corpus - one of the most substantial extant for the period - is placed centre-stage in the discussion of Hellenistic culture as a whole. Professor Netz argues that Hellenistic mathematical writings adopt a narrative strategy based on surprise, a compositional form based on a mosaic of apparently unrelated elements, and a carnivalesque profusion of detail. He further investigates how such stylistic preferences derive from, and throw light on, the style of Hellenistic poetry. This important book will be welcomed by all scholars of Hellenistic civilization as well as historians of ancient science and Western mathematics.

This book represents a new departure in science studies: an analysis of a scientific style of writing, situating it within the context of the contemporary style of literature. Its philosophical significance is that it provides a novel way of making sense of the notion of a scientific style. For the first time, the Hellenistic mathematical corpus - one of the most substantial extant for the period - is placed centre-stage in the discussion of Hellenistic culture as a whole. Professor Netz argues that Hellenistic mathematical writings adopt a narrative strategy based on surprise, a compositional form based on a mosaic of apparently unrelated elements, and a carnivalesque profusion of detail. He further investigates how such stylistic preferences derive from, and throw light on, the style of Hellenistic poetry. This important book will be welcomed by all scholars of Hellenistic civilization as well as historians of ancient science and Western mathematics.

The transformation of mathematics from ancient Greece to the medieval Arab-speaking world is here approached by focusing on a single problem proposed by Archimedes and the many solutions offered. In this trajectory Reviel Netz follows the change in the task from solving a geometrical problem to its expression as an equation, still formulated geometrically, and then on to an algebraic problem, now handled by procedures that are more like rules of manipulation. From a practice of mathematics based on the localized solution (and grounded in the polemical practices of early Greek science) we see a transition to a practice of mathematics based on the systematic approach (and grounded in the deuteronomic practices of Late Antiquity and the Middle Ages). With three chapters ranging chronologically from Hellenistic mathematics, through late Antiquity, to the medieval world, Reviel Netz offers an alternate interpretation of the historical journey of pre-modern mathematics.

The transformation of mathematics from its ancient Greek practice to its development in the medieval Arab-speaking world is approached by focusing on a single problem proposed by Archimedes and the many solutions offered. From a practice of mathematics based on the localized solution (originating in the polemical practices of early Greek science), we see a transition to a practice of mathematics based on the systematic approach (grounded in the deuteronomic practices of Late Antiquity and the Middle Ages). A radically new interpretation is accordingly offered of the historical trajectory of pre-modern mathematics.

This book provides a way to understand a momentous development in human intellectual history: the phenomenon of deductive argument in classical Greek mathematics. The argument rests on a close description of the practices of Greek mathematics, principally the use of lettered diagrams and the regulated, formulaic use of language.

This is the second volume of the first fully-fledged English translation of the works of Archimedes - antiquity's greatest scientist and one of the most important scientific figures in history. It covers On Spirals and is based on a reconsideration of the Greek text and diagrams, now made possible through new discoveries from the Archimedes Palimpsest. On Spirals is one of Archimedes' most dazzling geometrical tours de force, suggesting a manner of 'squaring the circle' and, along the way, introducing the attractive geometrical object of the spiral. The form of argument, no less than the results themselves, is striking, and Reviel Netz contributes extensive and insightful comments that focus on Archimedes' scientific style, making this volume indispensable for scholars of classics and the history of science, and of great interest for the scientists and mathematicians of today.

This book provides a way to understand a momentous development in human intellectual history: the phenomenon of deductive argument in classical Greek mathematics. The argument rests on a close description of the practices of Greek mathematics, principally the use of lettered diagrams and the regulated, formulaic use of language.

Greek culture matters because its unique pluralistic debate shaped modern discourses. This ground-breaking book explains this feature by retelling the history of ancient literary culture through the lenses of canon, space and scale. It proceeds from the invention of the performative 'author' in the archaic symposium through the 'polis of letters' enabled by Athenian democracy and into the Hellenistic era, where one's space mattered and culture became bifurcated between Athens and Alexandria. This duality was reconfigured into an eclectic variety consumed by Roman patrons and predicated on scale, with about a thousand authors active at any given moment. As patronage dried up in the third century CE, scale collapsed and literary culture was reduced to the teaching of a narrower field of authors, paving the way for the Middle Ages. The result is a new history of ancient culture which is sociological, quantitative, and all-encompassing, cutting through eras and genres.

Archimedes was the greatest scientist of antiquity and one of the greatest of all time. This book is Volume I of the first authoritative translation of his works into English. It is also the first publication of a major ancient Greek mathematician to include a critical edition of the diagrams and the first translation into English of Eutocius' ancient commentary on Archimedes. Furthermore, it is the first work to offer recent evidence based on the Archimedes Palimpsest, the major source for Archimedes, lost between 1915 and 1998. A commentary on the translated text studies the cognitive practice assumed in writing and reading the work, and it is Reviel Netz's aim to recover the original function of the text as an act of communication. Particular attention is paid to the aesthetic dimension of Archimedes' writings. Taken as a whole, the commentary offers a groundbreaking approach to the study of mathematical texts.

The story of the amazing discovery of Archimedes' lost works Drawings and writings by Archimedes, previously thought to have been destroyed, have been uncovered beneath the pages of a 13th-century monk's prayer book. These hidden texts, slowly being retrieved and deciphered by scientists, show that Archimedes' thinking (2,200 years ago) was even ahead of Isaac Newton in the 17th century. Archimedes discovered the value of Pi, he developed the theory of specific gravity and made steps towards the development of calculus. Everything we know about him comes from three manuscripts, two of which have disappeared. The third, currently in the Walters Art Museum, is a palimpsest - the text has been scraped off, the book taken apart and its parchment re-used, in this case as a prayer book. William Noel, the project director, and Reviel Netz, a historian of ancient mathematics, tell the enthralling story of the survival of that prayer book from 1229 to the present, and examine the process of recovering the invaluable text underneath as well as investigating into why that text is so important.

The Archimedes Palimpsest is the name given to a Byzantine prayer book that was written over a number of earlier manuscripts, including one that contained two unique works by Archimedes, unquestionably the greatest mathematician of antiquity. Sold at auction in 1998, it has since been the subject of a privately funded project to conserve, image, and transcribe its texts. Images and transcriptions of three of these manuscripts are provided here. The first contains seven treatises by Archimedes, including two unique texts, Method and Stomachion, as well as the only extant Greek version of Floating Bodies. Previously unknown speeches by Hyperides and a second- or third-century commentary on Aristotle's Categories follow. The product of ten years of conservation, imaging, and scholarship, this book will be of interest to manuscript scholars, classicists, and historians of science.

The Archimedes Palimpsest is the name given to a Byzantine prayer book that was written over a number of earlier manuscripts, including one that contained two unique works by Archimedes, unquestionably the greatest mathematician of antiquity. Sold at auction in 1998, it has since been the subject of a privately funded project to conserve, image, and transcribe its texts. In this volume the scientists, conservators, classicists, and historians involved in the project discuss in full their techniques and their discoveries. These include new speeches by the classical Athenian orator Hyperides, a lost commentary on Aristotle's Categories from the second or third century AD, and substantial re-readings and reinterpretations of the works by Archimedes. The book discusses the pioneering imaging and post-processing techniques used to reveal the texts, and includes detailed codicological descriptions of all eight manuscripts that constitute the Palimpsest. It will be of interest to manuscript scholars, conservators, classicists, and historians of science.