The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book "5000 Jahre Geometrie," in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering. Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first "Golden Age" in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries. Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometr y in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times. The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history. From letters to the authors for the German language edition I hope it gets a translation, as there is no comparable work. Prof. J. Grattan-Guinness (Middlesex University London) "Five Thousand Years of Geometry" - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically! Prof. J.W. Dauben (City University of New York) An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. ... The graphic design is also excellent. Prof. Z. Nadenik (Czech Technical University in Prague)

Writing the History of Mathematics provides both an intellectual and a social history of the development of the subject from the first such effort written in ancient Greece to recent efforts in the 20th century. A special project of the International Commission on History of Mathematics, this work is the result of more than ten years of collaboration by a team of 32 experts, each writing about the history of mathematics in their own countries or regions, and drawing upon extensive research and archival study. In addition to individuals, such institutions as universities, academies, institutes, libraries, and the like are also covered, including journals, encyclopedias, and other collective projects that promote history of mathematics. The book also includes portraits of twenty-five historians of mathematics.

Schon lange bevor die Schrift entwickelt wurde, hat der Mensch geometrische Strukturen wahrgenommen und systematisch verwendet. So entstehen beim Weben und Flechten einfache zweidimensionale Muster und ohne dreidimensionale Korper wie Quader, Wurfel oder Pyramide ist keine Bautatigkeit denkbar. Das vorliegende Buch gibt einen faszinierenden Uberblick uber die geometrischen Vorstellungen und Erkenntnisse der Menschen von der Urgesellschaft bis hin zu den komplexen mathematischen wie auch kunstlerischen Ideen des 20. Jahrhunderts. Neben vielen Abbildungen wird jede Epoche mit einer Tabelle zeit- und kulturgeschichtlicher Daten eingeleitet und mit einer tabellarischen Darstellung der wesentlichen Inhalte der Geometrie dieser Zeit abgeschlossen. Aufgaben am Ende jeden Kapitels laden den Leser ein, sich an den Problemen der alten Meister selber zu versuchen. Ein Buch fur alle, die der Lebendigkeit und Entwicklung der Geometrie als erste "Anwendungswissenschaft" nachspuren wollen.

Fur die 3. Auflage wurden neuste Forschungsergebnisse uber steinzeitliche Kreisgrabenanlagen und die Himmelsscheibe von Nebra aus der Bronzezeit aufgenommen. Zahlreiche Abbildungen, viele davon jetzt in Farbe, erhohen den Lesegenuss des Buches."

Containing many previously unpublished letters, this third volume of a six volume collection of the complete correspondence of John Wallis (1616-1703), documents an important period in the history of the Royal Society and the University of Oxford. By providing access to these letters, this painstakingly crafted edition will enable readers to gain a deeper and richer awareness of the intellectual culture on which the growth of scientific knowledge in early modern Europe was based.
Wallis was Savilian Professor of Geometry of Oxford from 1649 until his death, and was a founding member of the Royal Society and a central figure in the scientific and intellectual history of England. In the period covered Wallis is engaged in scientific debates on techniques for determining areas contained by curves (quadratures) and figures (cubatures), as well as on the theory of motion and the nature of the tides. He also continues to attack the mathematical undertakings of Thomas Hobbes and to respond to attacks which the philosopher in turn levels against him. We also find evidence for the consolidation of mathematics as an academic discipline in the University of Oxford just fifty years after the establishment of the first mathematical lecturerships. Wallis is called upon more than once to deliver ceremonial lectures on mathematical topics to foreign dignitaries visiting the University.
At the same time the volume allows us to witness the beginnings of a remarkable development in mathematical publishing. Many of Wallis's letters to Henry Oldenburg, secretary of the Royal Society, on a variety of topics in the mathematical and physical sciences, are transformed into articles and published in Oldenburg's journal, the Philosophical Transactions. Part of the reason for this development also becomes clear in the letters: the long and costly process of publishing mathematical books such as Wallis's three part Mechanica: sive de motu. This volume not only signals the modernization of mathematics in the second half of the seventeenth century but we also see two new figures emerge for the first time, whose careers are in different ways closely associated with Wallis: Isaac Newton and Gottfried Wilhelm Leibniz.

This is the first of a six volume edition of the correspondence of John Wallis, who was a central figure in the scientific revolution in 17th century England. The letters contained in this volume, which covers the mid-century, give unique insight into the scientific, cultural, and political developments of the time, against the background of the Civil Wars and the Commonwealth.

The Correspondence of John Wallis (1616 -1703) is a critically acclaimed resource in the history of early modern science. Volume IV covers the period from 1672 to April 1675 and contains over eighty previously unpublished letters. It documents Wallis's role in the crucial debate over the method of tangents involving figures such as Sluse, James Gregory, Hudde, Barrow, Newton, and Christiaan Huygens. In this way it illuminates further an important part of the history of the calculus. Wallis's letters also provide valuable new insights into mathematical book production and the importance of the international exchange of books in the growth and dissemination of mathematical knowledge. We learn more about the part played by the intelligencer John Collins and the astronomer royal John Flamsteed in the edition of Jeremiah Horrox's Opera posthuma, published by Wallis in 1673. There are also new insights on the background to Wallis's early work on equations, and the reasons why he criticized Gaston Pardies's proposed tract on motion. The causes of the breakdown in Wallis's epistolary relation to Christiaan Huygens following the publication of the Horologium oscillatorium in 1673 are also revealed. Many letters reflect Wallis's active involvement in the Royal Society. Through the medium of correspondence the Savilian professor participated in numerous debates such as those over the anomalous suspension of mercury in the Torricellian tube or Hevelius's use of plain sights in positional astronomy. The volume allows us to gain a deeper understanding of the background to these debates. Furthermore, the volume throws important new light on the history of the University of Oxford and of the University Press in the early modern period. As keeper of the University Archives, Wallis was one of the institution's highest officers. Scarcely any event of note concerning the University did not require his involvement in some way, and this is reflected in numerous letters and documents which the volume publishes for the first time.