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Marcel Berger Geometry I Translated from the French by M Cole and S Levy ABC Marcel Berger Institut des Hautes Etudes Scientifiques 35, route de Chartres 91440 Bures-sur-Yvette France Michael Cole Academic Industrial Epistemology 17 St Mary’s Mount Leyburn, North Yorkshire DL8 5JB England Silvio Levy Mathematical Sciences Research Institute 17 Gauss Way Berkeley, CA 94720-2211 USA Title of the original French edition: Géométrie (vols 1-5) Published by CEDIC and Fernand Nathan, Paris © CEDIC and Fernand Nathan, Paris 1977 Photograph of the author: © E Boubat Corrected Fourth Printing 2009 e-ISBN 978-3-540-93815-6 ISBN 978-3-540-11658-5 Mathematics Subject Classification (1991): 51-XX, 52-XX, 53-XX c 1987 Springer-Verlag Berlin Heidelberg This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broad- casting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Violations are liable to prosecution under the German Copyright Law The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper 987654321 springer.com