Sources and Studies in the History of Mathematics and Physical Sciences Editorial Board J.Z. Buchwald J. Lu¨tzen G.J. Toomer Advisory Board P.J. Davis T. Hawkins A.E. Shapiro D. Whiteside Gert Schubring Conflicts between Generalization, Rigor, and Intuition Number Concepts Underlying the Development of Analysis in 17–19th Century France and Germany With 21 Illustrations Gert Schubring Institut fu¨r Didaktik der Mathematik Universita¨t Bielefeld Universita¨tstraße 25 D-33615 Bielefeld Germany
[email protected] Sources and Studies Editor: Jed Buchwald Division of the Humanities and Social Sciences 228-77 California Institute of Technology Pasadena, CA 91125 USA Library of Congress Cataloging-in-Publication Data Schubring, Gert. Conflicts between generalization, rigor, and intuition / Gert Schubring. p. cm. — (Sources and studies in the history of mathematics and physical sciences) Includes bibliographical references and index. ISBN 0-387-22836-5 (acid-free paper) 1. Mathematical analysis—History—18th century. 2. Mathematical analysis—History—19th century. 3. Numbers, Negative—History. 4. Calculus—History. I. Title. II. Series. QA300.S377 2005 515′.09—dc22 2004058918 ISBN-10: 0-387-22836-5 ISBN-13: 978-0387-22836-5 Printed on acid-free paper. © 2005 Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring St., New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, com- puter software, or by similar or dissimilar methodology now known or hereafter developed is for- bidden.