The Evolution of the Euclidean Elements A Study of the Theory of Inc
The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incommensurable magnitudes beginning from the first discoveries by fifth-century Pythago reans, advancing through the achievement
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SYNTHESE HISTORICAL LIBRARY TEXTS AND STUDIES IN THE HISTORY OF LOGIC AND PHILOSOPHY
Editors: N. KRETZMANN,
G.
NUCHELMANS,
L. M. DE
RIJK,
Cornell University University of Leyden
University of Leyden
Editorial Board:
J. BERG, Munich Institute of Technology F.
DEL PUNT A,
D. P. HENRY,
J.
University of Manchester
Academy of Finland and Stanford University
HINTIKKA,
B. MATES,
J. E. G.
Linacre College, Oxford
University of California, Berkeley
MURDOCH,
PATZIG,
Harvard University
University ofGottingen
VOLUME 15
WILBUR RICHARD KNORR
THE EVOLUTION OF THE EUCLIDEAN ELEMENTS A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry
D. REIDEL PUBLISHING COMPANY DORDRECHT-HOLLAND / BOSTON-U.S.A.
Library of Congress Cataloging in Publication Data Knorr, Wilbur Richard, 1945The evolution of the Euclidean elements. Portions of this work originally included in the author's thesis, Harvard, 1973. Bibliography: p. Includes indexes. 1. Geometry - Early works to 1800. 2. Mathematics, Greek. I. ride. QA31.K59 516'.2 75-12831
ISBN-13: 978-90-277-1192-2 001: 10.1007/978-94-010-1754-1
e-ISBN-13: 978-94-010-1754-1
Published by D. Reidel Publishing Company, P.O. Box 17, Dordrecht, Holland Sold and distributed in the U.S.A., Canada, and Mexico by D. Reidel Publishing Company, Inc. 306 Dartmouth Street, Boston, Mass. 02116, U.S.A.
All Rights Reserved Copyright © 1975 by D. Reidel Publishing Company, Dordrecht, Holland Softcover reprint of the hardcover 1st edition 1975 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any informational storage and retrieval system, without permission from the copyright owner
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TABLE OF CONTENTS
ACKNOWLEDGMENTS I
I INTRODUCTION I. The Pre-Euclidean Theory of Incommensurable Magnitudes II. General Methodological Observations III. Indispensable Definitions
II
I THE SIDE AND
THE DIAMETER OF THE SQUARE
I. The Received Proof of the Incommensurability of the Side and Diameter of the Square II. Anthyphairesis and the Side and Diameter III. Impact of the Discovery of Incommensurability IV. Summary of the Early Studies III
I PLATO'S
I. II. III. IV. V. VI. VII. VIII.
ACCOUNT OF THE WORK OF THEODORUS
Formulation of the Problem: SuvaJJ£lC; The Role of Diagrams: 'Ypa
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