From Discrete to Continuous The Broadening of Number Concepts in
In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually desc
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AUSTRALASIAN STUDIES IN HISTORY AND PHILOSOPHY OF SCIENCE VOLUME 16
General Editor:
R. W. HOME, University 0/ Melboume Editorial Adv isory Board:
W. R. ALBURY, University 0/New South Wales D. W. CHAMBERS, Deakin University S. GAUKROGER, University 0/Sydney H. E. LE GRAND, University 0/Melboume A. MUSGRAVE, University ofOtago G. C. NERLICH, University 0/Adelaide D. R. OLDROYD, University 0/ New South Wales E. RICHARDS, University o/Wollongong J. SCHUSTER, University o/Wollongong R. YEO, Griffitb University
The titles published in this series are listed at the end of this volume.
KATHERINE NEAL The University 0/ Sydney, Sydney, Australia
FROM DISCRETE TO CONTINUOUS The Broadening 0/ Number Concepts in Early Modem England
Springer-Science+Business Media, B.Y.
Library of Congress Cataloging-in-Publication Data
ISBN 978-90-481-5993-2 ISBN 978-94-017-0077-1 (eBook) DOI 10.1007/978-94-017-0077-1
Printed on acid-free paper
All Rights Reserved © 2002 Springer Science +Business Media Dordrecht Originall y published by Kluwer Academic Publishers in 2002. Softco ver reprint ofthe hardco ver 1st edition 2002
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 inform ation storage and retrieval system , without written permission from the copyright owner.
For my grandmother Katherine Johnson and my daughter Elizabeth
TABLE OF CONTENTS
Acknowledgments:
ix
Cbapter 1:
Transformation of tbe Number Concept
Cbapter 2:
The Ancient Sources Aristotle Euclid Proclus Greek Atomists
22 25
Cbapter3:
The Contemporary Inßuences The Abacus Tradition Simon Stevin The Techniques of Viete Descartes Conclusion
28 28 33 36 39 45
Cbapter4:
Early Modern Englisb Algebra The Nature of the Texts Robert Recorde The Treatment of Numbers in Arithmetic Texts John Tapp Thomas Harriot's Arts Analyticae Praxis Oughtred's Clav is Mathematicae Conclusion
47 49 58 61 62 71
12
12 17
46
77
Cbapter 5:
Tbe Development of tbe Logaritbms: Napier and Briggs Napier's Background Algebra Napier's Logarithms Briggs and Numerical Methods Briggs' Method of Construction Conclusion
80 84 85 87 104 106 113
Cbapter6:
Isaac Barrow Background and Education Barrow's Mathematical Practice Foundational Issues in Barrow's Cambridge Lectures Conclusion
11S
John Wallis Background and Education Wallis' Mathernatical Practice The Composition of Continua Conclusion
138
Conclusion
158
Cbapter7:
Cbapter8:
116 121 132 136 139 143 151 155
References:
163
Indices:
171
ACKNOWLEDGMENTS
I have received financial help for this book from the University ofToronto in the form of a May Fellowship and from the University of Sydney. Several people have read this book in its many forms. I would like to thank Craig Fraser and Alexander Jones for their support in writing the original thesis , on which this book is based. The anonymous readers provided a great deal of valuable criticism, and I thank them for their detail
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