Calculus An Historical Approach (William McGowen Priestley)英文教材.pdf

Undergraduate Texts in Mathematics
Editors
F. W. Gehring
P. R. Halmas
Advisory Board
C. DePrima
I. Herstein
J. Kiefer
William McGowen Priestley
Calculus:
An Historical Approach
I
Springer-Verlag
New Y ork Heidelberg Berlin
W. M. Priestley
The University of the South
Depanment of Mathematil;:$
Sewanee, Tennessee 31375
USA
Editorial Board
P. R. Halmos
MQnQging Editor
Indiana University
Department of Mathemalies
BJoomington, Indiana 47401
USA
F. W. Gehring
University of Michigan
Dcpartmenl of Malhemalics
Ann Aroor, Michigan 48104
USA
AMS Subjecl Classifications: 26-01, 26A06
With 335 Figures
Library of Congress Cataloging in Publication Dat.
Priestley, William McGowen, 1940-
Calculus, an historical approach.
Includes nd i e:\.
l. Calcutus. 2. Mathematics-Hislory. 3. Calculus-History.
I. Title.
515 18-1368 1
All ri8hts reserved.
No part of this book may be translated or reproduced
in any fonn without written pennission from Springer-Verlag.
© 1979 by Springer-Verlag New York lne.
Soft cO\'cr reprint or tllc Ilardoo \'cr I Sll-dition 1979
9 8 7 6 5 4 3 2 1
ISBN 978-1-4684-9351-1 ISBN 978-1-4684-9349-8 (e Book)
00110. 10071978-1-4684-9349-8
To William Montgomery
and Thomas Carter,
Jor their delight in
sandpiles, seesaws, and pebbles.
Even now there is a very wavering grasp ofthe true position ofmathematics
as an element in the history of thought. I will not go so far as to say that to con•
struct a history of thought without profound study of the mathematical ideas
of essive epochs is like omitting Hamlet from the play which is named after
hirn. That would be claiming too much. But it is certainly analogous to cutting
out the part of Ophelia. This simile is singularly exact. For Ophelia is quite
essential to the play, she is very charming-and a !ittle mad. Let us grant that
the pursuit of mathematics is a divine madness of the human spir