The Historical Development of the Calculus

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Springer Science & Business Media, Aug 2, 1994 - Mathematics - 368 pages
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The calculus has served for three centuries as the principal quantitative language of Western science. In the course of its genesis and evolution some of the most fundamental problems of mathematics were first con fronted and, through the persistent labors of successive generations, finally resolved. Therefore, the historical development of the calculus holds a special interest for anyone who appreciates the value of a historical perspective in teaching, learning, and enjoying mathematics and its ap plications. My goal in writing this book was to present an account of this development that is accessible, not solely to students of the history of mathematics, but to the wider mathematical community for which my exposition is more specifically intended, including those who study, teach, and use calculus. The scope of this account can be delineated partly by comparison with previous works in the same general area. M. E. Baron's The Origins of the Infinitesimal Calculus (1969) provides an informative and reliable treat ment of the precalculus period up to, but not including (in any detail), the time of Newton and Leibniz, just when the interest and pace of the story begin to quicken and intensify. C. B. Boyer's well-known book (1949, 1959 reprint) met well the goals its author set for it, but it was more ap propriately titled in its original edition-The Concepts of the Calculus than in its reprinting.
  

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Contents

I
1
II
5
III
10
IV
12
V
16
VI
19
VII
24
VIII
28
LVII
176
LVIII
178
LIX
187
LX
189
LXII
190
LXIII
191
LXIV
194
LXV
196

IX
29
XI
31
XII
35
XIII
40
XIV
42
XV
54
XVII
62
XVIII
68
XIX
74
XX
75
XXI
77
XXIII
78
XXIV
80
XXV
81
XXVI
86
XXVII
91
XXVIII
93
XXIX
95
XXX
97
XXXI
98
XXXII
99
XXXIII
104
XXXIV
109
XXXV
113
XXXVI
118
XXXVII
120
XXXVIII
121
XXXIX
122
XL
125
XLI
127
XLII
132
XLIII
134
XLIV
138
XLV
141
XLVI
142
XLVII
143
XLVIII
148
XLIX
151
L
153
LI
154
LII
158
LIII
161
LIV
164
LV
166
LVI
170
LXVI
200
LXVII
201
LXVIII
204
LXIX
205
LXX
209
LXXI
210
LXXII
212
LXXIII
217
LXXIV
222
LXXV
224
LXXVI
226
LXXVII
230
LXXVIII
231
LXXX
234
LXXXI
239
LXXXII
245
LXXXIII
252
LXXXIV
258
LXXXV
260
LXXXVI
264
LXXXVII
265
LXXXVIII
267
LXXXIX
268
XC
270
XCI
272
XCII
275
XCIII
277
XCIV
281
XCV
287
XCVI
292
XCVII
299
XCVIII
301
C
304
CI
308
CII
312
CIII
317
CIV
322
CV
329
CVI
333
CVII
335
CIX
341
CX
346
CXI
347
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