The Development of Newtonian Calculus in Britain, 1700-1800

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Cambridge University Press, 2003 M11 13 - 244 páginas
Guicciardini presents a comprehensive survey of both the research and teaching of Newtonian calculus, the calculus of "fluxions", over the period between 1700 and 1810. Although Newton was one of the inventors of calculus, the developments in Britain remained separate from the rest of Europe for over a century. While it is usually maintained that after Newton there was a period of decline in British mathematics, the author's research demonstrates that the methods used by researchers of the period yielded considerable success in laying the foundations and investigating the applications of the calculus. Even when "decline" set in, in mid century, the foundations of the reform were being laid, which were to change the direction and nature of the mathematics community. The book considers the importance of Isaac Newton, Roger Cotes, Brook Taylor, James Stirling, Abraham de Moivre, Colin Maclaurin, Thomas Bayes, John Landen and Edward Waring. This will be a useful book for students and researchers in the history of science, philosophers of science and undergraduates studying the history of mathematics.
 

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Contenido

THE DIFFUSION OF THE CALCULUS 170030
11
11 Early initiates
12
12 Textbook writers
13
13 The teaching of the calculus in the universities
18
DEVELOPMENTS IN THE CALCULUS OF FLUXIONS 171433
28
21 Methods of integration
29
22 The Methodus differentialis
31
23 Geometry
36
83 Olynthus Gregory and Peter Barlow
112
84 The Royal Military College at Sandhurst
114
85 The Ladles Diary and the Mathematical Repository
115
86 Ivorys breakthrough
117
87 Other journals and the encyclopaedias
118
88 The Royal Naval Academy at Portsmouth
121
CAMBRIDGE AND DUBLIN 17901820
124
92 Robert Woodhouse
126

THE CONTROVERSY ON THE FOUNDATIONS OF THE CALCULUS 173442
38
32 The definitions of the basic terms of the calculus in the works of the early fluxionists
41
33 The doctrine of prime and ultimate ratios
43
34 The foundations of the calculus in Maclaurins Treatise of Fluxions
47
THE MIDDLE PERIOD
53
THE TEXTBOOKS ON FLUXIONS 173658
55
42 Textbooks on fluxions and the science books trade
60
SOME APPLICATIONS OF THE CALCULUS 17403
68
51 Maclaurins study of the attraction of ellipsoids
69
52 Simpsons study of the attraction of ellipsoids
73
53 Remarks on the use of partial differentials in Clairauts Theorie de la Figure de la Terre
79
THE ANALYTIC ART 175585
82
61 Simpsons methodology
83
62 Landens Residual Analysis
85
63 Warings work on partial fluxional equations
89
THE REFORM
93
SCOTLAND 17851809
95
72 John Playfair
99
73 Wallace and Ivory
103
74 Glenie and Spence
104
THE MILITARY SCHOOLS 17731819
108
81 The Royal Military Academy at Woolwich
109
82 Charles Hutton
111
93 Ireland in the eighteenth century
131
94 The reform of mathematics at the University of Dublin
132
95 The Analytical Society
135
CONCLUSION
139
TABLE OF CONTENTS OF FLUXIONARY TEXTBOOKS
143
A2 Table of contents of Thomas Simpsons The Doctrine and Application of Fluxions 1750c
146
A3 Table of contents of John Howes An Introduction to the Doctrine of Fluxions 1751
147
PRICE LIST OF MATHEMATICAL BOOKS PRINTED FOR JOHN NOURSE
148
CHAIRS IN THE UNIVERSITIES
150
C3 University of Oxford
151
C4 University of Edinburgh
152
C6 University of St Andrews
153
C8 University of Dublin
155
MILITARY ACADEMIES
156
D2 Royal Military College Sandhurst masters and professors of mathematics
157
D3 Royal Naval Academy at Portsmouth headmasters
158
SUBJECT INDEX OF PRIMARY LITERATURE
159
MANUSCRIPT SOURCES
165
Notes
167
Bibliography
183
Index
222
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Niccol- Guicciardini holds degrees in physics and philosophy awarded by the Universit... degli Studi di Milano. This book is the published version of his Ph.D. thesis in the history of mathematics, written under the supervision of Ivor Grattan-Guinness at Middlesex Polytechnic. Niccol- Guicciardini is Co-Editor in Chief of Historia Mathematica and is a recipient of the Sarton Medal for 2011-2012, awarded by the University of Ghent, Belgium.

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