By Niccolò Guicciardini
Publisher: Cambridge University Press
Print Publication Year: 1989
Online Publication Date:September 2009
Online ISBN:9780511524745
Hardback ISBN:9780521364669
Paperback ISBN:9780521524841
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511524745.004
Subjects: History, Philosophy and Foundations of Physics, History of science: general interest
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despite its minor role in the diffusion of Newtonian science, we might expect the calculus of fluxions to have been the main subject of research in early eighteenth-century British mathematics. Scientists of outstanding ability were active in Great Britain. Some of them, such as Cotes, Taylor, Maclaurin and Stirling, were good mathematicians who were able to master every aspect of Newton's work on fluxions. But British mathematicians devoted more attention to other branches of Newton's mathematics: i.e. the geometry of higher order curves and the method of series. The reason why the calculus of fluxions was not considered a fruitful area of research is that it appeared to have been developed by Newton to the highest level of perfection. For instance, in 1721 Colin Maclaurin wrote:
The Quadratures [i.e. Newton (1704c)] brought to such generall [sic] theorems that little further seems left to be done in that vast feild [sic] of Invention.
(Maclaurin (1982), p. 13)
The direct method allowed one to find the fluxion of all the known fluents, whereas the inverse method required term by term integration of power series. One of the problems left open was to speed up the convergence of series; a problem which could be treated by finding appropriate transformations involving finite differences. Newton's ‘Methodus differentialis’ (1711c) appeared more incomplete than ‘De quadratura’ (1704c). Also, Newton's ‘Enumeratio’ (1704b) was more problematic in the classification of cubics.
pp. i-ii
pp. iii-vi
pp. vii-xii
OVERTURE: NEWTON'S PUBLISHED WORK ON THE CALCULUS OF FLUXIONS : Read PDF
pp. 1-8
PART I - THE EARLY PERIOD : Read PDF
pp. 9-10
1 - THE DIFFUSION OF THE CALCULUS (1700–30) : Read PDF
pp. 11-27
2 - DEVELOPMENTS IN THE CALCULUS OF FLUXIONS (1714–33) : Read PDF
pp. 28-37
3 - THE CONTROVERSY ON THE FOUNDATIONS OF THE CALCULUS (1734–42) : Read PDF
pp. 38-52
PART II - THE MIDDLE PERIOD : Read PDF
pp. 53-54
4 - THE TEXTBOOKS ON FLUXIONS (1736–58) : Read PDF
pp. 55-67
5 - SOME APPLICATIONS OF THE CALCULUS (1740–3) : Read PDF
pp. 68-81
6 - THE ANALYTIC ART (1755–85) : Read PDF
pp. 82-92
PART III - THE REFORM : Read PDF
pp. 93-94
7 - SCOTLAND (1785–1809) : Read PDF
pp. 95-107
8 - THE MILITARY SCHOOLS (1773–1819) : Read PDF
pp. 108-123
9 - CAMBRIDGE AND DUBLIN (1790–1820) : Read PDF
pp. 124-138
pp. 139-142
APPENDIX A - TABLES OF CONTENTS OF FLUXIONARY TEXTBOOKS : Read PDF
pp. 143-147
APPENDIX B - PRICE LIST OF MATHEMATICAL BOOKS PRINTED FOR JOHN NOURSE : Read PDF
pp. 148-149
APPENDIX C - CHAIRS IN THE UNIVERSITIES : Read PDF
pp. 150-155
APPENDIX D - MILITARY ACADEMIES : Read PDF
pp. 156-158
APPENDIX E - SUBJECT INDEX OF PRIMARY LITERATURE : Read PDF
pp. 159-164
APPENDIX F - MANUSCRIPT SOURCES : Read PDF
pp. 165-166
pp. 167-182
pp. 183-221
pp. 222-228