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/CBO9780511524745.009
Subjects: History, Philosophy and Foundations of Physics, History of Science: General Interest
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the next three chapters are devoted to the attempts at reforming the calculus which were made in the late eighteenth century and early nineteenth century. The first location to which our attention is drawn is Scotland, where it was more likely that there were contacts with the continent. A geometric tradition was alive in Glasgow and Edinburgh, but this did not hinder several Scottish mathematicians from appreciating the importance of the ‘analysis’ elaborated by the continentals. John Playfair played a significant role in promoting the study of analytical mathematics. In his lectures on physical astronomy in Edinburgh he certainly introduced a taste of the new techniques of Laplace. Perhaps more influential were his reviews and historical accounts concerning the development of mathematics in which he was extremely critical of the fluxional tradition. His call for a change was taken up by two young Scots, Wallace and Ivory. Their researches on elliptic integrals, motivated by Landen (1775), led them to appreciate Legendre's work. I conclude the chapter with a few notes on a quite obscure outsider, William Spence, who adopted in the early nineteenth century the differential notation and, more importantly, some algebraical methods of Arbogast.
The universities and the Royal Society of Edinburgh
Mathematics was taught in all four of the Scottish universities. There were Chairs of Mathematics at Glasgow, Aberdeen, St Andrews and Edinburgh.
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