Guicciardini N. The Development of Newtonian Calculus in Britain, 1700-1800

Cambridge University Press, 2003. — 244 p. — ISBN 0-521-36466-3.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.Overture: newton's published work on the calculus of fluxions
The early period
The diffusion of the calculus (1700-1730)
Early initiates'
Textbook writers
The teaching of the calculus in the universities
Developments in the calculus of fluxions (1714-1733)
Methods of integration
The Methodus differentialis
Geometry
The controversy on the foundations of the calculus (1734-1742)
Berkeley's criticisms of the calculus
The definitions of the basic terms of the calculus in the works of the early fluxionists
The doctrine of prime and ultimate ratios
The foundations of the calculus in Maclaurin's Treatise of Fluxions
The middle period
The textbooks on fluxions (1736-1758)
Teaching the algorithm of fluxions
Textbooks on fluxions and the science books trade
Some applications of the calculus (1740-1743)
Maclaurin's study of the attraction of ellipsoids
Simpson's study of the attraction of ellipsoids
Remarks on the use of partial differentials in Clairaut's Theorie de la Figure de la Terre
The analytic art (1755-1785)
Simpson's methodology
Landen's Residual Analysis
Waring's work on partial fluxional equations
The reform
Scotland (1785-1809)
The universities and the Royal Society of Edinburgh
John Playfair
Wallace and Ivory
Glenie and Spence
The military schools (1773-1819)
The Royal Military Academy at Woolwich
Charles Hutton
Olynthus Gregory and Peter Barlow
The Royal Military College at Sandhurst
The Ladies' Diary and the Mathematical Repository
Ivory's break-through
Other journals and the encyclopaedias
The Royal Naval Academy at Portsmouth
Cambridge and Dublin (1790-1820)
Fluxions in Cambridge
Robert Woodhouse
Ireland in the eighteenth century
The reform of mathematics at the University of Dublin
The Analytical SocietyAppendixes
Tables of contents of fluxionary textbooks
Table of contents of William Emerson's The Doctrine of Fluxions (1743), (2nd ed., 1757)
Table of contents of Thomas Simpson's The Doctrine and Application of Fluxions (1750c)
Table of contents of John Rowe's An Introduction to the Doctrine of Fluxions (1751)
Price list of mathematical books printed for John Nourse
Chairs in the universities
The Gregory's family tree
University of Cambridge
University of Oxford
University of Edinburgh
University of Glasgow
University of St Andrews
University of Aberdeen
University of Dublin
Military academies
Royal Military Academy at Woolwich (masters and assistants of mathematics and fortification)
Royal Military College (Sandhurst) (masters and professors of mathematics)
Royal Naval Academy at Portsmouth (head-masters)
Subject index of primary literature
Manuscript sources
Notes