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

### Contents

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 |

222 | |

### Other editions - View all

The Development of Newtonian Calculus in Britain, 1700-1800 Niccol- Guicciardini Limited preview - 2003 |

The Development of Newtonian Calculus in Britain, 1700-1800 Niccol- Guicciardini No preview available - 1989 |

### Common terms and phrases

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