## The Mathematical Papers of Isaac Newton:When Newton left Cambridge in April 1696 to take up, at the age of 53, a new career at the London Mint, he did not entirely 'leave off Mathematicks' as he so often publicly declared. This last volume of his mathematical papers presents the extant record of the investigations which for one reason and another he pursued during the last quarter of his life. In January 1697 Newton was tempted to respond to two challenges issued by Johann Bernoulli to the international community of mathematicians, one the celebrated problem of identifying the brachistochrone; both he resolved within the space of an evening, producing an elegant construction of the cycloid which he identified to be the curve of fall in least time. In the autumn of 1703, the appearance of work on 'inverse fluxions' by George Cheyne similarly provoked him to prepare his own ten-year-old treatise De Quadratura Curvarum for publication, and more importantly to write a long introduction to it where he set down what became his best-known statement of the nature and purpose of his fluxional calculus. |

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### Contents

LIST OF PLATES | lvi |

477r A fleshedout | 1 |

THE DE QUADRATURA AMPLIFIED AS AN ANALYSIS | 5 |

The twin problems of Johann Bernoullis Programma of New Years Day solved by Newton | 7 |

constructing the radius of curvature at a general point of an ellipse 161 3 Add | 8 |

Machins ineffective attempt 1718 to extend this to a general centralforce field | 13 |

literal truth of Leibniz standpoint was soon lost from sight 28 The text of the De Quadratura | 14 |

nomical daytoday arithmetical computations of the period 36 More sustained reworkings | 43 |

115v116v A first | 227 |

THE METHOD OF FINITE DIFFERENCES 1710 | 236 |

the text as printed by Jones in his 1711 Analysis Pro | 246 |

From these there is given the curve of parabolic kind which shall pass | 252 |

QUANTITATES FLUENTES ET EARUM MOMENTA 1712 | 258 |

Appendix Prior computations and drafts for the Analysis 1 private Calculation | 300 |

PROPOSITION X OF THE PRINCIPIAs SECOND BOOK | 312 |

1 Tottering steps towards achieving a valid resolution of this basic problem in the resisted | 326 |

that the calculus of fluxions was not begotten before the calculus of differences sent privately | 58 |

to observed reality 386 Including Rule 7 the rule of false position employed | 64 |

descent to differentiodifferentials which might be put to the English to test their mathe | 66 |

THE TWIN PROBLEMS OF BERNOULLIS 1697 PROGRAMMA | 72 |

The full Latin text of Bernoullis printed Programma of New Years | 80 |

THE de quadratura curvarum REVISED | 92 |

Given any relationship of fluents to find that of their fluxions 92 | 102 |

207 + 7 88209211 | 110 |

its limitincrement is expanded as a Taylor series 112 The dotsymbols for fluxions | 118 |

3 The final text of the augmented introduction and refurbished concluding portion | 129 |

61v A rough draft of the terminal scholium | 166 |

algebra symbolic arithmetic uses | 188 |

113r114v117r118r On the construction of geometrical problems | 212 |

115r116r A first | 220 |

the semicircle 326 If carried through these would determine the resistance to be twice | 337 |

and gravity are conceived to act over infinitesimalmoments of time not continuously | 369 |

Initial attempts by Newton late September 1712 to locate the defect in | 413 |

for ascertaining the curvature radius in partial derivatives | 423 |

Appendix The wouldbe General Solution turned by Newton into Latin 1 Add | 435 |

3 A first full rendering in Latin of Newtons Method of Solution 437 4 private | 441 |

minor complements to the arithmetica | 460 |

28r Deriving the Cartesian equation of the nodal cubic described by | 468 |

public his early mathematical papers content in England as Leibniz in Germany to | 471 |

plagiarism from the Principia in his 1689 Acta essays 499 Attempts by Chamberlayne | 503 |

4rff | 510 |

challengeproblem on constructing orthogonals to a family of curves | 523 |

N B Unless otherwise specified citations here and below are of manuscripts in | 539 |

### Other editions - View all

The Mathematical Papers of Isaac Newton, Volume 2 Isaac Newton,D. T. Whiteside,M. A. Hoskin No preview available - 1968 |

### Common terms and phrases

Abraham de Moivre abscissa Acta Eruditorum algebraic Analysis Appendix Arithmetica autem brachistochrone calculus Cambridge Commercium compare note construction corpus Correspondence Cotes cujus curva curvature curve cycloid datam dato datum David Gregory densitas differentia draft editio editio princeps edition ejus ensuing epistola equation equivalent erit etiam fluent fluxionum geometrical given Gregory haec hyperbola ibid increment initially inter Invenire Isaac Newton Johann Bernoulli Jones Keill latus rectum Leibniz letter linea London manuscript mathematical mathematicians method of fluxions Moivre motion numeros Opticks Ordinata ordinate parabola perpendicular possunt Postulata Postulate preceding Principia printed Prob problem Problemata Prop Proposition published puncta punctum Quadratura Curvarum quadrature quae quam quantities quod ratio recta reproduced resistance to gravity resistentia Roger Cotes scholium Schriften secunda seriei solution straight line sunt tangent termini tract Wallis