## The Mathematical Papers of Isaac Newton:The main part of the third volume of Dr Whiteside's annotated and critical edition of all the known mathematical papers of Isaac Newton reproduces, from the original autograph, Newton's elaborate tract on infinite series and fluxions (the so-called Methodus Fluxionum), including a formerly unpublished appendix on geometrical fluxions. Ancillary documents include, in Part 1, papers on the integration of algebraic functions and, in Part 2, short texts dealing with geometry and simple harmonic motion in a cycloidal arc. Part 3 reproduces, from both manuscript versions of Newton's Lectiones Opticae and from his Waste Book, mathematical excerpts from his researches into light and the theory of lenses at this period. An appendix summarizes mathematical highlights in his contemporary correspondence. |

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### Contents

and composite curves influence of James Gregory and Barrow 128 Mode 2 focus | 4 |

Barrow reports on a new Newtonian treatise of infinite series December 1670 3 Newton | 13 |

538r Newtons citation of the 1671 tract in a draft preface | 20 |

PRELIMINARY SCHEME FOR A TREATISE ON FLUXIONS | 28 |

to infinite series by division 38 Examples of reduction by extracting roots as infinite | 60 |

Newton generalizes Gregorys concept of a double series convergens | 68 |

modified Huddenian multipliers in simple cases 74 Geometrical justification and Ferma | 78 |

Use of inverse Huddenian multipliers to determine finite solutions by inspection | 104 |

fluxion of the area of a rectangle and triangle as one side flows parallel to itself | 344 |

That of the area generated by a rotating radius vector 346 That of an arc intercepted | 350 |

THE QUADRATURE OF CURVES DEFINED BY POLYNOMIALS | 373 |

PART 2 | 383 |

INTRODUCTION | 389 |

Brounckers first attempts to confirm Huygens result JanuaryFebruary 1662 395 Hookes | 400 |

RESEARCH INTO THE ELEMENTARY GEOMETRY | 408 |

cycloid is proportional to the distance of fall along it to its lowest point 420 Hence | 424 |

solutiones particulares of two de Beaune equations 108 Examples where series solution | 110 |

Example 2 is the general cycloid | 146 |

the curvature is that of the osculating circle 150 Possible defining symptoms | 180 |

of inequability of curvature by the ratio of the fluxion of the curvature radius to that of | 194 |

general observations 198 Examples in geometrical | 202 |

exemplified in the cycloid and sinusoid 204 Cavalierian areapreserving convolu | 208 |

their conversion to common form | 232 |

and y dzXli1e +fzvf h + izvv in terms of the areas s and a of these 244 Observations | 262 |

correctly choosing bounds 264 Similar tables might be constructed | 268 |

simple examples 116 List of nine problems to which | 289 |

The cissoid and conchoid 270 The quartic y2c2 z2 z2 + bz c2 272 The quadra | 290 |

3346 An intended addendum on geometrical fluxions | 338 |

RESEARCHES IN GEOMETRICAL OPTICS | 433 |

of elemental coloured rays each separately refracted 438 The preamble to his first lecture | 441 |

Pembertons or Jones? editorial description of the Opticas Pars prima | 449 |

the resulting quartic is solved in Cartesian style | 462 |

MISCELLANEOUS RESEARCHES INTO REFRACTION | 514 |

72v73r insert | 536 |

strong enough to cause a sensible Bow | 544 |

428 6fr3970 9 615r617r The general problem | 552 |

NEWTONS MATHEMATICAL CORRESPONDENCE | 559 |

I could give exacter solutions | 567 |

573 | |

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### Common terms and phrases

Adeoqj aequatio aequationem aequationibus AFDB alijs angle applicata Archimedean spiral aream autem Barrow cancelled Cartesian centre centrum circle circuli Collins compare note contact angle contactus cujus curvae Curvarum curvature curve cycloid datam defined Descartes dimensionum earum ejus emerget equal equation equivalent erit etiam Example exposita fluent quantities fluxions fluxionum Geometria geometrical given Gregory hujus Huygens hyperbola inde indefinitely infinite series inter Isaac Barrow Isaac Newton James Gregory Johann Bernoulli juxta latus rectum Leibniz method Method of Fluxions modum nempe ordinate parabola perpendicular possunt potest Prob Problem puncto punctum quadrature quae quam quantitatum quibus quod quotient radius ratio recta relatio relationem root scholium sive spiral straight line substitution summa sunt tangent tantum terminos thence tract valor variable