## The Mathematical Papers of Isaac Newton:The bringing together, in an annotated and critical edition, of all the known mathematical papers of Isaac Newton marks a step forward in the publication of the works of this great natural philosopher. In all, there are eight volumes in this present edition. Translations of papers in Latin face the original text and notes are printed on the page-openings to which they refer, so far as possible. Each volume contains a short index of names only and an analytical table of contents; a comprehensive index to the complete work is included in Volume VIII. Volume I covers three exceptionally productive years: Newton's final year as an undergraduate at Trinity College, Cambridge, and the two following years, part of which were spent at his home in Lincolnshire on account of the closure of the university during an outbreak of bubonic plague. |

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### Contents

FOREWORD TO VOLUME I | xlvii |

Early education and innate mathematical abilities 3 Undergraduate years and first scientific | 10 |

ANNOTATIONS FROM OUGHTRED DESCARTES SCHOOTEN | 25 |

ANNOTATIONS FROM VIETE AND OUGHTRED | 64 |

ANNOTATIONS FROM WALLIS | 89 |

INTRODUCTION | 145 |

Fermat and Descartes 148 That to Barrow Hudde and Wallis 150 Description ofhis early | 151 |

23v27v A The general rule of 5 simplified by considering | 203 |

57r57v An algorithm for finding the fluxion of a given fluent | 382 |

51r51v 1 A general account of the limitmotion of points | 392 |

THE OCTOBER 1666 TRACT ON FLUXIONS | 400 |

2 The former Theorems applyed to resolving of Problems Tangents to geometrical | 440 |

3 Of Gravity The center of Motion in any body and its construction examples | 446 |

PROMINENCE OF | 451 |

of a parabolic template 462 6 Constructions of the parabola by points | 463 |

THE THEORY AND CONSTRUCTION OF EQUATIONS 16651666 | 489 |

D The vertex of a curve found as its meet with its axis illustrated by the preceding | 210 |

WORK ON THE CARTESIAN SUBNORMAL WINTER 1 6645 | 213 |

93v116r First systematic evaluation of derivatives by applying | 219 |

MISCELLANEOUS PROBLEMS IN ANALYTICAL GEOMETRY | 234 |

85r86r The squareing of severall croked lines of ye Seacond | 241 |

THE CALCULUS BECOMES AN ALGORITHM MID1665 | 298 |

30v 30r 1 The derivation of firstorder fluxional equations from | 367 |

MISCELLANEOUS RESEARCHES IN ARITHMETIC NUMBER | 540 |

APPENDIX | 547 |

THE ESSAY OF REFRACTIONS WINTER 16656? | 559 |

THE REFRACTION OF LIGHT AT A SPHERICAL SURFACE | 577 |

587 | |

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### Common terms and phrases

algebraic algebraic curve angle Arithmetica Universalis asymptotes axis bee found calculations Cambridge Cartesian circle Clavis co-ordinates coefficients Compare Conduitt construction corresponding crooked line crookednesse cubic cubic parabola curvature curve defining equation derivative Descartes describe diameter dimensions divided divisors draw ellipse equall Example Exercitationes figure find ye fluxions follows Geometria geometrical given hath Hudde's Huygens hyperbola intersection Isaac Newton John Conduitt John Wallis latus rectum Leibniz Lord Portsmouth manuscript mathematical method multiply Newton has cancelled ordinate Oughtred papers parabola parallel perpendicular printed Prob problem Prop radius Read refracted relation twixt rule Scholium Schooten's Sir Isaac soe yl square subnormal suppose tangent termes theorem tract velocity vertex Vieta Viete's Wallis y.dx y*5 line ye 2d ye area ye equation ye line ye point ye valor