## The Mathematical Papers of Isaac Newton:This volume reproduces mathematically significant extracts from the extant manuscript record of Newton's researches during 1684-5 into the dynamical motion of bodies under the deviating action of a central force, and his subsequent struggles thereby to explain the observed motions of solar comets and of the moon. The short tract De motu Corporum, which Newton initially composed on this topic in the early autumn of 1684, was primarily built around his earlier proof that in the absence of external perturbation a planetary eclipse may be traversed under an inverse-square force pull to its solar focus, but also discussed the simplest case of resisted ballistic motion. In epilogue, excerpts from his abandoned grand scheme for revising the Principia in the early 1690s detail Newton's planned refinements to his printed exposition of central force, both simplifying and extending it, introducing therein a novel general fluxional measure of such force - but failing adequately to apply it to the primary case of conic motion. |

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### Contents

3 Computation of the hourly rate of motion of the moons apogee and of its mean | 3 |

is so constructed 24252 The name conic is taken in its broadest sense and includes | 4 |

the disturbing central force which effects a given rotation of orbit 35860 Proposition | 6 |

the influence upon him | 8 |

Additions and corrections to the scholium to Proposition XXXI | 17 |

is at first reluctant to take up Hookes notion 9 Newton initially suggests a spiral path of fall | 22 |

FUNDAMENTAL INVESTIGATIONS ON THE MOTION OF BODIES | 30 |

derivation of the sinelaw | 65 |

that stated for the Borellian case of constant gravity is only loosely accurate 14850 | 162 |

The gravitational attraction of a thin circular ring upon an externalinternal | 206 |

48v55r40r47r88r103r32r39r80r87r72r79v Articles IVX | 229 |

repeats Newtons earlier construction of the distance | 259 |

repeats the previous exact construction of the parabolic case 2 | 308 |

restates Wrens construction of the elliptical case by means of | 322 |

APPROACHES TO THE SOLUTION OF PARTICULAR PROBLEMS | 456 |

THE DE MOTU GORPORUM LIBER PRIMUS REMODELLED | 538 |

30515 Resisted oscillation in a cycloidal pendulum | 96 |

the last ratios of arc chord and tangent as their included contact angle vanishes | 114 |

repeats the earlier derivation | 132 |

the law of force to its centre inducing motion in an ellipse is again shown | 146 |

facing p 46 Revised corollaries to the new Proposi | 565 |

611 | |

### Common terms and phrases

adeo afterwards angle anguli Appendix area EPS attraction autem axis body Cambridge centre centripetal force centrum Christiaan Huygens circle circuli conic Corol Corollary corporis corpus Correspondence curve datam dato describe diameter distance distantia distantiarum duplicata ratione dvjdt eadem Edmond Halley ejus ellipse Ellipseos eodem equal equation Ergo erit erunt figure focus given gravity haec Halley hence Hooke hyperbola ibid ilia infinite inter inverse-square invicem ipsi Johann Bernoulli Kepler's latera latus rectum Leibniz Lemma let fall linea mathematical motion motu Corporum Liber orbit parabola parallel perpendicular planets primus principal vertex Problem Prop proportional proportionalis Proposition published Principia puncta punctum quae quam quod radius ratio reciproce recta rectangulum reproduced resistentia revised Robert Hooke scholium secundum semper speed sphaerae straight line sunt tangent temporis Theorem trajectory triangle ultima umbilico velocitas vis centripeta