## Newton's Principia for the Common ReaderRepresenting a decade's work from one of the world's most distinguished physicists, this major publication is, as far as is known, the first comprehensive analysis of Newton's Principia without recourse to secondary sources. Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law of gravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty, clarity, and breathtaking economy of Newton's methods. This book will stimulate great interest and debate among the scientific community, illuminating the brilliance of Newton's work under the steady gaze of Chandrasekhar's rare perception. |

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### Efni

1 The beginnings and the writing of the Principia | 1 |

Definitions and Axioms | 17 |

3 On the notion of limits and the ratios of evanescent quantities | 43 |

an introduction to Newtons treatment | 57 |

5 The law of areas and some relations which follow | 67 |

6 The motion of bodies along conic sections | 93 |

on dual laws of centripetal attraction | 114 |

7 Keplers equation and its solution | 127 |

16 Attraction by nonspherical bodies | 303 |

17 A digression into Opticks | 323 |

Introduction to Newtons System of the World Book III | 343 |

18 Prolegomenon | 345 |

19 The universal law of gravitation | 353 |

20 The figure of the Earth and of the planets | 381 |

21 On the theory of tides | 399 |

22 The lunar theory | 419 |

8 The rectilinear ascent and descent of bodies | 143 |

9 The conservation of energy and the initialvalue problem | 165 |

10 On revolving orbits | 183 |

11 A pause | 201 |

12 The twobody problem | 205 |

an introduction to Propositions LXVLXIX | 219 |

the foundations of Newtons lunar theory | 235 |

15 The superb theorems | 269 |

23 The precession of the equinoxes | 455 |

24 On comets | 477 |

25 The effect of airdrag on the descent of bodies | 539 |

26 The solid of least resistance | 555 |

27 The problem of the brachistochrone | 571 |

28 The velocity of sound and of long waves in canals | 579 |

Epilogue | 595 |

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### Common terms and phrases

accelerative angle apse apsides attracting body axis Book centre of gravity centre of mass centripetal attraction centripetal force Chapter circle circular orbit comet common centre conic sections constant of areas context Corollary corpuscle cos2 curve cycloid deﬁned deﬁnition denotes density derived descend diagram direction distance Earth ellipse elliptic orbit equal equation equation 11 ﬁgure ﬁnally ﬁnd ﬁnite ﬁrst focus follows formula given Hence hyperbola inﬁnitely integral intersections inverse-square law inversely Kepler’s latus rectum law of attraction law of centripetal Laws of Motion Lemma Moon nodes observations obtain orbital plane parabola parallel particles pendulum perpendicular precession Principia problem Prop proportional Proposition LX quadratures radii radius ratio relation revolution revolving orbit right line Scholium semilatus rectum semimajor axis sin2 solution sphere spherical spheroid square surface syzygies tangent Theorem variation vector velocity VIII weight