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Acknowledgements | ||
Prologue | ||
1 | The beginnings and the writing of the Principia | 1 |
2 | Basic concepts: Definitions and Axioms | 17 |
3 | On the notion of limits and the ratios of evanescent quantities | 43 |
4 | On the motion of particles under centripetal attraction: an introduction to Newton's treatment | 57 |
5 | The law of areas and some relations which follow | 67 |
6 | The motion of bodies along conic sections | 93 |
7 | Kepler's equation and its solution | 127 |
8 | The rectilinear ascent and descent of bodies | 143 |
9 | The conservation of energy and the initial-value problem | 165 |
10 | On revolving orbits | 183 |
11 | A pause | 201 |
12 | The two-body problem | 205 |
13 | The method of the variation of the elements of a Kepler orbit and Newton's lunar theory: an introduction to Propositions LXV-LXIX | 219 |
14 | The three-body problem: the foundations of Newton's lunar theory | 235 |
15 | 'The superb theorems' | 269 |
16 | Attraction by non-spherical bodies | 303 |
17 | A digression into Opticks | 323 |
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 |
23 | The precession of the equinoxes | 455 |
24 | On comets | 477 |
25 | The effect of air-drag 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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