| Preface | |
| Acknowledgments | |
| Pt. I | Early Career, 1768-1778 | |
| Ch. 1 | Youth, Education, and Election to the Academy | 3 |
| Ch. 2 | Finite Differences, Recurrent Series, and Theory of Chance | 7 |
| Ch. 3 | Probability of Events and of Their Causes: The Origin of Statistical Inference | 13 |
| Ch. 4 | Universal Gravitation | 29 |
| Ch. 5 | Distribution of Comets | 38 |
| Ch. 6 | Partial Differential Equations, Determinants, and Variation of Constants | 44 |
| Ch. 7 | The Figure of the Earth and the Motion of the Seas | 51 |
| Pt. II | Laplace in his Prime, 1778-1789 | |
| Ch. 8 | Influence and Reputation | 67 |
| Ch. 9 | Variation of Constants, Differential Operators | 70 |
| Ch. 10 | Probability Matured | 72 |
| Ch. 11 | Generating Functions and Definite Integrals | 86 |
| Ch. 12 | Population | 93 |
| Ch. 13 | Determination of the Orbits of Comets | 96 |
| Ch. 14 | Lavoisier and Laplace: Chemical Physics of Heat | 101 |
| Ch. 15 | Attraction of Spheroids | 109 |
| Ch. 16 | Planetary Astronomy | 124 |
| Pt. III | Synthesis and Scientific Statesmanship | |
| Ch. 17 | The Revolution and the Metric System | 149 |
| Ch. 18 | Scientific Work in the Early Revolution | 156 |
| Ch. 19 | Exposition du systeme du monde | 166 |
| Ch. 20 | A Scientific Eminence | 176 |
| Ch. 21 | Traite de mecanique celeste | 184 |
| Pt. IV | Laplacian Physics and Probability | |
| Ch. 22 | The Velocity of Sound | 199 |
| Ch. 23 | Short-Range Forces | 203 |
| Ch. 24 | The Laplacian School | 209 |
| Ch. 25 | Theory of Error | 216 |
| Ch. 26 | Probability: Theorie analytique and Essai philosophique | 224 |
| Ch. 27 | Loss of Influence | 243 |
| Ch. 28 | The Last Analysis | 250 |
| Pt. V | The Laplace Transform | |
| Ch. 29 | Laplace's Integral Solutions to Partial Differential Equations | 259 |
| Conclusion | 271 |
| Abbreviations | 280 |
| Bibliography | 281 |
| Index | 319 |
