## Pierre-Simon Laplace Philosophical Essay on Probabilities: Translated from the fifth French edition of 1825 With Notes by the TranslatorPierre-Simon Laplace (1749-1827) is remembered amoung probabilitists today particularly for his "Theorie analytique des probabilites", published in 1812. The "Essai philosophique dur les probabilites" is his introduction for the second edition of this work. Here Laplace provided a popular exposition on his "Theorie". The "Essai", based on a lecture on probability given by Laplace in 1794, underwent sweeping changes, almost doubling in size, in the various editions published during Laplace's lifetime. Translations of various editions in different languages have apeared over the years. The only English translation of 1902 reads awkwardly today. This is a thorough and modern translation based on the recent re-issue, with its voluminous notes, of the fifth edition of 1826, with preface by Rene Thom and postscript by Bernard Bru. In the second part of the book, the reader is provided with an extensive commentary by the translator including valuable histographical and mathematical remarks and various proofs. |

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### Table des matières

PHILOSOPHICAL ESSAY ON PROBABILITIES | 1 |

On probability | 2 |

General principles of the probability calculus | 6 |

On expectation | 11 |

On analytical methods in the probability calculus | 14 |

Applications of the probability calculus | 33 |

On unknown inequalities that may exist between supposedly equal chances | 34 |

On laws of probability resulting from the indefinite repetition of events | 36 |

On elections and decisions of assemblies | 74 |

On the probability of judicial decisions | 77 |

On tables of mortality and the mean duration of life marriages and associations in general | 81 |

On the benefits of institutions that depend on the probability of events | 86 |

On illusions in the estimation of probabilities | 91 |

On various approaches to certainty | 112 |

Historical note on the probability calculus | 117 |

NOTES | 125 |

Application of the probability calculus to natural philosophy | 43 |

Application of the probability calculus to the moral sciences | 61 |

On the means of the results of a large number of observations | 62 |

On the probability of testimony | 65 |

Editions of the Essai | 225 |

BIBLIOGRAPHY | 227 |

GLOSSARY | 253 |

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### Expressions et termes fréquents

advantage analysis annuity astronomer Bernoulli binomial black balls causes chance coefficient comet considered Daniel Bernoulli denote determine difference equation differential calculus discussed draw drawn Earth edition equal equation of condition error Essai Euvres Completes example expression favourable Fermat finite difference follows fraction geometric progression give hypothesis I'Academie royale impressions increase indicated integral James Bernoulli Jupiter Laplace Laplace's large number Leibniz lottery mathematical mathematician mean mean lifetime Memoires de I'Academie method moon moral motion multiplied nature necessary notes number of balls number of observations observed event obtained orbits phenomena philosopher planets players possible powers preceding primitive function principle Probabilites probability calculus probability of getting probability theory Published ratio Rene Thom Reprinted in Euvres result royale des Sciences secular equations sensorium sequence stars suppose tails testimony theorem theory tion toss translation truth urn contains variable white ball witness

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Page 233 - MORGAN -AN ESSAY ON PROBABILITIES, And on their Application to Life Contingencies and Insurance Offices.