Pierre-Simon Laplace (1749-1827) is remembered amoung probabilitists today particularly for his "Theorie analytique des probabilites", published in 1812. 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.

Philosophical Essay on Probabilities.- On probability.- General principles of the probability calculus.- On expectation.- On analytical methods in the probability calculus.- Applications of the probability calculus.- On games of chance.- On unknown inequalities that may exist on between supposedly equal chances.- On laws of probability resulting from the indefinite repetition of events.- Application of the probability calculus to natural philosophy.- Application of the probability calculus to the moral sciences.- On the means of the results of a large number of observations.- On the probability of testimony.- On elections and decisions of assemblies.- On the probability of judicial decisions.- On tables of mortality and the mean duration of life, marriages and associations in general.- On the benefits of institutions that depend on the probability of events.- On illusions in the estimation of probabilities.- On various approaches to certainty.- Historical note on the probability calculus.- Notes.