LAPLACE (Pierre-Simon). Analytical theory of probabilities. Second part. Paris, Ve Courcier, 1812. In-4, pink boards, smooth spine, untrimmed (contemporary binding). Extremely rare first edition of the first fundamental treatise on the theory of probability. Second part only, devoted to the General Theory of Probabilities (Book II). The first part, published a few months earlier, dealt with the Calculus of Generating Functions (Book I). Four supplements were published between 1816 and 1820. The work gives the first version of the central limit theorem, for a two-state variable. Laplace's method for the asymptotic evaluation of certain integrals also appears in this treatise. A precious copy given by the author to Gaspard de Prony with this autograph letter on the first cover of the binding: Pour Monsieur Prony de la part de l'Auteur. Gaspard Riche de Prony (1755-1839) was a Ponts et Chaussées engineer and one of the great names in science and civil engineering of his time. After supervising work on the Louis XVI bridge (Pont de la Concorde) in Paris and working on France's general land register, in 1794 he took part in the creation of the École Polytechnique, of which he was one of the main professors, and was director of the École des Ponts et Chaussées from 1798 to 1839. A copy with full margins in period condition, complete with the final errata. From the Talleyrand library at the Château de Valençay, with bookplate. The Valençay catalogue describes two other works by Laplace, Traité de mécanique céleste and Exposition du système du monde (1899, nos. 159-160), but not this one. - Wet stamp F. Carin at the top of the title. Boards partially faded; headpieces worn; some scattered foxing.