# With all the supplements

## Theorie analytique des probabilités. Troisième édition, revue et augmentée par l'auteur. [With:] Supplement [Premiere - Deuxieme - Troisieme - Quatrième].

Paris: Courcier, 1820.

3rd Edition. Hardcover. 4to - over 9¾ - 12" tall. Very Good. Item #003061

1820, 1816-1825. 4to (250 x 200 mm). [4], cxlii [1], 4-506, [2]; 34; 50; 36; [2], 28 pp. Includes errata leaf, bound without half-title, all supplements separately paged and preceded by a half title each. Contemporary mottled calf, rebacked preserving original spine label, gilt stamp of Francis Egerton (probably 1st Earl of Ellesmere, 1800-1857) to boards, marbled endpapers, all edges gilt. Internally very little browned only, occasional minor spotting, a few leaves with soiling at top margin. Provenance: Rothamsted, Lawes Agricultural Trust collection (stamp to first free endpaper). A very good copy with ample margins. ----

D.S.B. XV, pp. 367-376; Evans, *First Editions of Epochal Achievements*, 12; S. Stigler, *History of Statistics*, pp. 146-148; Honeyman 1923; PMM 252 (note).

EXCEPTIONALLY RARE THIRD EDITION, INCLUDING ALL FOUR SUPPLEMENTS, of Laplace's seminal work in probability theory, providing for the first time an important theory of error, lacking in previous studies. Both, the third edition as well as the second edition published in 1814 are of greatest rarity, much rarer than the first edition, with no copy recorded at auction in the past 50+ years (a copy of the third edition apparently lacking the supplements was sold at Sothebys, London in 1962).

In 1812, Laplace issued his *Théorie analytique des probabilités* in which he laid down many fundamental results in statistics. The first half of this treatise was concerned with probability methods and problems, the second half applies those methods to a variety of problems in error theory, decision theory, judicial probability and credibility of witnesses. The first chapter opens with the famous characterization of probability as a branch of knowledge both required by the limitation of human intelligence and serving, in part, to repair its deficiencies. "Rather than drawing together the lifework of a leading contributor to a vast and classical area of science, it was the first full-scale study completely devoted to a new specialty, building out from old and often hackneyed problems into areas where quantification had been nonexistent or chimerical. Later commentators have also sometimes castigated the obscurity and lack of rigor in many passages of the analysis. Once again, it may be so. It is constitutionally and temperamentally very difficult, however, for many mathematicians to enter sympathetically into what was once the forefront of research. Important parts of *Mécanique céleste* were also in the front lines, of course-but that was the location of *Théorie analytique des probabilités* as a whole. What no one has denied is that it was a seminal if not a fully systematic work" (DSB).

A second edition appeared in 1814. This new edition added an introduction of 106 pages, which includes the *Essai philosophique sur les probabilités*. The text expanded from 445 to 481 in length as a result of additions. The dedication to Napolean was replaced with the following foreword by Laplace: The first edition appeared in the course of 1812, namely, the first Part around the beginning of the year, and the second Part some months after the first. Since this time, the Author has occupied himself especially to perfect it, either by correcting slight faults which were slipped into it, or by some useful additions. The principal is a quite extended Introduction, in which the principles of the Theory of Probabilities and their most interesting applications are exposed without the help of the calculus. This Introduction, which serves as preface to the Work, appears yet separately under this title: Essai philosophique sur les Probabilités. The theory of the probability of testimonies, omitted in the first edition, is here presented with the development which its importance requires. Many analytic theorems, to which the Author had arrived by some indirect paths, are demonstrated directly in the Additions, which contain, moreover, a short extract of the Arithmetic of the infinity of Wallis, one of the Works which have most contributed to the progress of Analysis and where we find the germ of the theory of the definite integrals, one of the foundations of this new Calculus of Probabilities. The Author desires that his Work, increasing by one third at least by these diverse Additions, merits the attention of the geometers, and excites them to cultivate a branch so curious and so important to human knowledge. With this third edition, dated 1820, Laplace further expanded the introduction to 142 pages but kept the text of the main section the same as in the second. Most importantly, three supplements were added with the issuing. The first two of these supplements were already separately published in 1816 and 1818 respectively, and the third at the time of this new edition. The fourth supplement, published in 1825, was added by Laplace to those copies of this third edition which were still at his disposal. A second foreword by Laplace is added to this edition, which reads as follows: This third Edition differs from the preceding: 1 by a new Introduction which has appeared last year, under this title: *Essai philosophique sur les Probabilités*, fourth Edition; 2 by three Supplements which are related to the application of the Calculus of Probabilities in the natural sciences and to the geodesic operations. The first two have already been published separately; the third, relative to the operations of surveying, is terminated by the exposition of a general method of the Calculus of Probabilities, whatever be the sources of error.

Content: 1. Calcul des fonctions génératrices - 2. Théorie générale des probabilités - Additions - Supplément a la théorie analytique des probabilités - Deuxième supplément a la théorie analytique des probabilités - Troisième supplément a la théorie analytique des probabilités - Quatrième supplément a la théorie analytique des probabilités.

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