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Probability theory (Ars conjectandi): Part I, II, III, IV. (Wahrscheinlichkeitsrechnung (Ars conjectandi): I., II., III. und IV. Theil . Übersetzt und herausgegeben von R. Haussner. Mit dem Anhange: Brief an einen Freund über das Ballspiel (Jeu de paume).) (German) Zbl 0957.01032
Ostwalds Klassiker der Exakten Wissenschaften. 107/108. Frankfurt/Main: Harri Deutsch. Reprint der Bände 107 und 108 (1713). 2. Aufl. (1999).
Bernoulli’s Latin book, “Ars Conjectandi”, and his French piece, “Lettre... sur les parties du jeu de paume”, were published posthumously in 1713. They both, together with related material including the probability-theoretic part of his “Meditationes” [Diary], are now available in their original languages, and complete with commentaries, in Bernoulli’s “Werke”, Bd. 3 (Basel, 1975). Pt. 2 of the “Ars” was translated into English (1795), and pt. 1, into French (1801); pt. 4 exists in a Russian (1913 and 1986), and English (1966) and a French (1987) version, and the entire “Ars” was translated into German (1899), – together with the “Lettre”, – but did not appear in any other living language. “Ars” contains a reprint of Huygens’s treatise on probability (1657) with essential comment (pt. 1); a study of combinatorial analysis where the author introduced and applied the “Bernoulli numbers” (pt. 2); solutions of problems concerning games of chance (pt. 3); and, in pt. 4, an attempt to create a calculus of stochastic propositions and the proof of the law of large numbers (LLN) with an unfulfilled promise of applying the law to “civil, moral and economic issues”. For a large number of observations, the LLN established parity between theoretical and statistical probabilities (i.e., between deduction and induction) and thus furnished a foundation for statistical inquiries. Being unable to use the yet unknown Stirling formula, Bernoulli had not provided a practically effective law, and Karl Pearson (1924) harshly and unjustly commented on this point. Niklaus Bernoulli adduced a preface to the “Ars” (omitted from the translation). Before that, in 1709, he borrowed from the text (and even from the “Meditationes”, never meant for publication). In his “Lettre”, Jakob calculated the players’ expectations of winning in different situations of the game. The translator commented on the texts and adduced helpful information about the history of probability and Jakob’s contributions.

MSC:
01A75 Collected or selected works; reprintings or translations of classics
60-03 History of probability theory
60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
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