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Mathematical Treasures - Jacob Bernoulli's Ars Conjectandi

Frank J. Swetz and Victor J. Katz


This is the title page of Jacob Bernoulli's Ars Conjectandi (The Art of Conjecturing), published posthumously in 1713 by his nephew Nicolaus I Bernoulli. The Ars Conjectandi is famous for Bernoulli's statement of a general rule for summing integral powers as well as for the first statement and proof of the Law of Large Numbers. The first parts of the book contain an extensive treatment of the theory of probability, mostly based on earlier work of Huygens and others. The final section is entitled "The Use and Application of the Preceding Doctrine in Civil, Moral, and Economic Matters." It is here that the Law of Large Numbers is stated, but despite the imposing title of the section, it is quite short. Evidently, Bernoulli found it difficult actually to apply probability to "civil, moral, and economic" matters. Note that the book as published includes a treatise on infinite series and a letter Bernoulli wrote to a friend about probabilities in the game of tennis.

A complete translation of the Ars Conjectandi is available as Jacob Bernoulli, The Art of Conjecturing, together with Letter to a Friend on Sets in Court Tennis, translated by Edith Dudley Sylla (Baltimore: Johns Hopkins University Press, 2006).

Index to Mathematical Treasures

Frank J. Swetz and Victor J. Katz, "Mathematical Treasures - Jacob Bernoulli's Ars Conjectandi," Convergence (January 2011)

Mathematical Treasures from the Smith and Plimpton Collections at Columbia University