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Mathematical Treasures - Lacroix's Calculus of Probability

Frank J. Swetz and Victor J. Katz



This is the title page of Calculus of Probability, published in 1816.  It was written by Sylvestre Lacroix (1765 - 1843).  Lacroix taught at the Ecόle Polytechnique, where he assisted Monge in producing his book on descriptive geometry. He later became a Professor of Mathematics at Collége de France. Lacroix produced textbooks based on his lecture notes. These books were well received and their style and form were emulated by other European textbook writers of this period.




Here, on pages 122-123 of the Calculus of Probability, Lacroix discusses the “St. Petersburg Paradox” first proposed by Nicolaus Bernoulli  in 1713.  The problem is as follows: “A fair coin will be tossed until heads appears; if the first head appears on the nth toss, then the payoff is 2n ducats.  How much should one pay to play this game?”