A. de Moivre: 'De Mensura Sortis' or 'On the Measurement of Chance'
1984; Wiley; Volume: 52; Issue: 3 Linguagem: Inglês
10.2307/1403045
ISSN1751-5823
AutoresA. Hald, Abraham de Moivre, Bruce McClintock,
Tópico(s)Mathematical Dynamics and Fractals
ResumoIt is generally agreed that probability theory was born in 1654 by the correspondence between Pascal and Fermat on the division problem (the problem of points) even if a beginning had been made previously by Cardano and Galileo. The Pascal-Fermat letters were only published much later, but as usual at this time their contents were communicated to a number of colleagues. However, an essential part of Pascal's contribution is also included in his Traitg du Triangle arithmitique published in 1665. Pascal and Fermat used the addition theorem and the multiplication theorem for independent events without comments as if these theorems were generally known. They solved the division problem in two ways: by combinatorial methods and by a recursive method (a difference equation). Their results were expressed by means of the negative binomial distribution and the binomial distribution for p = . During a visit to Paris in 1655 Huygens heard about these problems and after his return to the Netherlands he wrote his treatise De Ratiociniis in Aleae Ludo which was published in 1657 and for the next 50 years was the only treatise on probability theory. Huygens solved the division problem and many other problems by recursion; he did not use combinatorial methods. At the end of his treatise he formulated five problems as a challenge to other mathematicians. Solutions, interpretations and generalizations of these problems were discussed by Huygens himself and by Hudde, Spinoza, Bernoulli, Montmort, de Moivre and Struyck. It is a peculiar fact that no essential contribution to probability theory was published between 1657 and the publication in 1708 of Montmort's book Essay d'Analyse sur les
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