History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace |
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Algebra approximately Bernoulli's theorem Calcul des Probabilités cards Chapter coefficient Condorcet Conjectandi considers contains D'Alembert Daniel Bernoulli date of publication deduced demonstration denote deux dice discussed Doctrine of Chances Duration of Play entitled enunciated equal equation error essay Euler event example expression favourable Finite Differences formula given in Art given number happen Hence Huygens integral investigation James Bernoulli John Bernoulli l'on Lagrange Laplace Laplace's large number Leibnitz letter mathematical memoir occupies pages method Moivre Moivre's Montmort n games Nicolas Bernoulli nombre noticed in Art number of games observations obtain Pascal player Problem of Points proceeds proposed published qu'il remarks required the probability respect result says shew small-pox solution solved stake Suppose theorem Théorie...des Prob Theory of Probability throws tion treatise Trembley volume white balls whole number
Popular passages
Page 33 - The general formula for the number of combinations of n things taken r at a time is C(n,r) = r\(nr)\ We have to find the number of combinations of 12 things taken 9 at a time.
Page xii - The present work, though principally a history, may claim the title of a comprehensive treatise on the Theory of Probability, for it assumes in the reader only so much knowledge as can be gained from an elementary...
Page 587 - ON THE ALGEBRAICAL AND NUMERICAL THEORY OF ERRORS OF OBSERVATIONS AND THE COMBINATION OF OBSERVATIONS.
Page 82 - We may remark that in order to denote the number of combinations of n things taken r at a time, Montmort uses the symbol of a small rectangle with n above it and r below it.
Page 64 - He then proceeds to find what we should call the number of combinations of n things taken r at a time...
Page 38 - London, and having always observed, that most of them who constantly took in the weekly Bills of Mortality, made little other use of them...
Page 133 - De Moivre, he knows these things better than I do." In the long list of men ennobled by genius, virtue, and misfortune, who have found an asylum in England, it would be difficult to name one who has conferred more honour on his adopted country than De Moivre/ I.
Page 51 - The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc'd to a Mathematical Reasoning; and when they cannot, it's a sign our Knowledge of them is very small and confus'd...
Page 501 - It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge. . . . The most important questions of life are, for the most part, really only problems of probability.
Page 502 - The subject of generating functions, strictly so called, forms only the first part of the book ; the second part is devoted to the consideration of the approximate calculation of various expressions which occur in the Theory of Probability.