PREFACE. 



IN order to explain the particular object of this Trea- 

 tise, it will be necessary to give a brief account of the 

 science on which it treats. 



At the end of the seventeenth century, the theory of 

 probabilities was contained in a few isolated problems, 

 which had been solved by Pascal*, Huyghens, James 

 Bernoulli, and others. They consisted of questions re- 

 lating to the chances of different kinds of play, beyond 

 which it was then impossible to proceed : for the dif- 

 ficulty of a question of chances depending almost en- 

 tirely upon the number of combinations which may 

 arise, the actual and exact calculation of a result be- 

 comes exceedingly laborious when the possible cases are 

 numerous. A handful of dice, or even a single pack of 

 cards, may have its combinations exhausted by a mode- 

 rate degree of industry : but when a question involves 

 the chances of a thousand dice, or a thousand throws 

 with one die, though its correct principle of solution 

 would have been as clear to a mathematician of the six- 

 teenth century as if only half a dozen throws had been 

 considered ; yet the largeness of the numbers, and the 



* Un probleme relatif aux jeux de hasard, propose & un austere janse- 

 niste par un homme du monde, a ete 1'origine du calcul des probabilites. 



Poisson. 



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