Hiero, King of Syracuse, suspecting the honesty of a goldsmith, and desiring, without injuring his 
crown, to determine the purity of the gold, applied to Archimedes, who thus, through his 
instrumentality, discovered the fundamental principle of hydrostatics, one of the most brilliant 
discoveries of antiquity. 
The curioso who asked, after having observed the seven bridges between the two branches of the 
river Pregel and the island of Kneiphof, whether it were possible to cross them successively without 
passing twice over the same, and he who wished to know how the knight could move over the sixty-four 
squares of the chess-board without returning twice to the same square, became involved in that 
geometry of position, (glanced at by Leibnitz,) which never makes use of the magnitudes of 
quantities. 
Finally, the speculations of a gambler, belonging to the aristocratic circles, the Chevalier de 
Méré, first suggested, in the reign of Louis XIV, the calculation of probabilities, or at least 
directed toward it the attention of Pascal and Fermat, two of the most wonderful geniuses of whom 
France is so deservedly proud.  
This last branch of applied mathematics, although called, by an illustrious geometer, “common 
sense reduced to calculation,” was not received without opposition. 
Even now public opinion will scarcely admit that analytical formulas are capable of determining the 
secret of judiciary decisions; or of giving the comparative values of judgments pronounced by 
tribunals differently constituted; it unwillingly adopts, also, the numerical limits in which have 
been included the mean result of several series of distinct and more or less concordant 
observations. When there is a question of an order of problems less subtle, all understanding play 
require but the most ordinary intelligence to see at a glance that the aid of algebra can here be 
satisfactorily called in, but even here are met, in the details and applications, real difficulties, 
requiring the skill of professional men. 
Every one readily understands the danger, the stakes being equal, of playing when the conditions of 
the game give to one greater chances of winning; every one sees, too, at the first glance, that if 
the chances of the two players are unequal, the stakes should be so too; that if the chances of one, 
for example, are tenfold those of his adversary, the respective stakes, the sums risked upon the 
game, should be in the proportion of ten to one; that this exact proportionality of the stakes to 
the chances is the necessary and characteristic rule, sufficient for all fair play. There are cases, 
however, where, in spite of the observance of these mathematical conditions, a prudent man would 
decline to play. Who, for instance, with a million of chances against one in his favor, would risk a 
million to gain one franc? 
In order to explain this anomaly, this disagreement between the results of calculation and the 
inspirations of common sense, Buffon found