284 A SHORT HISTORY OF SCIENCE 



Learning geometry surreptitiously at 12 years, he had at 18 

 written an essay on conic sections and constructed the first com- 

 puting machine. While most of his later life was devoted to re- 

 ligion, theology, and literature, he undertook a wide range of 

 physical experimentation, and made important contributions to 

 the then new theories of numbers and probability, besides a 

 discussion of the cycloid. The juvenile essay on conic sections 

 contains the beautiful theorem since named for him that the 

 opposite sides of a hexagon inscribed in a conic section meet in a 

 straight line. Of geometry and logic Pascal says : 



Logic has borrowed the rules of geometry without understanding 

 its power. ... I am far from placing logicians by the side of geom- 

 eters who teach the true way to guide the reason. . . . The method 

 of avoiding error is sought by every one. The logicians profess to 

 lead the way, the geometers alone reach it, and aside from their science 

 there is no true demonstration. 



His work on probability connected itself with the problem of 

 two players of equal skill wishing to close their play, of which 

 Fermat's solution has been given above. 



The following is my method for determining the share of each 

 player when, for example, two players play a game of three points 

 and each player has staked 32 pistoles. 



Suppose that the first player has gained two points and the second 

 player one point ; they have now to play for a point on this condition, 

 that if the first player gain, he takes all the money which is at stake, 

 namely 64 pistoles ; while if the second player gain, each player has 

 two points, so that they are on terms of equality, and if they leave 

 off playing, each ought to take 32 pistoles. Thus if the first player 

 gain, then 64 pistoles belong to him, and if he lose, then 32 pistoles 

 belong to him. If therefore the players do not wish to play this game, 

 but separate without playing it, the first player would say to the 

 second, ' I am certain of 32 pistoles, even if I lose this point, and as 

 for the other 32 pistoles, perhaps I shall have them and perhaps you 

 will have them ; the chances are equal. Let us then divide these 32 

 pistoles equally, and give me also the 32 pistoles of which I am certain.' 

 Thus the first player will have 48 pistoles and the second 16 pistoles. 



