LEIBXITZ. 47 



played at it with so much fury ; it was at the request of the Marquis 

 of Dangeau that Sauveur undertook the investigation of the 

 chances of the game. Sauveur was in consequence introduced at 

 court, and had the honour of explaining his calculations to the 

 King and Queen. See also Montmor^t, page xxxix. 



75. James Bernoulli proposed for solution two problems in 

 chances in the Journal des Sgavans for 1685. They are as 

 follows : 



1. A and B play with a die, on condition that he who first 

 throws an ace wins. First A throws once, then B throws once, 

 then A throws twice, then B throws twice, then A throws three 

 times, then B throws three times, and so on until ace is thrown. 



2. Or first A throws once, then B twice, then A three times, 

 then B four times, and so on. 



The problems remained unsolved until James Bernoulli himself 

 gave the results in the Acta Eruditorum for 1690. Afterwards in 

 the same volume Leibnitz gave the rcsidts. The chances involve 

 infinite series which are not summed. 



James Bernoulli's solutions are reprinted in the collected 

 edition of his works, Geneva, 17^4 ; see pages 207 and 430. The 

 problems are also solved in the Ars Conjectandi, pages 52 — oG. 



76. Leibnitz took great interest in the Theory of Probability 

 and shewed that he was fully alive to its importance, although he 

 cannot be said himself to have contributed to its advance. There 

 was one subject which especially attracted his attention, namely 

 that of games of all kinds ; he himself here found an exercise for 

 his inventive powers. He believed that men had noAvhere shewn 

 more ingenuity than in their amusements, and that even those of 

 children might usefully engage the attention of the greatest mathe- 

 maticians. He wished to have a systematic treatise on games, 

 comprising first those which depended on numbers alone, secondly 

 those which depended on position, like chess, and lastly those 

 which depended on motion, like billiards. This he considered 

 would be useful in bringing to perfection the art of invention, or 



