CHAPTER XII. 



EULER, 



428. EULER was bora in 1707, and died in 1783. His 

 industry and genius have left permanent impressions in every 

 field of mathematics ; and although his contributions to the 

 Theory of Probability relate to subjects of comparatively small 

 importance, yet they will be found not unworthy of his own great 

 powers and fame. 



429. Euler's first memoir is entitled Calcul de la Prohahilite 

 dans le Jeu de Rencontre. This memoir is published in the volume 

 for 1751 of the Histoire de V Acad ... Berlin ; the date of pub- 

 lication is 1753 : the memoir occupies pages 255 — 270 of the 

 volume. 



430. The problem discussed is that which is called the game 

 of Treize, by Montmort and Nicolas Bernoulli-; see Art. 162. 

 Euler proceeds in a way which is very common with him ; he 

 supposes first one card, then two cards, then three, then four, and 

 exhibits definitely the various cases which may occur. After- 

 wards, by an undemonstrated inductive process, he arrives at the 

 general law. 



The results obtained by Euler had been given more briefly 

 and simply by Nicolas Bernoulli, and published by Montmort in 

 his page 301 ; so we must conclude that Euler had not read 

 Montmort's book. 



When n is infinite, the expression given in Art. 161 for the 



