128 MONTMORT. 



220. Montmort quotes the following sentence from a letter 

 written by Pascal to Format. 



Pour vous parler francliement de la Geometrie, je la trouve le plus 

 haut exercice de I'espritj mais en meme temps je la connois pour si 

 invitile, que je fais peu de difference entre un homme qui n'est que 

 Geometre et un habile Artisan; aussi je I'appelle le plus beau metier 

 du monde; mais enfin ce n'est qu'un metier: et j'ai souvent dit qu'elle 

 est bonne pour faire I'essai, mais non pas I'emploi de notre force. 



Montmort naturally objects to this decision as severe and humi- 

 liating, and probably not that which Pascal himself would have 

 pronounced in his earlier days. 



221. The next letter is also from Montmort to Nicolas Ber- 

 noulli; it occupies pages 361 — 370. Montmort says he has just 

 received Do Moivre's book, by which he means the memoir De 

 Mensura Sortis, published by De Moivre in the Philosophical 

 Transactions ; and he proceeds to analyse this memoir. Montmort 

 certainly does not do justice to De Moivre. Montmort in fact 

 considers that the first edition of his own work contained im- 

 plicitly all that had been given in the De Mensura Sortis; and he 

 seems almost to fancy that the circumstance that a problem had 

 been discussed in the correspondence between himself and the 

 Bernoullis was sufficient ground to deprive De Moivre of the credit 

 of originality. The opinion of Nicolas Bernoulli was far more favour- 

 able to De Moivre ; see Montmort's pages 862, 375, 378, 386. 



De Moivre in his Miscellanea Analytica replied to Montmort, 

 as we shall see hereafter. 



222. On his page 365 Montmort gives some remarks on the 

 second of the five problems which Huygens proposed for solution ; 

 see Art. 35. 



Suppose there are three players ; lot a be the number of 

 white balls, and h of black balls ; let c = a-\- h. The balls are 

 supposed not to be replaced after being drawn ; then the chance of 

 the first player is 



a h{h-V) (h-2)a b(h-l) .,.(h-5)a 

 ,c+c(c-l)(c-2)(c-3) c(c-l) ... (c-6) '^ '" 



