12 PASCAL AND FERMAT. 



geom^tre ou analyste, rdsolut a la verite ces derni^res, qui ne sont 

 pas bien difficiles ; mais il echoua pour le precedent, ainsi que 

 Roberval, a qui Pascal le proposa." p. 384. These words would 

 seem to imply that, in Montucla's opinion, M. de Mere was not the 

 person alluded to by Pascal in the passage we have quoted in 

 Article 14. We may remark that Montucla was not justified in 

 suofsrestinof that M. de Mere must have been an indifferent mathe- 

 matician, because he could not solve the Problem of Points ; for 

 the case of Roberval shews that an eminent mathematician at that 

 time might find the problem too difficult. 



Leibnitz says of M. de Mere, " II est vrai cependant que le Che- 

 valier avoit quelque genie extraordinaire, meme pour les Mathe- 

 matiques ;" and these words seem intended seriously, although in 

 the context of this passage Leibnitz is depreciating M. de Merd. 

 Leibnitii, Opera Omnia, ed. Dutens, Vol. ii. part 1. p. 92. 



In the Nouveaiix Essais, Li v. IV. Chap. 16, Leibnitz says, 

 *' Le Chevalier de Mere dont les Agrements et les autres ouvrages 

 ont ete imprimes, homme d'un esprit jDenetrant et qui etoit joueur 

 et philosophe." 



It must be confessed that Leibnitz speaks far less favourably of 

 M. de Mere in another place. Opera, Vol. V. p. 203. From this pas- 

 sage, and from a note in the article on Zeno in Bayle's Dictionary, 

 to which Leibnitz refers, it appears that M. de Mere maintained 

 that a magnitude was not infinitely divisible : this assists in identi- 

 fying him with Pascal's friend who would have been jDerfect had it 

 not been for this single error. 



On the whole, in spite of the difficulty which we have pointed 

 out, we conclude that M. de Mer^ really was the person who so 

 strenuously asserted that the propositions of Arithmetic were in- 

 consistent with themselves ; and although it may be unfortunate 

 for him that he is now known principally for his error, it is some 

 compensation that his name is indissolubly associated with those of 

 Pascal and Fermat in the history of the Theory of Probability. 



16. The remainder of Pascal's letter relates to other mathe- 

 matical topics. Fermat's reply is not extant ; but the nature of it 

 may be inferred from Pascal's next letter. It appears that Fermat 



