292 d'alembekt. 



Or tlie third question may mean that Paul undertakes to be 

 right twice at least in the course of the seven cases, or in other 

 words he undertakes to be right twice and undertakes nothing 

 more. His chance is to be found by subtracting from unity his 

 chance of being never right, and also his chance of being right only 

 once. Thus his chance is 



1_1/1 1 1 



8 8 1 7 "^ 6 "^ 5 



^ + 5+9 + ... + i). 



53-i. Another problem is given unconnected with the one we 

 have noticed, and is solved correctly. 



The article in the Encyclopedie Metliodique is signed with the 

 letter which denotes D'Alembert. The date of the volume is 1784, 

 which is subsequent to D'Alembert's death ; but as the work was 

 published in parts this article may have appeared during D'Alem- 

 bert's life, or the article may have been taken from his manu- 

 scripts even if published after his death. I have not found it in 

 the original EncycloiJedie : it is certainly not under the title Cartes, 

 nor under any other which a person would naturally consult. It 

 seems strange that such errors should have been admitted into the 

 Encyclopedie Methodique. 



Some time after I read the article Cartes and noticed the 

 errors in it, I found that I had been anticipated by Binet in the 

 Comptes Rendus ... Vol. xix. 1844. Binet does not exhibit any 

 doubts as to the authorship of the article ; he says that the three 

 problems are wrong and gives the correct solution of the first. 



535. We will in conclusion briefly notice some remarks which 

 have been made respecting D'Alembert by other writers. 



536. Montucla after alluding to the article Croix ou Pile says 

 on his page 406, 



D'Alembert ne s'est pas borne a cet exemple, il en a accumule plu- 

 sieurs autres, soit dans le qiiatrieme volume de ses Opuscules, 1768, page 

 73, et page 283 du cinquieme; il s'est aussi etaye dii suffrage de divers 

 geometres qu'il qiialifie de distingues. Condorcet a appuye ces objec- 

 tions dans plusieurs articles de rEiicyclopedie methodique ou par ordre 

 de matieres. D'un autre cote, divers autres geometres out entrepris 



