CONDORCET. 377 



Without undertaking the defence of BufFon we may remark 

 that the illustration given by Condorcet is not fortunate ; for the 

 student of Geometry knows that it is highly important and useful 

 in many cases to regard an asymptote as a tangent at a very re- 

 mote point. 



Secondly, Condorcet adverts to the subject of Mathematical 

 Expectation; see his pages LXXV and 142. He intimates that 

 Daniel Bernoulli had first pointed out the inconveniences of the 

 ordinary rule and had tried to remedy them, and that D'Alembert 

 had afterwards attacked the rule itself; see Arts. 378, 4G9, 471. 



694. The second part of Condorcet's Essay presents nothing 

 remarkable; the formuloe of the first part are now employed again, 

 with an interchange of given and sought quantities. Methods of 

 approximating to the values of certain series occupy pages 155 — 171. 

 Condorcet quotes from Euler what we now call Stirling's theorem 

 for the ajDproximate calculation of \x ; Condorcet also uses the 



formula, due to Lagrange, which we now usually express symboli- 

 cally thus 



AX=(e'^-l)X- 

 See also Lacroix, Traite du Cole. Diff. ... Vol. iii. jDage 92. 



Condorcet's investigations in these approximations are dis- 

 figured and obscured by numerous misprints. The method which 

 he gives on his pages 168, 169 for successive approximation to a 

 required numerical result seems unintelligible. 



695. We now arrive at Condorcet's third part which occupies 

 his pages 176 — 241. Condorcet says on his page 176, 



Nous avons suffisammeiit expose Tobjet ole cette troisieme Partie : on 

 a vu qu'elle devoit renfermer I'examen de deux questions differentes. 

 Dans la premiere, il s'agit de conuoitre, d'apres I'observatiou, la proba- 

 bilite des jugemens d'uii Tribunal ou de la voix de chaque Votant ; dans 

 la seconde, il s'agit de determiner le degre de probabilite necessaire ])0\\v 

 qu'on puisse agir dans differentes circonstances, soit avec prudence, soit 

 avec justice. 



Mais il est aise de voir que I'examen de ces deux questions demaude 

 d'abord qu'on ait etabli en general les j^rincipes d'apres lesquels on peut 

 determiner la probabilite d'un ^venement futur ou inconnu, nou par la 



