DE MOIVRE. 14y 



the ninth problem of the De Mensura Sortis. De Moivre how- 

 ever renounces for himself the claim to the merit of the solu- 

 tion. This renunciation he repeats in the Miscellanea Analytica, 

 page 206, where he names the author of the simple solution 

 which we have already given. He says, 



Ego vere illucl ante libenter fassus sum, idque ipsum etiamnum 

 libenter fateor, quamvis solutio Problematis mei noni causam fortasse 

 dederit hiijus solutionis, me tamen nihil juris in eam habere, eamque 

 CI. ilhus Autori ascribi lequum esse. 



Septem aut octo abliinc annis D. Stevens Int. Tempi. Socius, Yir 

 ingenuus, singulari sagacitate prseditus, id sibi propositum habens ut 

 Problema superius allatum solveret, hac ratione solutionem facile asse- 

 cutus est, quam mihi his verbis exhibuit. 



Then follows the solution, after which De Moivre adds, 



Doctissimus adolescens D. Cranmei', apud Genevenses MatliematicaB 

 Professor dignissiraus, cujus recordatio seque ac Collegae ejus i)eritissimi 

 D. Calandrin mihi est perjucunda, cum superiore anno Londini com- 

 moraretur, narravit milii se ex Uteris D. Nic. Bernoulli ad se datis acce- 

 pisse CI. Yirum novam solutionem hujus Problematis adeptum esse, 

 quani prioribus autor anteponebat ; cum vcro nihil de via solutionis 

 dixerit, si mihi conjicere liceat qualis ea sit, banc opinor eandem esse 

 atque illam quam raodo attuli. 



271. We have already spoken of Problems x. and xi. in 

 Art. 247. In his solution of Problem x. De Moivre uses the 

 theorem for the summation of series to which we have refen^ed 

 in Art. 152. A corollary was added in the second edition and 

 was expanded in the third edition, on which we Avill make a 

 remark. 



Suppose that A, B, and C throw in order a die of n faces, 

 and that a faces are favourable to A, and h to B, and c to (7, 

 where a ■\- h + c = n. Required the chances wdiich A, B, and G 

 have respectively of being the first to throw a corresponding face. 

 It may be easily shewn that the chances are proportional to 

 air, (h + c) hn, and (h + c) {a + c) c, respectively. De Moivre, in 

 his third edition, page Qo, seems to imply tliat before the order 

 was fixed, the chances would be proportional to ^, h, c. This 

 must of course mean that such would be the case if there were 



