178 DE MOIVRE. 



of Play to test the value of an approximation proposed by Mont- 

 mort ; we have already referred to this point in Art. 184. 



316. It remains to trace the history of De Moivre's investi- 

 gations on this subject. 



The memoir De Mensura Sortis contains the following Pro- 

 blems out of those which appear in the Doctrine of Chances, 

 LVIII, LX, LXII, LXIII, the first solution of LXV, LXVI. The first 

 edition of the Doctrine of Chances contains all that the third does, 

 except the Problems LXVIII. and LXix ; these were added in the 

 second edition. As we proceed with our history we shall find 

 that the subject engaged the attention of Lagrange and Laplace, 

 the latter of whom has embodied the researches of his prede- 

 cessors in the Theorie...des Proh. pages 225 — 238. 



317. With one slight exception noticed in Art. 322, the re- 

 mainder of the Doctrine of Chances was not in the first edition but 

 was added in the second edition. 



318. The pages 220 — 229 of the Doctrine of Chances, form 

 a digression on a subject, which is one of De Moivre's most 

 valuable contributions to mathematics, namely that of Recurring 

 Series. He says, page 220, 



The E-eader may have perceived that the Sohition of several Pro- 

 blems relating to Chance depends upon the Summation of Series; I 

 have, as occasion has offered, given the Method of summing them up; 

 but as there are others that may occur, I think it necessary to give 

 a summary Yiew of what is most requisite to be known in this matter; 

 desiring the Reader to excuse me, if I do not give the Demonstrations, 

 which would swell this Tract too much; especially considering that I 

 have already given them in my Miscellanea Analytica. 



319. These pages of the Doctrine of Chances will not present 

 any difficulty to a student who is acquainted with the subject of 

 Recurring Series, as it is now explained in works on Algebra ; 

 De Moivre however gives some propositions which are not usually 

 reproduced in the present day. 



320. One theorem may be noticed which is enunciated by 

 De Moivre, on his page 224, and also on page 167 of the Miscellanea 

 Analytica. 



