XIV CONTENTS. 



PAGE 



problem on Duration of Play, 6i ; he points out a plausible mistake, 63; 

 treats of Permutations and Combinations, 64 ; his Numbers, 65 ; Pro- 

 blem of Points, 66 ; his problem with a false but plausible solution, 67 ; 

 his famous Theorem, 71 ; memoir on infinite series, 73; letter on the game 

 of Tennis, 75. Gouraud's opinion, 77. 



Chapter VIII. Montmoet 78 



Fontenelle's Eloge, 78. Two editions of Montmort's book, 79 ; contents of the 

 book, 80; De Moivre's reference to Montmort, 81; Montmort treats 

 of Combinations and the Binomial Theorem, 82 ; demonstrates a formula 

 given by De Moivre, 84 ; sums certain Series, 86 ; his researches on Pha- 

 raon, 87; Treize, 91; Bassette, 93. Problem sob ed by a lady, 95. Pro- 

 blem of Points, 96; Bowls, 100; Duration of 1 lay, loi ; Her, 106; 

 Tas, no. Letter from John Bernoulli, 113. Nicolas Bernoulli's game of 

 chance, 116. Treize, 120. Summation of Series, 121. Waldegrave's 

 problem, 122, Summation of Series, 125. Malebranche, 126. Pascal, 128. 

 Sum of a series, 129. Argument by Arbuthnot and 's Gravesande on 

 Divine Providence, 130. James Bernoulli's Theorem, 131. Montmort's 

 views on a History of Mathematics, 132. Problems by Nicolas Ber- 

 noulli, 133. Petersburg Problem, 134. 



Chapter IX. De Moivre 135 



Testimony of John Bernoulli and of Newton, 135. Editions of the Doc- 

 trine of Chances, 136. De Mensura Sortis, 137. De Moivre's approximate 

 formula, 138; his Lemma, 138; Waldegrave's problem, 139; Duration 

 of Play, 140; Doctrine of Chances, 141; Litroduction to it, 142; con- 

 tinued fractions, 143; De Moivre's approximate formula, 144; Duration 

 of Play, 147; Woodcock's problem, 147; Bassette and Pharaon, 150; 

 Numbers of Bernoulli, 151; Pharaon, 152; Treize or Rencontre, 153; 

 Bowls, 159; Problem on Dice, 160; Waldegrave's problem, 162; 

 Hazard, 163; Whist, 164; Piquet, 166; Dirration of Play, 167; Recur- 

 ring Series, 178; Cuming's problem, 182 ; James Bernoulli's Theorem, 183 ; 

 problem on a Run of Events, 184; Miscellanea Analytica, 187; contro- 

 versy with Montmort, 188; Stirling's theorem, 189; Arbuthnot's argu- 

 ment, 193. 



Chapter X. Miscellaneous Investigations BET^yEEN 



THE YEARS 1700 AND 1750 191? 



Nicolas Bernoulli, 194. Barbeyrac, 196. Arbuthnot's argument on Divine 

 Providence, 197. Waldegrave's problem, 199. Browne's translation of 

 Huygens's treatise, 199. Mairan on Odd and Even, 200. Nicole, 201. 

 BufFon, 203. Ham, 203. Trente-et-quarante, 205. Simpson's Nature and 

 Laws of Chance, 206; he adds something to De Moivre's results, 207; 

 sums certain Series, 210; his Miscellaneous Tracts, ■21 1. Problem by John 

 Bernoulli, 212. 



