70 JAMES BERNOULLI. 



James Bernoulli devotes eiglit pages to it, his object being to 

 estimate the advantage of the banker at the game. See Art. 74>. 



The last three problems which James Bernoulli discusses 

 arose from his observing that a certain stroller, in order to entice 

 persons to play with him, offered them among the conditions of 

 the game one which was apparently to their advantage, but 

 which on investigation was shewn to be really pernicious ; see his 

 pages 208, 209. 



121. The fourth part of the Ay^s Conjectandi occupies pages 

 210 — 239 ; it is entitled Pars Quai'ta, tradens usum et apj^licatio- 

 nem prwcedentis Doctrince in Civilibus, Moralihus et Oeconomicis. It 

 was unfortunately left incomplete by the author; but nevertheless 

 it may be considered the most important part of the whole work. 

 It is divided into five Chapters, of which we will give the titles. 



I. Prceliminaria qucedam de Certitudine, Prohahilitate, Neces- 

 sitate, et Contingentia Rerum. 



II. De Scieniia et Conjectura. De Arte Conjectandi. De 

 Argumentis Conjecturanmi, Axiomata quwdam generalia hue 

 pertinentia. 



III. De variis argiimentorum generihus, et quomodo eorum 

 pondera wstimentur ad supputandas rerum prohahilitates. 



lY. De duplici Modo investigandi mimeros casiium. Quid 

 sentiendum de illo, qui instituitur per experimenta. Prohlenia 

 singulare eani in rem propositum, &c. 



V. Solutio Prohlematis prcecedentis. 



122. We will briefly notice the results of James Bernoulli 

 as to the probability of arguments. He distinguishes arguments 

 into two kinds, pure and mixed. He says, Pura voco, quoe in qui- 

 busdam casibus ita rem probant, ut in aliis nihil positive probent : 

 Mixta, quae ita rem probant in casibus nonnullis, ut in cieteris 

 probent contrarium rei. 



Suppose now we have three arguments of the pure kind lead- 

 ing to the same conclusion; let their respective probabilities be 



