CARAMUEL. 45 



serio disputans. This treatise includes a reprint of tlie treatise of 

 Huygens, which however is attributed to another person. Cara- 

 muel says, page 984, 



Dum hoc Syntagma Perilhistri Domino N. Viro eruditissimo com- 

 municarem, ostendit etiam mihi ingeniosam quamdam de eodem argu- 

 ment© Diatribam, quam ^ Christiano Severino Longomontano fuisse 

 scriptam putabat, et, quia est curiosa, et brevis, debuit huic Qusestioni 

 subjungi... 



In the table of contents to his work, page xxviii, Caramuel 

 speaks of the tract of Huygens as 



Diatribe ingeniose a Longomontano, ut putatur, de hoc eodem argu- 

 mento scripta : nescio an evulgata. 



Longomontanus was a Danish astronomer who lived from 15G2 

 to 1647. 



72. Nicolas Bernoulli speaks very severely of Caramuel. He 

 says XJn Jesuite nomme Caramuel, que j'ai citd dans ma These... 

 mais comme tout ce qu'il donne n'est qu'un amas de paralogismes, 

 je ne le compte pour rien. Montmort, p. 387. 



By his T}ie$e Nicolas Bernoulli probably means his Specimina 

 Artis conjectandi..., which will be noticed in a subsequent Chapter, 

 but Caramuel's name is not mentioned in that essay as reprinted 

 in the A da Erud. . . . Suppl. 



John Bernoulli in a letter to Leibnitz speaks more favourably 

 of Caramuel ; see page 715 of the volume cited in Art. 59. 



73. Nicolas Bernoulli has exaggerated the Jesuit's blunders. 

 Caramuel touches on the following points, and correctly : the 

 chances of the throws with two dice ; simple cases of the Problem 

 of Points for two players ; the chance of throwing an ace once at 

 least in two throws, or in three throws ; the game of Passe-dix. 



He goes Avrong in trying the Problem of Points for three 

 players, which he does for two simple cases ; and also in two other 

 problems, one of which is the fourteenth of Huygens's treatise, and 

 the otlier is of exactly the same kind. 



Caramuel's method with the fourteenth problem of Huygens's 

 treatise is as follows. Suppose the stake to be 36 ; then A's chance 



