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Additional info for A History of the mathematical theory of probability from the time of Pascal to that of Laplace
THE present chapter will contain notices of various contributions to our subject, which were made between the publication of the. treatise by Huygens and of the more elaborate works by James Bernoulli, Montmorl, and De Moivre. 70. A Jesuit named John Caramuel published in 1670, under the title of Mathesis Biceps, two folio volumes of a course of Mathematics; it appears from the list of the author's works at the beginning of the first volume that the entire course was to have comprised four volumes.
Montmort, p. 387. • , which will be noticed in a subsequent Chapter. Acta Entil. 8uppl. Art. 59. 73. Nicolas Bemoulli 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 PaBSe-diD:. He goes wrong in trying the Problem of Points for three players, which he does for two simple cases; and also in two other prob~ems, one of which is the fourteenth of Huygens's treatise, and the other is of e:mct1y the same kind.
This is the form with which we are now most familiar. It may be immediately shewn to agree with the form given before by Pascal, by cancelling or introducing factors into both numerator and denominator. Pascal however says, Excellentem hanc solu- 80 SCHOO TEN. c etiam demonstrandam proposuit, ipsam ego sani!! miratus sum, sed difficultate territus vix opus suscepi, at ipsi authori relinquendum existimavi; attamen trianguli arithmetici auxilio, sic proclivis facta est via. Pascal then establishes the correctness of the rule by the aid of his A rithmetica1 Triangle; aftet which he concludes thus, Hac demonstratione W'lsecutA, jam reliqua.