CHAPTER I. 



CARDAN. KEPLER. GALILEO. 



1. The practice of games of chance must at all times have 

 directed attention to some of the elementary considerations of the 

 Theory of Probability. Libri finds in a commentary on the Divina 

 Commedia of Dante the earliest indication of the different proba- 

 bility of the various throws which can be made with three dice. 

 The passage from the commentary is quoted by Libri ; it relates to 

 the first line of the sixth canto of the Purgatorio. The com- 

 mentary was published at Venice in 1477. See Libri, Histoire 

 des Sciences Mathematiques en Italie, Vol. ii. p. 188. 



2. Some other intimations of traces of our subject in older 

 writers are given by Gouraud in the following passage, unfor- 

 tunately without any precise reference. 



Les anciens paraissent avoir eutierement ignore cette sorte de calcul. 

 L'eruditioii moderne en a, il est vrai, trouve quelques traces dans un 

 poeme en latin barbare intitule : De Vetidq, oeuvre d'un nioine du Bas- 

 Empire, dans un commentaire de Dante de la fin du XY^ siecle, et 

 dans les ecrits de plusieurs matliematiciens italiens du moyeu age et 



de la renaissance, Pacioli, Tartaglia, Peverone ; Go\irsi\\d,IIisto{re 



du Calcul des Frohahilites, page 3. 



3. A treatise by Cardan entitled De Ludo Alece next claims 

 our attention. This treatise was published in 1663, in the first 

 volume of the edition of Cardan's collected works, long after 

 Cardan's death, which took -place in 1576. 



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