JEROME CARDAN 77 



this new process, and was about to hold a public dis- 

 putation at Venice with Niccolo Tartaglia, a mathe- 

 matician of considerable repute, he fancied that possibly 

 there would be game about well worth the hunting. 



Fiore had already challenged divers opponents of less 

 weight in the other towns of Italy, but now that he 

 ventured to attack the well-known Brescian student, 

 mathematicians began to anticipate an encounter of 

 more than common interest. According to the custom 

 of the time, a wager was laid on the result of the contest, 

 and it was settled as a preliminary that each one of the 

 competitors should ask of the other thirty questions. 

 For several weeks before the time fixed for the contest 

 Tartaglia studied hard ; and such good use did he 

 make of his time that, when the day of the encounter 

 came, he not only fathomed the formula upon which 

 Fiore's hopes were based, but, over and beyond this, 

 elaborated two other cases of his own which neither 

 Fiore nor his master Ferreo had ever dreamt of. 



The case which Ferreo had solved by some unknown 

 process was the equation x* + p x = q, and the new 

 forms of cubic equation which Tartaglia elaborated were 

 as follows: x* + P x* = q : and x* p X 2 = q. Before 

 the date of the meeting, Tartaglia was assured that the 

 victory would be his, and Fiore was probably just as 

 confident. Fiore put his questions, all of which hinged 

 upon the rule of Ferreo which Tartaglia had already 

 mastered, and these questions his opponent answered 

 without difficulty ; but when the turn of the other side 

 came, Tartaglia completely puzzled the unfortunate 

 Fiore, who managed indeed to solve one of Tartaglia's 

 questions, but not till after all his own had been 

 answered. By this triumph the fame of Tartaglia 

 spread far and wide, and Jerome Cardan, in consequence 



