TARTAGLIA DISCOVERS CERTAIN RULES. 219 



guages, for he translated Euclid, and was compelled to 

 study Latin works on mathematics. 



Tartaglia then, settled in Venice, set to work with all 

 his might to prepare himself for his contest with the 

 before-mentioned Antonio Maria Fior ; and while in bed 

 one night, eight days in advance of the time of meeting, 

 he thought out his rival's secret; discovering not only the 

 rule of Scipio Ferreus for the case x 3 -^- bx = c, but also 

 a rule for the case x 3 = bx + c. He prepared himself 

 accordingly. He took care to propose for the perplexing 

 of his antagonist several problems that could be solved only 

 according to the latter rule, then first discovered by him- 

 self. The questions put to him in return he knew would 

 hinge upon the rule of Ferreus. The event proved that 

 he was right; and when the day of trial came Tartaglia 

 answered all the questions on the list presented to him by 

 his adversary in two hours, before Florido had solved one 

 of the problems offered to him. The victor waived his right 

 to thirty entertainments, but achieved a lasting triumph. 



These rules were discovered by Tartaglia on the 12th 

 and 13th of February, 1535. Five years earlier he had 

 discovered two other rules (for the cases x 3 -J- ax 2 = c 

 and x 3 = ax 2 -[- c) on the occasion of questions proposed 

 by a schoolmaster at Brescia, Zuanne da Coi (which would 

 in English be, John Hill). 



Except these discoveries, there was nothing in the 



