io8 THE POPULAR SCIENCE MONTHLY. 



he had been informed in a dream of all that was to happen to 

 him. His costume, his bearing, corresponded with his strange 

 character. He appeared sometimes in rags, sometimes splendidly 

 dressed ; ran through the streets at night, and the next day was 

 drawn in a three-wheeled carriage. Yet he published a treatise 

 on mathematics, Ars magnet, which was remarkable for the age. 

 Pertinently to the publication of this work he had controversies 

 with Tartaglia, of which something should be said, for the curi- 

 ous picture they offer of the manners of the learned world in the 

 sixteenth century. 



Tartaglia, as we have said, discovered the solution of cubic 

 equations. Cardan employed toward him all the persuasions in 

 his power to obtain a communication to himself of the famous 

 discovery. " I swear to you on the holy gospels," he promised, 

 " that if you teach me your discoveries I will never publish them, 

 and will, besides, record them for myself in cipher, so that no one 

 shall be able to understand them after my death." Tartaglia, 

 trusting in Cardan's good faith, communicated to him his rules 

 summarized in twenty-seven mnemotechnic verses, in three 

 strophes of nine verses each. Cardan, assisted by his pupil Fer- 

 rari, succeeded in extending the rules, solved equations of the 

 fourth degree, and published the whole in the Ars magna. Tar- 

 taglia, irritated at the algebraist astrologer's violation of his 

 word, fell into a violent rage. He sent to his enemy, according 

 to the fashion of the time, several challenges, and in one of them 

 went so far as to threaten Cardan and his pupil that he would 

 wash their heads together and at the same time, " a thing which 

 no barber in Italy could do." Cardan finally agreed to attend a 

 disputation, which was to be held in a church in Milan on the 

 10th of August, 1548. He did not appear, but sent his pupil Fer- 

 rari. Ferrari bore his part in the contest alone, and the affair 

 would have resulted in favor of Tartaglia if the hostile attitude 

 of Cardan's friends had not caused him to leave Milan by a by- 

 road. "These mathematical jousts," says M. Victorien Sardou, 

 " these challenges proclaimed by heralds and trumpets, with great 

 parade of pompouswords and swelling eulogies, were more be- 

 coming to charlatans than to really learned men ; but charlatan- 

 ism was then in fashion ; a discovery was the finder's secret, and 

 a method of calculating was speculated upon as if it was a new 

 medicinal powder." We do not wholly agree with M. Sardou. 

 We see an example of intellectual activity and find a proof of the 

 importance that was attached to algebraic discoveries in these sci- 

 entific tournaments in which all classes of society are interested 

 as formerly, in ancient Greece, they applauded the challenges of 

 poets and the contests of athletes. 



Leaving the Italian mathematicians and crossing the Alps, we 



