JEROME CARDAN 97 



former students of the Art, and attributes to each his 

 particular contribution to the mass of knowledge which 

 he here presents to the world. Leonardo da Pisa, 1 

 Fra Luca da Borgo, and Scipio Ferreo all receive due 

 credit for their work, and then Cardan goes on to speak 

 of " my friend Niccolo Tartaglia of Brescia, who, in his 

 contest with Antonio Maria Fiore, the pupil of Ferreo, 

 elaborated this rule to assure him of victory, a rule 

 which he made known to me in answer to my many 

 prayers." He goes on to acknowledge other obligations 

 to Tartaglia : 2 how the Brescian had first taught him that 

 algebraical discovery could be most effectively advanced 

 by geometrical demonstration, and how he himself had 

 followed this counsel, and had been careful to give the 

 demonstration aforesaid for every rule he laid down. 



The Book of the Great Art was not published 

 till six years after Cardan had become the sharer of 

 Tartaglia's secret, which had thus had ample time to 

 germinate and bear fruit in the fertile brain upon which 

 it was cast. It is almost certain that the treatise as a 

 whole leaving out of account the special question of 

 the solution of cubic equations must have gained 

 enormously in completeness and lucidity from the fresh 

 knowledge revealed to the writer thereof by Tartaglia's 

 reluctant disclosure, and, over and beyond this, it must 

 be borne in mind that Cardan had been working for 

 several years at Giovanni Colla's questions in conjunction 



1 Leonardo knew that quadratic equations might have two 

 positive roots, and Cardan pursued this farther by the discovery 

 that they might also have negative roots. 



2 " Caput xxviii. De capitulo generali cubi et rerum aequalium 

 numero, Magistri Nicolai Tartaglias, Brixiensis Hoc capitulum 

 habui a prefato viro ante considerationem demonstrationum 

 secundi libri super Euclidem, et aequatio haec cadit in I&. cu v 

 binomii ex genere binomii secundi et quinti m. $. cuba uni- 

 versali recisi ejusdem binomii." Opera, torn. iv. p. 341. 



