JEROME CARDAN 75 



the rule of the cubus and the res equal to the numerus 

 (x 3 + pxq)> truly a beautiful and admirable dis- 

 covery. For this Algebraic art outdoes all other subtlety 

 of man, and outshines the clearest exposition mortal wit 

 can achieve : a heavenly gift indeed, and a test of the 

 powers of a man's mind. So excellent is it in itself that 

 whosoever shall get possession thereof, will be assured 

 that no problem exists too difficult for him to disentangle. 

 As a rival of Ferreo, Niccolo Tartaglia of Brescia, my 

 friend, at that time when he engaged in a contest with 

 Antonio Maria Fiore, the pupil of Ferreo, made out this 

 same rule to help secure the victory, and this rule he 

 imparted to me after I had diligently besought him 

 thereanent. I, indeed, had been deceived by the words 

 of Luca Paciolus, who denied that there could be any 

 general rule besides these which he had published, so I 

 was not moved to seek that which I despaired of finding ; 

 but, having made myself master of Tartaglia's method of 

 demonstration, I understood how many other results 

 might be attained ; and, having taken fresh courage, 

 I worked these out, partly by myself and partly by the 

 aid of Ludovico Ferrari, a former pupil of mine. Now 

 all the discoveries made by the men aforesaid are 

 here marked with their names. Those unsigned were 

 found out by me ; and the demonstrations are all mine, 

 except three discovered by Mahomet and two by 

 Ludovico." l 



This is Cardan's account of the scheme and origin of 

 his book, and the succeeding pages will be mainly an 

 amplification thereof. The earliest work on Algebra 

 used in Italy was a translation of the MS. treatise of 

 Mahommed ben Musa of Corasan, and next in order is 

 a MS. written by a certain Leonardo da Pisa in 1202. 



torn. iv. p. 222. 



