214 JEROME CARDAN. 



quadratic equations, of which only the positive roots were 

 used ; there was but one unknown quantity assumed, and 

 there was no use made of marks or signs, except a few 

 abbreviations. Algebra was then used only for the solu- 

 tion of a small class of numeral problems. 



In or about the year 1505, the first rule for resolving 

 one case of a complex cubic equation (x 3 -J- bx = c) was 

 discovered by Scipio Ferreus, of Bologna. This is the 

 discovery to which a reference was made at the beginning 

 of the ninth chapter of the present work; and from 

 this point the history of Algebra in Italy has an im- 

 mediate bearing on the story of Cardan. Ferreus taught 

 his rule to a pupil named Antonio Maria Fior (Latin- 

 ised, Florido, or, we should say in English, Flower), who, 

 thirty years afterwards, presuming on his knowledge of it, 

 challenged and triumphed over his contemporaries. It 

 was at that time usual for men skilled in any art or science 

 to send tough questions to each other for solution, and 

 to provoke each other to stake money or reputation upon 

 intellectual encounters. The advancement of learning 

 was unquestionably hastened by such means. Master 

 Flower's unanswerable problems, and the pains he took to 

 flout his knowledge of a secret rule in the face of his 

 brother mathematicians, caused him to be rather trouble- 



the innumerable fragments of alabaster, porphyry, and serpentine, to 

 which Era Luca called attention, no trace, I believe, remains to excite 

 notice in the present day. 



