264 JEROME CARDAN. 



having had some contests with their ancient rival, desired 

 Tartalea to assist in capturing the ground which Zuanne 

 held as his exclusive property. To this letter Nicolo 

 added in his diary a number of saturnine and mathema- 

 tical comments, and summed up by waiting that he 

 should not choose to send Cardan an answer, because he 

 said " I have no more affection for him than for Messer 

 Zuanne, and therefore I shall leave them to themselves 1 .'* 

 One of the questions put by the pertinacious Messer 

 Zuanne Tonini da Coi, not soluble at the time by any 

 one, and thought insoluble by some, was the following: 

 " Find me three numbers continually proportional, of 

 which the sum is ten and the product of the second by 

 the first is six." This led to the following troublesome 

 equation: z 4 -}- 6# 3 + 36 rr 60#. Cardan worked very 

 industriously at it, and urged his friend and pupil Lodo- 

 vico Ferrari to do the same. Tartalea, we have seen, de- 

 clined contemptuously to take the field. An ingenious 

 method of solution was eventually discovered by Ferrari, 

 which consisted in adding to each side of the equation 

 arranged in a certain way quadratic and simple quan- 

 tities, of a kind calculated to render the extraction of the 

 square root of each possible. By this method of resolving 



1 " Non li uoglio dar altra risposta, perche fe non ui ho phi afletione 

 a lui che a Messer Zuanne, e pero li utiglio lassar far tra loro." Tar- 

 talea, p. 129. 



