TARTAGLIA'S VISIT TO CARDAN. 247 



the subject of the cosa and cube equal to the number, 

 especially when I had so much entreated for it." 



To this the reply of Tartalea was not unreasonable, and 

 it may be well to say beforehand that it is to be read as 

 in every main point true. He not only was at that time 

 translating Euclid, but he was also reserving himself for a 

 work of his own on arithmetic, geometry, and algebra, 

 which he in the end did publish at Venice, seventeen 

 years .afterwards that is to say, just before his death. 

 It extended even then no further than quadratic equa- 

 tions, being his Book the First of Algebra, and did not 

 contain the whole of his knowledge, nor does his know- 

 ledge of the two contested rules appear to have fructified 

 at all in his own mind during all that time, as he justly 

 supposed that it might, and as it began to do the moment 

 it had found its way into the richer soil of Cardan's 

 genius. Nicolo replied thus : 



" NICOLO. I tell you that I am not so very chary on 

 account of the simple rule or the calculation made by use 

 of it, but on account of those things that by knowledge 

 of it may be discovered, because it is a key that opens the 

 way to the investigation of an infinity of other rules, and 

 if I were not at present occupied upon a translation of 

 Euclid into the vulgar tongue (and by this time I have 

 translated as far as his thirteenth book), I should have 

 already found a general rule for many other cases. As 



