CARDAN'S DISCOVERIES IN ALGEBRA. 275 



fore, Cardan prosecuted, and the result was a work of 

 remarkable completeness and originality. In it he laid 

 down rules for all forms and varieties of cubic equations, 

 having all their terms or wanting any of them, and having 

 all possible varieties of signs. Every rule given he demon- 

 strated geometrically. He treated very fully of almost all 

 kinds of transformations of equations, in a manner before 

 wholly unknown. In the same book he for the first time 

 made frequent use of the literal notation, a, b, c, d. He 

 therein gave a rule for biquadratics suiting all their cases, 

 and in the invention of that rule made use of an assumed 

 indeterminate quantity, and afterwards found its value by 

 the arbitrary assumption of a relation between the terms. 

 He therein first applied algebra to the resolution of 

 geometrical problems. 



The list could be made more minute, but it would in 







that case be more technical ; the citation of those main 

 points is enough to show the very great importance of 

 Cardan's Book of the Great Art, in which the whole doc- 

 trine of cubic equations was first published to the world 1 . 

 In that department of algebra, Tartalea had indeed turned 

 the first sod, but it was Cardan who ploughed the field 

 and raised the crop upon it. No algebraical book equal in 



1 In Button's Mathematical Dictionary, art. Algebra, there may be 

 seen a list of the chief improvements introduced into the art by Car- 

 dan, sixteen in number. 



T 2 



