shct. i.] DISSERTATION SECOND. 23 



from a very weak and imperfect stale, till it has reached 

 the condition in which it is now found. 



Though in all this the moderns received none of their 

 information from the Greeks, yet a work in the Greek 

 language, treating of arithmetical questions, in a manner 

 that may be accounted algebraick, was discovered in the 

 course of (he next century, and given to the world, in a 

 Latin translation, by Xylander, in 1575. This is the work 

 of Diophantus of Alexandria, who had composed thirteen 

 books of Arithmetical Questions, and is supposed to have 

 flourished about 150 years after the Christian era. The 

 questions he resolves are often of considerable difficulty ; 

 and a great deal of address is displayed in stating them, so 

 as to bring out equations of such a form, as to involve 

 only one power of the unknown quantity. The expression 

 is that of common language, abbreviated and assisted by a 

 few symbols. The investigations do not extend beyond 

 quadratick equations ; they are, however, extremely in- 

 genious, and prove the author to have been a man of talent, 

 though the instrument he worked with was weak and im- 

 perfect. 



The name of Cardan is famous in the history of Algebra. 

 He was born at Milan in 150 J, and was a man in whose 

 character good and ill, strength and weakness, were mixed 

 up in singular profusion. With great talents and industry, 

 he was capricious, insincere, and vainglorious to excess. 

 Though a man of real science, he professed divination, and 

 was such a believer in the influence of the stars, that be 

 died to accomplish an astrological prediction. He remains, 

 accordingly, a melancholy proof, that there is no folly or 

 weakness too great to be united to high intellectual attain- 

 ments. 



Before his time very little advance had been made in 

 the solution of any equations higher than the second de- 



