This  increase  of  difficulty  is  so  great,  that  the  resolu-
fS'cf  c"":  tion  of  algebraic  equations  is  as  yet  known  to  us  only
''"'"■  in  the  iirst  four  degrees.     In  this  respect,  algebra  has

advanced  but  little  since  the  labors  of  Descartes  and  the  Italian
analysts  of  the  sixteenth  century ;  though  there  has  probably  not
been  a  single  geometer  for  two  centuries  past  who  has  not  striven
to  advance  the  resolution  of  equations.  The  general  equation  of
the  fifth  degree  has  itself,  thus  far,  resisted  all  attempts.  The  for-
mula of  the  fourth  degree  is  so  difficult  as  to  be  almost  inapplicable  ;
and  analysts,  while  by  no  means  despairing  of  the  resolution  of
equations  of  the  fifth,  and  even  higher  degrees,  being  obtained,  have
tacitly  agreed  to  give  up  such  researches.
