[ 73 ] 



Toot of the firft transformed is its abfolute quantity divided by 

 the root of the final equation. 



Let the equation when its roots are encreafed by e, be 

 I 



z^ +qz' + rpz + r- =0 



3 V 27 r 



r 



When t"he value of e, by which the roots are to be encreafed 

 (or diminifhed) is impoflible the coefficients of the transformed 



equation will be impoffible binomials •.' a = — — r' an impoffibic 



binome (unlefs in particular cafes the coeiF. of the impoffible part 

 vanilhes) hence it appears that ^, and e, will be poffible or im- 

 poffible in the fame cafes. 



, Vol. VII. K If 



* Since the equation z' + ^z* 4- »-/)2 -f- >•* may be thus eipreflcd 



3 9 27 27 



