X20 METH. FACIL. ATQ}'E EXPEDIT I^TECR. 



hibcantiir , in qnibiis fidorcs jmaginarii contincantnr. Sit 

 itaquc p-\- rx-hq^-x liuinsnnxli t-ictor trinomialis ipfins 

 N, cnins ia<florcs fimpliccs fint imaginarii , crit ^pq^rr 

 fcu TT^j << I . Dcnotabit igitnr ,Jp,j cofmnm cniuspiam 

 nngnli qni fit (^ , ita vt fit r^^ — cof A . (p ct r — 

 n V pq. coL A (p. Qiiamobrcm gcncralis forma huinsmodi 

 fa<ftoiis trinomialis erit 



p— zxV pq . coC A $) -f- ^A-.v 

 atquc idco in hoc nobis ent cLiborandnm , vt inucniamn* 

 an hninsmodi faftorcs trinomialcs in dcnominatore N con- 

 tincantur , ct quot fint futuri , ct qualcs. Patct nutcm in 

 hac torma trinomiali ctiam fi(florcs fimplictb rcalcs com- 

 prchcndi , fi fiat CP — o ^ tum cnim ob col'. A . CP — i , 

 erit fidor illc trinomialis =: ( ^''p— -vV^ )', indicabitquc 

 dcnominatorcm N diuifibilcm cflc pcr Vp — xVq^ ctfi 

 cohcliidi non potclt , ctiam ipfius qnadratnm (V p—xVqy 

 eflc diuiforcm ipfius N : inncfiigatio cnim diiii(()rum ae- 

 qiialinm ex alio fontc cfi pctcnda. Qiiamobrcm fi dctcr- 

 minaucrimus, qnot variis miKiis cxprclVio p — zx Vpq • cof. 

 A^P-hqxx tanquam factor in dcnominatorc N continca- 

 tur , tum (imnl tum omncs fitfiorcs trinomialcs in imagi- 

 airios rcfolubilcs , qnam ctiam ip(()s fi(ft()rcs fimpliccs rca- 

 les aflcqucmur. Atqnc hiiic etiam , fi ifla inucfiiguio pcr- 

 pctuo potcrit ubfolui , intclligctur, quod (iipra iam prohaui- 

 mus , onincs fiiL^orcs fiiiipliccs imigiiiarios ad fa(ftorcs tri- 

 nomialcs realcs reduci po(lc. 



§23. Ponamus crgo dcnominatoris N facflorcm eflc 

 p—zxVpq. co(. A (J) -f - qxx 



is 



