Dj; AEQUAT. TRINOMIALIBUS ETC. 341 



Transoamus nunc ad aequaliones irinoraiales tertii gnulus sci- 

 licet ad aequaiioues formae x* — px — ^ = 0. 



Posito 

 x=:a-^bq-i-Cff '^-^-dq^-\-eq "-h/'^ ^-{-gl ^-^H ' -H^7 ®-f-/<7 ' etc. 

 subslitualur haec series in aequatione loco incognitae x; eiit. 



—pa-^bq -^-Zb'^aq'^-^^q^-^'ib'^cq^-k- 'ib'^dq^-\-2>b'^eq'^ -^ibyq'' -<- etc. 



— q —pcq "^-^-dabcq 3-»-3c '^aq ''-(-Sc "^bq *-l-C ^q ^■^■Zc'^dq ^-H etc. 



— pdq^'i-Gabdq^-i-Oabeq^-^-Zd^aq^-i-'id'^bq'' -{-elc. 



•^eq ^ -\-Gacdq ^-^-Gab/q^-^-Gabgq'^^etc. 



—pfq ^-t-Crtce^fi-t-Gflc/^ ''-+- etc. 



-^Gbcdq ^-^Gadeq '-H etc. 



— pgqG-^-Gbccq"^-^ etc. 



— ^A^'^-f- etc. / 



Hinc aequationes 



a ' — pa=.0 



Za^b—pb—1=0 



Za^c-i-Zb'^a--f}C=.0 



Za'^d-^b ^-^Gabc — pd=:0 



3rt 2e-f-3Z» 2c-(-3c '^a-i-Gabd — pe^O 



ia'^/-^-ib^d-i-'ic'^b^abe-+Sacd — pf=0 



'ia'^g-i-Zb^e-{-c^-i-'id^a-\~Gab/-^Gace-i-Gbcd — pg=0 



3a'^h-hZb'^/-^'5c'^d-i-Zd'^b-{-Gabg-{-Gac/-+-Gade-^bce—ph=fi 



etc. etc. etc. 



Ex priori aequatione habemus 



a = rt=|//> a = — i/p. 

 Siimpto a = inveniemus 



1 1 3 12 55 



_273 



Coefficientes numerici 3,12,55^ 273 etc. reducualur ad ex- 

 pressiones sequeates 



— 



