s8o DE mTEGRATlOmBrS 



Computo iam reae inftituto , reperientur valores optati 

 tam coefficientium quam exponentiumj quemadmoduni 

 fequitur, fciltcet 



a — ^ — 



te — r ~ 2"a ~*~ 



eb — ac-^a^fhb-^2hc_^cc — 4««} 



'^ 2v'{&&-4-2bc-4-cc"Z:4.'ae 



— a6_f_ac-j-aV(b?'-f_2&c-4_cc 40«) 



— 2y' {bb^2bc~i-cc-^ae) 



Ubi notandum , pofle hos valores flmplicius exprimij re- 

 ducendo nempex in utroquefadorebinomiali ad com- 

 munem denominatorem za, & hunc poftea omittendo ^ 

 ficuti etiam dividendo exponentcs inventos percommu- 

 nem quantitatem a : 2V{bb-\-Qbc-\-cc—i^ae). Liquet e- 

 nim , fi [x-^-ayY x(;r-f-§rf fuerit— conftanti , fore et- 



iam [^ax-\-iacLyY •^[zax-^Q.a^}'^- -n conftanti. His ita 

 monitis , & fcripto brevitatis gratia m pro 

 'V{)}h-\-2bc-\-CQ—^at) atque C maiufculo pro quantitatc 

 conftanti arbitraria , dico hanc agquationem finitam 

 {iax^[h-\-c-m)y)^' -^ '"Jx [^ax-\- [h^c^m) y/-^-+-^-^™i 

 zziC y efte integralem sequationis difFerentialis canonicae 

 primi ordinis [ax-\-hy)dx-\-[cx-\-eyYy~'^ •> omnespoffi- 

 biles cafus particulares huius ordinis in fe complecflentis. 

 Poteft vero inventa illa sequatio finita mutariin hancfor- 

 mam , adhibita aliqua dexteritate , [axx-\-hyx-\-eyX'\-' 

 y -^-+-^-^"^)x(2^Ar-}-(^-+-r-h^)j) ('^-''^z=C,vel in hanc 

 aham nonnihil diverfam(^.r.r-|-^:r-f-0''^-i-C'^)^^-*^'*^"*^ 

 '^[^ax-^^h-^-c-^-m^yY-'''''^'-')-^, 



CoroU. I. 

 XVII. Hinc fi bzzc , erit tunc in prima sequa- 



tio- 



