i8o DE INFINITIS CVRVIS 



feparatac. Modiihiris vero acqnatio hoc modo inuenic- 

 tiir : Qiiiii eft jQ^dzzrJV dx differcntietur \trumque 

 membrum ponendo etiiim a \niiabili ope dVzzAdx 

 -\-Bda et dQ^zr.Cdz-{-i:) da. Erit crgo Q_dz-{- 

 dajDclz~Vdx-\'dajBdx feu ddz-z? dx -\-da 

 iJBdx—JDdz). Qiiae aequatio, Ci JBdx ctJDdz 

 poterunt eliminari , dabit modularem quaefitam, 



§. 34. Sit P fundio '"~' dimenfionum ipfirum a 

 ct X , ct Q_ funclio "~' dimenfionum ipl-u um a et z. 

 His pofitis erit Di^. J ? d x - '^^'■^^"^'^ , et 

 Diff. }q_^~-'!±^-±:^^^:'''). Ex quo eruitur ida ae- 



quatio {m — 7i)JVdxzz.— — ^'a — d^i — f^t> JVdx 



zzzjQ^dz. Qiiare fi fuerit?«~;2, crit Q_adz-Q_zda 

 z^V adx — Vxda. quac ell aequatio modularis, feu 



ia qdz — Td x 



« — (^2. — Px" 



§. 35. Sin vcro m ct n non fint acqualcs, ae- 

 quatio modularis erit differentialis fecundi gradus. Nam 



r^ 1 \ CV) J CL(adz — zda) — '^[adx — xda) • t^- rr 



cum lit {m — n)jVdxz:z^^ (^^ erit DifF. 



Q,(adz — zda) — Fjadx — xda) m(m — W^dafPd x , {m — v^^Ti a- ix — xda ) 



da a 1 o~ 



7nQj.adz-zda)-nP{adx~xda) „ • n 1 1 • 



c=z —i . Qiiac acquatio elt modulans 



quaefita. 



§. 3<5- Si in acquatione propofita dz-{-V dxmo 

 indetcrminatae non fucrint a fc inuiccm fcparatac, 

 ita vt P fit fundio involucns .v ct x:; ct ^; dcbcbit 

 per quantitatem quandam R multiplicari , quo formu- 

 la Rdz-\-VKdx \t diffcrentiale intcgralis cuiusdam 

 S poffit confidcrari. Erit itaquc dS—Kdz-\-VRdx:zzOy 



idcoquc 



