MQFATlONm NFFERmriAUFIIi. 59 



Fonatur -^nrpj = 2, feu j» = ,-^r? , cnt 



, dK — zdM-4-Mdz — Niz — zdN-f-zzdNi 



«r = Tr=^r* 



quibus valoribus in aequatione propofita fubftitutis, et tota 

 aequatione per (i — z) 2 multiplicata, prodibit : 

 (i-z)dMMi-z)dN^M-N)dz+?(i>-z)Mdx-?(i-z)Nzdx 

 +QMMdx-2QMNzdx-i-QNNzzdx~\-R(i-zydxzzo. 



Iam pro dM et dN fubftituantur valores ex binis fu- 

 perioribus aequationibus difFerentialibus oriundi : 



— P(i-*)M^-Q(i-z)M a <&-R(i-sy* 

 +Ps( i -z)Ndx+Qz( i -z) N 2 dx+Rz( i -z)dx-\-(M-N)dz~o 

 + ?(i-z)Mdx+QM*dx -4- R(i -zydx 

 — ?z{ i —z)Ndx-2QMNzdx 

 -+- QN*zzdx 

 <jua aequatione in ordinem redacla , orietur : 



Q* M*dx •+- Qz N 2 dx - 2 QM N *<fa-i-(M-N)<fc=0 

 feu Q(M-N)</#-f-^=o, ita vt fit : 



vnde aequatio integrata generalis erit: 



^/a(M — u)d X 



^rrConft. 



Pro multiplicatore autem inueniendo , notetur, aequatio- 

 nem propofitam, fa&a fubftitutione primum per(i— z) z t 

 efie multiplicatam , tum vero diuifam per s(M — N) 

 euafifle integrabilem. Statim ergo per ( (M 1n£ m ulti- 

 plicata fiet integrabilis : ex quo fador crit [inj^» qui 

 ob zzz.fz^ hanc indnet fbrmam : 



M- N 



H 2 Proble* 



