1^6 DE CRITERIIS INTEGRABlL. 



diuntur. Requifua igitur integ^rabilitatis formukc 

 dxfV dx^ fequeiitibus duabus aequatioaibus conti- 

 nentur : 



^P dd(l /R d^^l} _ 



id(l 3ddR 4/S __- ^^-'U 

 ax dx Hx dx 



pofito nimirum 

 dV — fAdx-^-Ndy-i-Vdp-^-Q^dq . . . . + Wz/. 



1,2. Quum formula differentialis V d x inte- 

 grabilis efle nequeat , nifi formulae M' d x et N'dx 

 integratlonem admittant , liquet hinc non folum for- 

 mulas Mdx et Ndx, fed etiam dxfMdXy 

 dxfN dx integrabiles efle debere. Porro ex pofte- 

 riori integrabilitatis criterio patet /P ^a; verum quo- 

 ^jue e£[c .integrale., quum fiat : 



3^R _ d^^-^V 



iDeinde qaum per prius integrabilit^ti^ requifitum , 

 formula d x (1 Q^— 2f? d x -\- 2 f^'^ ISlJ x) integra- 

 bilis fit , ex pofteriori autem intelligatur formulam 

 d X {f? d X — 2. Q^) integrationem admittere; addendo 

 iftasformulas, obtinebimus hanc dxC^f^^^^dx-f^dx), 

 quam igitur quoque integrabilem .eflTe oportct. VI- 

 terius ob integrabilitatem formularum : 

 dx{3^—ifQJx+f^'y?dx) et zdxiK-fQdx-^^f^^^^dx 



-f^'ll<ldx) 



patet 



