FORMVLARVM DlFFERENIIALIVM. i7p 



formuhie d xJV d x, pro qiia vnlor ipfius dV idem 

 ell , quem modo attulimus. Primum enim quia 

 dxfy dx iiuegrationem admittere non poflit , nifi 

 V^.v fit intcgnibilc , pcrfpicuum eft omnium primo 

 rcquiri , vt formnlac modo nllitae integrabilcs fint, 

 iis tamen requifitis non omnia expkri quae pro iii- 

 tegranda formula d x f\ d x requiruntur. At vcro 

 quum f II. Diflert. I, demonflratum fit , poflcrius 

 criterium, ex quo de intcgrabilitatc fbrmulae noftrae 

 iudicium peti dcbct , hac aequatioae contincri 



2VQ 3j^m 4^'S _ ffl. /^"' - ■ U _ 



'17'^ dx' ~ dx' "^ dx^-' ^^ 



nunc quidem plures hinc deriuare hcet formulas , 

 quas integrabilcs c(Te oportet. Practerquam enim quod 

 iam euidcns fit , iplam formulam V d x per fe effe 

 integrabilem , nec non d x {? x -\- i(^) integratio- 

 nem admittcix , omnino quoqne patet his fbrmulis : 



dx{ 4- S - 3/R^.v-i- 2.l^'~'QJx-j^'^?dx] etc. 



certa competere integralia. Si vero nunc valores 

 *integra'cs cuohiantur, quemadmodum § lo Difllrt. I. 

 docuimus , indc has obtincbimus formulas ; 



^.v(Fx+2Q) 



</x(P.v' + 2. 2. Q..V+-3. 2R) 



dx[?x+i. 3 Q.a'+3. 3- - R.v + 4. 3. iS) 



dx[ P x-'"-^ + 2 ( w - 2) Q.v'"-' -\- 3 {m - 2) (w - 3) R A-"'-* 

 4-4.(wi-2)(w-3)(^«-4)S.v'"-^+t:tc.) 



Z 2 quibus 



