1 1 8 METH. FJCIL. ATQl'E EXPEDIT INTECR. 



Patct autcm, vt i tolLmir , cfTc dcbcrc V=:i-}-X, quo 

 fubaitiito lucc qiuiuitas XH-.v"-l- X.v" diuinbilis crt red- 

 dcnd.i pcr .v "". Pcrlpicuum nutcm cft fi fiicrit m < n , 

 tum diuifioncm fucccdcre fi X— o , idcotjuc cafu w; < n 



in fradione — ;r- ; — -. continctur hacc fimplicior — . 



.V ( I -+- .v ) A 



Qiiod fi autcm fit ;/;>« tum ponatur X — Y — .v", ha- 



bcbiturque Y — .v'"-!- Y.v" diuilibilc pcr x^ : cucnit hoc 



fi m <^itt pofito Y m o i quare fi t/i > tt ct w << z ;;, tum 



erit X~-.v'' ct V— i— .v". Hinc facile conlequimut 



V I - .v^-h.V "-.v'" -h.v" - etc. 

 gcncratim fradioncm -7^ forc 



m 



in cuius numcratore tot tppicndi funt tcrmini , quoad ad 

 exponcntcm ipfius .v mniorcm quam ;;; pcrucniatur. In 



foimula creo diftercntiali '-— ex dcnonunatoris 



° .v"\ I -h.v") 



fodore x^ liacc clicitur intcgraiis pnrs 



^dx p dx ^ d X ^ d X 



cousquc continuanda , doncc cxponcntcs ipfius x fiant nc- 

 gatiui : ifta aiittm intcgralis pai-s hoc p;!(flo multo facilius 

 rcf critur , quani pcr dificrcntiationcs antc indicatas. 



§.21. Expofiiimus igitiir modiim fliciUm ntquc cx- 

 peditum cx facftoribus fimplicibus dcnominatoris N in for- 

 muJa d.ffcrcntiali f; </.v , ac potcfiatibus corum, quac qui- 

 dcm in N coiuincntur , partcs iiucgiali^ quatfiti itliion- 

 dcntcs inucnitndi. Totum tmm intcgrale fc)inuilac — ^ 

 cumponiiur cx partibus , tjuac tum cx quautitatibus 



iuicgris 



