«71 



_>c 



DIFFERENTIAUBJ r S. 5 x 



femperfitintegrabilis, fi fuerit yel H^ ^ fefedg^ 

 numenis integer affirrnatiuiis. 



§. i<5\ Ponamus primo bc—afzzo (eu/irz^; et 



aeq.iatio inuenta tranfibit in hanc dy -{- x*y* d x -+- 



(p-\-ifdx (a-cfdx (g-\-bx n )dx r _ 



~ — x__: — — — - ^. -+- ,— — r*_ — ____: " , quae fi fit 



g——cm—am(m—i-) et /?__=—-( ^/_-4—tffe(fc — 1)) 7 m- 



tegrabilis exiftit , fi t_d___r| i ___±£ fu er jt numerus integer fiue 



affirmatiuus fiue negatiuus. Ponamus porro czza, quo 



t (p-Hi)V_. 



prodeat ifta aequatio dy -\- x*j d x -\— *_j_^ — = 



4.v 



(aimn-\-bkkx n )dx . . fc+m . 



*. — - / n , __*.■, 1 quae lntegrabilis ent fi -£- fuerit nume- 

 (a-\-bx n )x*~* 



rus integer. 



§. 17. Ponamus in aequatione generali vltimo §. 



15. inuenta bzzzzo , quo meri termini fimplices prodeant, 



_ (p-\-i)"dx 

 habebitur ifta aequatio dy-\-x*y dx -+- --p 



(a—cfdx gdx. (af—naf-\-iah-cf)x n dx ffx" n dx 



400X*** + tfA-^ 2 "^ Zttx**" ~~ 555*** 



_______), quae pofito g— — ^w— am(m— 1 ) et hzzzz—fk in- 



tegrabilis exiftit , ii vel ( *-+- w ~ -i_i=__. foerit numerus integer 

 affirmatiuus , vel fi fit fzzzzo, qui quidem cailis per fe 

 Conftat. Ponamus d[p-\-\f— [a— c) 2 -\-^agzzzzaa' , atque af 



-naf-iafk-cfzzzgaf ent ^zz et 



4^ 



^-.«^ 2 ^-^). vn de erit g ^-^^-^ - ^± ^ 



G 2 qui- 



