A B 



iblvenda esfet in r-rir — 4- + r- , ' 3- etc. Sit igitur 



f ;^4:/ Turn ^ + ^a:-j.c^» ^-z/x^ =/f+5C^4-p) 



'¥C(^x^py''¥D(x'¥py GO 



Jam Jnvenire posiimus A^ B ^ C qz D fi evolvanius digni- 

 tates hnius (^x^p) atque cum hanc partem aequationis 

 disponamiis fecundum dignitates variabilis ^, , nt ita 

 cum priore aequationis parte comparetur. Verum calcu- 

 lus differentialis methodum exliibet longe faciliorem. lam 

 continue fi ponamus AT^i^i^t invenimus a ^ hp-^-cp^ 

 ^— dp^ zz A^ Si difFerentiemus aequationera (I) mm ha- 

 bemus: 



{h ^ 2 c a;^ 3 dx^f^x:^. (^Bj^^C (x^p^ 4.Z) (x^pT^x; 

 five ^ 4- 2 c ^; 4- 3 dx^ r^ i5 + 2 C (x^-p) + 3 i) (x-^pj^ (II.} 

 Pofito denuo xzz-^ p^ invenimus i' — 2 (7^ 4- 3 dp^ zz B, , 

 Si diiTerenciemus aequationem (IL) habemu's: 



i^cj^ 2. 3 dx''fcl'X:=^C^<i C+ 2. 3D r^ +•/>) )^x (ill.) 

 Hve 2 r + 2. 3 i.v =: 2 (7+ 2. 3 Z) C^ +/>)• 

 Unde^ pofito a*ir-/', invenimus c -3^/) z=C, 

 DilFerentianda aequatione (IIL), Qst: 



2. 3 d^xzz 2. 3 Z).^:i"5 unde esc : ^ssZ). 



§ X. 



Ergo gcneratini fi liabemus partiendam fractioneni: 



a 



