72 OBSERVATIONES 



quae ergo hanc aeqnationem integralem ^''zz^zz-^u 

 in fe compkditur^ idque cafu quo conftans Ci: — 9» 

 propterea quod eft jznlu+^.u -{-'^u + Qtc. ideoque 

 fumto u infinite paruo zzzi^^V ^u. 



XXII. 



Cum nulla Yij pateat, lianc aequationem diflfe- 

 rentialem fecundi gradus Tlterius reducendi , operae 

 pretium erit inueftigare , quomodo et quatenus ea 

 cum aequatione finita z* z:: ^ z z -^ 3« conueniat. 

 In hunc finem repraefentemus aequationem differen- 

 tialem hac forma : 



Lzddz-^^Mzdudz^VlS^z^duz^^Cdu 



\t fitL3:()4( !-«'); Mzz-g^uw^ et N=^su 

 at aequatio finita differentiata dat 



%z' dzzz%zdz—:^du feu Sdz{u—zz)zzzdu 

 vnde fit porro difFercntiando : 



Sddziu-zz^zniCzdz^-^dudzzz^j^^^^du^ 



Cum ergo fit 



dz z p*. ddz 9 g^ — y u 2 



du »(u — zz) cTu- — ' 6a[u-zz)^ 



prodibit fada fublUtutione haec aequatio 



(l U^^^Z^irZZ 'U) 12UUZ+ 



JrSUZ*=:zC feu 



(U S^zP J4 ZZ 



(i-u^z^^zz-^ju^-i^uu-^-su^z^z^iu-zzY+Ciu-zzyzio 

 quae euoluta et ope aequationis z^zz^zz — ^u^d 

 poteftates ipfius z odaua minores deprefla perducit 

 ad hanc : 



(9 + C) 



