l 52 



s ei z ita a fc invicem pendent, ul fit j — (i — x/""- ^" % 

 five f — (i — af-"-*. 



5. iT. Vorum ex pofteriorc nequatione difTcrentio- 

 difTerentiali melhodo dircfla eadem feries pro 2 elici potcft. 

 Ciim enim cx ferie priori, pofito x = o, fiat j — i, nunc 

 autcm pofueriinus Z — (i — x)' "*" ^" -" " j, codem cafu x n: o 

 fiet z — S — 1. lloc nolato pro z fnigamus lianc feriem: 



2 — I -h A X -h B X -\- C x^ + D x' 4- ctc. 

 iindc fit 



d z z= A -h ^Jl X -\- 3 C x= 4- 4 D x^ -f- 5 E X* -h etc. et 

 9^2 = B-t-6Cx-+- i2Dx--{- 2cExM-3cFx^H- ctc. 

 quibus valoribiis fubftitutis prodibit 



1(1 — x) c) c)2. :iz . . . -H 2 Bx-H C C jr -+-iiDx^ -+- ctc. 



— c B X* — 6 C x' -+ etc, 



c^ z= . . .. Ac-HsBc-f- sCc -+- /i- D c -+ cic. 



^(x-hfi-hj)x^Z— - ( i-+-f3-t- 1 iA-c(a-H p-H I . B-3(-^ +-f3 >- 1 )C -ctc. 



— a (3 z — -a|3-Aa|3 — B t (3 — C a (3 -elc. 



r(r — x^DSz-l-cDz — (a-i-f3-t-i)xc^2 — a (: z ~ o. 



5. i:. Singulis i^itur lcrminis ad niiiilum rcduQis 

 nancisccmur lcqucntes acquationes : 

 I. A c — a (3 izz o 

 Ji. ; B (r -H 1) — (* -+- ('^ -^ A = o 



III. 3C(c-}-2) — («-f- 2)r(3 } =) B = o 



IV. 4 D c -i- :,) - (v. -\- 3) (.3 -f- 3 . C = o 



V. 5 E(c-H4) — (<='-+-4)(.3-H4)l^~o 



ctc. 



J. 13. 



