128 



A=a-|-p; A=a — otp; 



T j- ' / -^ Ci o I 



A z= a H- (nb 4- ac -f- . . . 4- ^^^'0 P = '=^3 — ^^Pi 

 et generatim (D) A^ma, — %-iP- 



§. 6. QLiodsi in aequatione (C) litera S adhibetur 

 ad designandas summas, qiiae in aequatione (A) per lite- 

 rani R significantur (§. 1,), obtinemus 



S nR -t-p, S^nR^H-jo^ etc. in génère (E) S^,i:R^-4- jD*". 

 Jam vero in aequatione (E) pro R'" substituto ejusdem va- 

 lore ex aequatione (B) , qui quidem valor non nisi a 

 r in 1 usque ad ?'m?i demonstratus fuit (§. 3.), sequens 

 nascitur aequatio : 



(F)S=//-i-aR -t- a R -h .... -^ a R ^-^ :. 



H- a R -H r . Ci . 



r— I 1 r ■ 



§. 7. Q.uum aequatio (B) similiter competat valori 

 r — 1 (§. 3.), substituatur in ea r— 1 loco r, atque sin- 

 gulis terminis ductis in p, oritur 

 O^pR -apR — a pR —....— a pR , — a pR^ ^— 



/ r— I 1' r— 2 o' r— 3 m— 2' 1 — m+t m— 1' r~m 



et hac aequatione, quae nihilo aequatur, addita secundae 

 parti aequationis (F), obtinemus 



(G) S^ - p'" -+- (a^ -^ p) R^.__ -^- (a^ - a^p) R^_^4- (a - a^p) R^_^-t- .. 



-+- fa — a p) R , -4- (a — a p) R ■+• 



\ m— I m— 2' / r— m+i \ m m—jl / r— m 



H-(a —a p)R -f-(a —a p)R -f-r.a —(r—l).a p. 

 §. 8. Substitutis jam in aequatione (G), loco R^_j!. 



\ 



\ 



