I o/j. O P U S C U L A 



§ III. 



Forinuhi generalis cxprimens proximum valorem 

 quantitatis e^ . 



Revertamiir ad aequalioncs («) , (Z<) , (c) , (^) , etc. Posilo 

 in («) successive a: = e, = e^ , =e^ , =e^ etc. habebimus 



c2 1 2 2= 23 2' 



^ =Y+ 1 -f-Y 4- 2T3 +2X4 "^ 2.3.4.5 "^ "'• 

 c^ 1 3 3^ 3^ 3' 



T = 3 '+-'' -^2' -*-2l'^23r4"^ 2-Xr5 +^"^- 

 e* 1 4 42 43 4« 



_ = -4-1 4.- + 2I +2X4-*- 2.^5 -^ '^"-■• 

 e^ 1 5 52 63 5« 



T = T -<- ^ -*-T -^ 273 •+- 2~X-4 -^ 2T3X5 + '^•" 



etc. etc. etc. 



ex quibus seriebus generatim deducitur 



cT 1 y y- y'' y' y-- 



7=7"^^ "^"2 "^ 2.1 "^2731 "^ 2T3.475 "^ 2.3.4.5.6 "^ *""• 



ideoque 



, . . y^ , y* , y' y* y* 



ey z= 1 4- y + -2 -H 273 ^- 2T4 •*- i.zJTs ^ 2X47576 "^ *'^ • 

 iiii notum est. 



Posito x=e, =^2, =e3, =e* etc, iu aequationc (1^) ha- 

 bebimus 



12 3 4 5 



.0=._1+- +^+2-374 + 273X5-^ 23X1-6 -^'■^■ 



e-^ 1 1 2.2 4.3 8.4 16.5 



2~ -^ 2^3 "^ 2.3.4 "^2.3.4.5 "^ 2.3.4.: 

 1 3.2 9.3 27.4 81.-5 



t — ~4 "^ 2 -^2.3"^ 2.3.4 '^2.3.4.5-^2.3.4.5.r.-+""- 



• 4- etc. 



2 ^2.3 ' 2.3.4^2.3.4.5 ' 2.3.4.5.6 



1 4.2 16.3 64.4 25fi..5 



— 4_ — 4. 4, . 4- ■ .4- '■ic. 



2 ^2.3^2 3. 4^2. 3.4. 5^-J. J. 4.5. (i ^ 



