Simulac autem Lemma conceditur pro potentia n , 

 valebit quoque pro potentia n -+- i , quod fequente modo 

 demonftrabimus. Curn in genere fit 



Ax' l + l — (x-hi)^ 1 - x 71 ^ 1 _- (n-+-i) x n 4- ( ^i«x n ~ z -+- cet. 

 «t pofiio x.-f- J loco x, 



7 A x*^ 1 _=' (w-f-0 (x-f-i) n -f- ( -±|_ (x +-I)' 1 " 1 -h cet. 



ubi Coefficientes ex Theoremate Binomiali cognitae funt , 

 fequitur 



^x^^^x^^-Ax^^-frt + iJtfx+if-xl. 

 H- ( B . o rn [(x -f- if- 1 — x 1 - 1 ] -4- cet. 



_r (n + ilAxV ^^^ f-^ ^^-^ Aaf^+cet 



V / x. 2 I- 2. 3. 



unde fcripto i-j-i loco x fit 



/ A 2 x ^i _ ^ _^_ ,j j-( x + 2 y _ ^ x+ ,^-j 



+ i*±*nfo ^ 2 y~x __(-£_<_ i)^if_|Icet. 



= (/i-f-0 ^.iV^^f^+ ^ V'""" 11 -**"'-*-<**■ 



x / X 54" X=-2. 3 



ideoque 



A J *W=_ / A 8 x n - + - r — A* x n + I __ (rc-+-i) ( _ x n — A x n ) -+- cefc 

 __ (n-+- i) A 2 x n -+- ( - n -±- 1 - A 2 x n - X -+-_±1^LI__> A 2 x ,x ~ 2 -+- cet. 



V- . / I. X X. 2- 3 



Cum haec expremo fubdita fit legi 



quae quidem lex modo demonftrata fuit cafu r_-i, r_2, 

 r _ 3 , facile oftenditur, fi lex valeat pro r, eandem quo- 

 que valere pro r+i. Subftituto fcilicet in hac expreffio- 

 ne x -+- i loco x, obtinetur 



/ A r l n + I =_-("rn-i) / A r "~ I V -+■ ___£_ _ r - 1 ' x 71 - 1 -*- cet. 



ideo- 



