+ a H I S T O 1 R E, 



Theorema. (*) 



$. 4, Series 



j + L_ Q jf -J- r.Cr-j) gf^+x] 00 X 2H 



p ' 1-2 pip I 1 



r^-lVr-2> < ? pj+-D</7-'*2l £3 ~.3u _|_ t 



1-2. 3 pip-i Ihp-r-2) r 



aequalis eft feriei 



V P L p \i-+-f?xV J. 2 p(p * 1) 



xf -A^ Y_r...(r-0(p-g)...(p - g/ -,) / ff Y _, 1 

 \i-t-|3xV 1.2.3 pp+^to+O \i+^/ J 



DemonfTratio. 

 Sufficit , demonftraffe Theorema pro (3 _S 1 , n _z 1» 

 |am aliimde conftat (**), poilto 



S = a+bx + cf + d^-|- etc. , efife 

 Afl + B()X + Ccx 2 + D(lx 3 + etc z= 



A p _1_ A A «^ _i_ -£ A 3:2 d2 s i_ A3 A x3 d3 s , _,__ 



Aj + AA d, + -ri' T>r + **_ • T,r + etc * 

 Sit igitur 



a — j, b-.r, c — ^f^- 1 , etc ^ 



A=i,B~i-,Cz: *&_^fj , etc. 



p ' p ip -t-D 



erit primo 



S-(i+xr, J-inrfi+xr 1 , 



£i-r(r~i)(i-+-xr- 2 , etc. 



Dein- 



( # ) Ad hoc theorema alia ocrafione pervenf, eiusque demonflrationem aliun- 

 de pefitJin exhibui (in DJsquififionibus anal\ticis, Disquifit. II. §. XXV.) 



(,*f) L. Euleri Inflitutt. C.tc. difler. Pars II. Cap. II. §. _6. 



