44« 



H I S T O I R E. 



Porro, fumto r =z — i, habetur 



2. ) i — _£_ q x 71 -+- g(g-+-n 6 2 x 2 * 



(3 3 x 3 " 



3 ( 9 -)- I > ( 7 -*- 2J) 



■f3x* 



(p-q) 



-O (P -r- 



f3x u 



etc 



.(P'<1)(P-<1 



-4- 



p \ i + p x n 

 (p-q)...(p-q^i) 



P(P-+ 



fix n 



l±2l(JL x * \ 



i) \i-+-(2xV 



4- etc. 



P(P+- x )(P+-~) V-f-X / j 



Quarum aequationum ope , feries ufiatae (t.) (?.) (J. 3.) 

 pro /x^hfA+ff fponte transformantur in feriem no- 

 vam Euleri (a) (J. 1.). Pofito nimirum in aequatione (1) 

 P.= l" a p-J;+r, r = >, feries (1) (J. 3.) abit in feriem 

 (a) (J. 1.); quae eadem feries oritur ex ferie (2) (J. 3.), 

 ope aequationis (2), fumendo (3 zzr 1 3 j» — 12- -h 1 3 g — 

 I + H 1 - Simili modo feries (.3.) (J. 3.) fuppeditat fe- 

 riem (c) (J. 2.), adhibita aequatione (2), et pofito in hac 

 pro q , ~ * 4- 1 - pro p , — £ — A -f- 1 ; pio- n , 

 pro (3, A. 



?i ; 



Corollarium 2. 



J. 6. Sumatur in theoremate J. 4. r zr numero in-, 

 tegro affirmativo, ac fenerum fibi invicem aequalium termi- 

 ni ordine irivierfo coilocentnr; tum erit : 



Q (q -+- 1 ) . . . (q -+- r — 1 ) 



p(pH-i)...(pn-r-i 



£Tx™ 



1 -4- 



(p 



) 



Sx' 1 



'(r — 1 ) (jP-»-r— 1) (p + r — 2 ) 1 

 1.2 *(9- + - r -i)(9-+-r-2)'^x^ r 



H- etc 



•1 



