54 H I S T >0 I fR E. 



>. - 



ubi d~x pro differentiali conftanti habetur. JJinc pro inte* 

 guili propofito obtinetur feries fine iine procedens haec: 



tyx^dx — J—x^^y — . 1 x m "^ 2 ^ 



JJ-m-t-l J (ra-t-i (-n+2) g* 



~i_ ? x m ~^ 3 — etc 



-Corollarium. 



$. 14. 1.) Poflto m ~ o, ex formula generali modo 

 demonftrata fequittir haec: 



/"rax = xy- x2dy 4- -* 3 - 8 *^- — -^ 4 ^ 3 -^- -4- etc. 



qnae fub nomine feriei Bernoullianae futis nofa eft. Quae- 

 rebam equidem, nam -ex hacferie integrationem Euleri (J 1 ) 

 deducere liceret: quod cum haud fucceffit, ad formulam ge- 

 neraliorem perveni , ex qua iam pofito — — 1 loco m , et 

 ( \ -h x) K pro y j, feries Euleri ftatim colligi poteft.: dum 

 polt evolutionem integralis in feriem pro x ponatur x n . 



2.) Quodfi in formula Bemoulliana (1.) pro y pona- 

 tur y x m ? erit 



fy *■ 8 x = a»-* y - * d <* x ™ 2 + *' "' { ? *! > - etc. 



1. 2 d x 1. 2. 3 ox 2 



five, evolvendo difTerentiaJia produ&orum, s 



= x*+*y 



— £- 2 (mx™-*y-t-x m li) 



4- J^. [m (ifi — 1 ) x m ~ 2 y -4- 2 wi x 171 - 1 ** -+- x m ^\ 



I. 2. 3 x / •/ d X o -^ 2 



— jf 4 [» I ^- 1 )( m - 2 ) xm ~ 3 7 + 3m(w-i)x m ~ 2 ^ 



3wx m - I | 2 4-+-x n, ^4J 



