307 



quac ad rationalitatem perducta hans induct forinam : 



P >• o h l e m a 2. 



§. 6. Denotanle i numerum qxiemcunque , sac mtegnim , sive 

 fractum, ad rationalitatem perducere formulam : 



J (y-H gx'")"- y {a -h bx""}-^ ' 



S 1 u t i 0. 



Ponamus „ — zz: v , ita ut habeamus — rx ;? n^V^^ 



}/ (a 4- Z^a;'") ^ a-f-èx'" if' 



sumtisque logarithmis erit 



n ly zzz in Ix — l{ a ~\- J.r'") 



unde sumtis differentialibus fiet 



èy aihx 



Hinc autem sequitur fore 



aix'^ ^'dx 



(a -I- b x'") y^a-i-b .x'") 

 e» quo concluditur fore 

 x'-^dx 



(a-hbxfn)^y 



ya-f-bx'" "' 



Est vero a:'" = ^-^"-^ , ideoque 



a -f- bx'" z= — ? — 

 unde porro fit 



x'-^dx 



dy 



"yCa-i-bx'") '(1 — fc>") 



Tum vero , quoniam est 



39 • 



