227 



ent 



8. /■''"- 



— 1 — 



~" 4 ~ 



4. 6 

 ///__3. 5. 7--. 2 5 



2.Ci 



2.(3 



z 2,y 



4. 6. 8 



etc. 



erit quoque 

 s = 2 . log. 2 = log. 4 ^ hinc 

 / ~a[log. 4-hi] 

 ^'' =:(3[log.4-+-i-+-i] • 



y//. 



:y[log.4-+-n-|H-|] 

 etc. 



Etfi fortaffe fLimmationes iftae propofitarum ferierum iam 

 aliunde conftant, neque etiam methodus, qua in iis inueni- 

 endis vfus fum , difficulter ex principiis calculi integralis 

 lepetitur; eam tamen vt breuiter fubiungerem , ordo trafta- 

 tionis poftulare videbatur. 



Demondratio. 



J. 3. Seriebus propofitis fequentes tribuantur formae 

 generales charaQeribus %, X^, ^''^, etc. defignatae: 



ax4-ipx--f-|yx^-}-^5x4 4- —^, 



|3 X -+- i y X- H- ^ J x^ -h I f x^ + —%' , 



y X -^l ^ ^ -\-Ib x' -\-l^ x' -\- :=%'', 



lx-\-l^yr-\-l^x'-\-\yix^-\' —^''', 



etc. 



ita^ vt pofito X =: I fiat 2 = ^; X^ nz /; X^'' — /''; etcJ 

 Cum igitur lit ^ 



I -I- a X -H (3 x'^ ^- y x^ -h etc. = (i — x) ^; 

 differentiando et pro cl, ^, y, etc. fubftituendo valores nu- 

 mericos, colligitur: 



2. 3 S^— I. 3 5i=z 2. 



9 X 



d X 



K» y ( I — jc) 



^.dX''-:i.dl.'~^. 



d X 



Ff 2 



— 3. 



X Y (, z — X ) 

 d X 



2 . 



3 X 



X2 



d X 



d X '"! 



«s/l 



J2 — 4. ilJ2 -f- ^ 



I — «] ~ x3 x^ 



6.d 



