->Ui ) 38 ( |<^<- 



§. 16. ViciiTim igitur, fi proponatur ifta feries lo- 

 garithmorum : 



s =^l I— /2-4-/3— /4-4-/5— /5-h-/7 etc. 

 eius fumma affignari potcrit. Cum enim fit S- 2 j- — -/i — o, 

 ohS—J'- erit j — 5/i- — /V^; fuie cum fit 7r>2 erit 

 s:iz — iy~: ifta fcilicet fumma s erit negatiua. 



Exemplum II. quo b — i Qt n — 3. 



§. 1 7. Hoc igitur cafu , quo a~ 2 ^ formula inte- 

 granda propofita erit 



f xdx ( ■ — x )- _— rxdx^ i — r 



J Ix ' I — x^ ~ ■^ Ix ' ' -i- X -+- X X 



deinde cum fit fin. ^ = '^;^, valor quaefitus erit S = /*-;^^;at 

 vero idem Talor S per rcriem logarithmorum exprelTus ob 

 a z^ 2. -j b — c — 1 et jj — 3 erit 



r /2+/5-f /8H- /ii+/i + -f /17 f etc. 

 S — : <— 2/3 — 2/6 — 2/9 — 2/12 — 2/15— etc. 

 C 4- /4 -f / 7 -f / 1 o -f y 1 3 -f / 1(5 4- / 1 9 -f etc._ 

 {lcque ergo erit 



S=:/2-2/3-H/4 + /5-i/<J'i-/7 -f-/8-i/9^-/io 



-}-/ii-2/i2-f-/i3-f-/i4 etc. 

 cuius ergo feriei fatis rcgulaiis liimma eft Sn/^~. 



Exemplum Ili. quo ^ = 2 et « = 3- 



§. 18. Hoc igitnr cafu crit a—j et formula no- 

 ftra integralis fict 



S — /"■— ( ' — X xj^ — rd^x ( I — x)( t -hx ) 

 ~^J Ix ' V^x"' J Ix ' i-+-3c-Ha:Jc 



cuius ergo valor crit Szr/i^^at vero idcm valor S per 

 feriem logarithmorum exprcffus ob a—i, b — c~ 2 et 



/i -f/44. /7-f/io-f/i3+ ctc. ■ 

 S~ -^— 2/3 — 2/(j— 2/9 — 2/12 — etc. 



-1-/5 4- / 8 +/11 4-/ 14 + etc. fic- 



