unde dedacitur iftci fiiepiffime occiinens . 



/ " "- ^ \ - ^ =r a •/ - I Arc. tane;. i . 

 Porro cliam notetcir haec formula: 



l a (cof. a -h / — I fin. a) zz: l a -{- oc Y — r, 

 Pro arcubus autem has adepti fumus formulas[: 



Arc. tang. (a -h b /- i) = ^ Arc. tang. -_^— _ 



I V — I /,(i -4- &S")- --^ " " 

 • "*" 4 (X— 6,2-t-oa' 



vel etiam 



Arc. tang. a (cof. a -f- /— i fin. a) — ? Arc. tang. =_l£i^ 



• — I / I -t- 2 ajm..a -f- a a 



I — ;; a //n. a -t- a a 



J, 13. . His fundamentis conftitntis confideremus ca- 

 fus, quibus integrale fZdz per logarithmos ct arcus cir- 

 culares exprimi poteft, id quod femper evcnit, quando Z 

 eft funclio rationahs ipfius z, tum autem integrale compo- 

 nitur ex huiusmodi partibus: 



I. /(i±^); 



II. / ( I — 2 z cof. a -f- z s) ; 

 III. Arc. tang. - ^•^'^•'' : 



vel faltem integralia, qtiae reperiuntur, facile ad tales for- 

 mas redigi poffunt; Harum ergo rcfolutionem, quando fta- 

 tuitur -2: :r=j(cof. -f- /— 1 lin. (?) , nonnullas in fequentibus 

 problcmatibus expediemus. 



Problcma i. 



5. i.^. Ilanc fonnalam logarithmicam l(i zt '''')» pofito 

 z=zycof6 -t- / — ifm. ^) 

 ad formam generahm A-{-By — i reduccre. 



NQvaAUaAcad.Imp.Scient.Tom.XIL ' B Solu- 



