iio METH. FACIL. ATOVE EXPEDIT. I^JTECR. 



^ — — I. Via crgo priori cft S m i -}- 2.v -i- s.v.v 

 -+- 2x' , ct 5 — ; pofito .vz=. 1 \ \nJc inagralis p.irs 

 ex faclorc i — .v oriundi crit ;/,'*^ — — J l{i — x). 

 Via aiitem polkriori cft </N ~ </.v — S .vV.v , ct -j^ 

 ^ -l^j^zrT — f poHto .V — i , prorfib vt antc. 



§. 14. Qii:irnqu:im Iv.icc mcthodus pcipctuo tiita niil- 



lisquc difficultatibus obnoxii videatur , taincn ciu:; vHis 



pcnitus cclHit , fi dcnominiuor N duos plurcsuc Iwbcit 



fnflorcs intcr (c acqualcs. Poniunus cuim denominntorcm 



N diuilibilcm cnc pcr ( /> -f- -? v )* ; crit C(^fficicns portio 



nis intcgralis /jT^ pro vno fictorc p-\-qx vti vidimus 



— ^ pofito p -f- qx ~ o fcu X zr — ^. Qiioninm vcro 



eft S rz r^ \ crit S etiamnunc prr p -}- qx diuifibilc 



idcoquc fiAo xn: — ^ fict S in o , hincque cocfikicns g 



abibic in infuiitum. Vtriu^quc crgo portionis intcgralis 



/{1^ cx binis fadoribus p-\-qx ct p-^-qx oriundac 



cocthcicns fict infinitus, altcrius quidcm affirmatiuus , altc« 



rius ncgatiuus , ita vt intcgralis portio cx biuis coninnc- 



tim oriunda fit ditKrcntia intcr duo infuiit.i, quam finit.im 



eflc pofTc cx natura infiniti latis liquct. Qiianta auttm 



fit ca diffcrcntia , cx alio fontc dccidi opoitct , qucm 



mox apcricmus. 



§ 15. Ponamus igitur fracflionis ^- dcnominatorcm N 

 duos habcrc fidorcs acqtialcs fcu diuifibilcm clfc pcr [p 

 H-<7.v)', ita \t fit N 1:1 (p-i-^.v)' S , atquc partcm 

 fracftionis •; , quac cx hoc fidlorc quadrato (p-H^.v)* ori- 

 tur, fcorfim inuefligcmus. Sit igitur pars illa znrzr—j.-^- 

 (^.^^^ i ac rcliqua pars , quac cuin hac fra<flioiKm jj 



conlli- 



