^ DE FRODFCnS EX INFINTnS 



erga redudtione in mfinkiim contimiata prodibit : fx^'*djt 



V Jq m • ^Ai-Httjj {m~i-ztLq) ■-.... (mT^oore^) 



fic^oo.n-r^x{i'X''^)l Ac fmiili modo t[\ Jx^-^dx^i^-x''^)^ 



___ (M^-4-(p -M)n)(u-4> (pH-:<7;^)(H--f-(P-H - q>0 ^f^-t-(p- 4-cx3^):ir .^-^Oon^l^,' 



M. ((AH-/15J (/x-f-^ri^.) . . . . ■ {\x-k-Oonq) •^'^ 



<^t(i -x^^^jl ; dnmmodo ;;/, ctnq^ct ^ fint niimeri affir- 

 iiiatiui ,, leu iiiliilo maiores.. 



§. 4Q. Qiioniam autem fi m efl: infinitiira £t fx^^dk 



(i-X'^^)|=/v'^^-V.r(i~-x^?)|, quiciinque numerus finitus. 

 loco ot accipiatur, Yti ex paragr, 3S colligitup, erit quow 

 que fx'^-^^''^--^dx{i^x''^)^-fx^-^^^^-^dx{i-x''% Quam. 

 obrem fi praecedentium expreffionum altera per alteram 



diuidatur , prouemet ifla aeQ;iatio :. '— — '-J^Z^Jl. — 



fx^-^dxXi-x''^ ~ 



t!»(m-.4-(j>-4^)n)(fx-f^/?)(mw >r j)-f-2^)nX>A^-gn^)(m-h rp-H;<7);i)(fx-4-;ng) . 



infinitum, cuius expreflionis ope innumerabilia produAa: 

 ex infinitis fadoribus conflantia exhiberi pofTunt , quorurat 

 "Valores per quadraturas curuarum aflignari poterunt- 



§. 41. Si altera formula integralis admittat integra^ 

 tionem , tum commoda expreifio infinita pro altero inte- 

 grali habebitur. Sit enim [jl==:«^, trit fx^'~'dx(i-x''^)^' 

 zn: ^^4^-> ^"^ ^^^^^^ fiibflituto prodibit /x^-^^Jtti-A;"^)| 



' ^ ngrm-t - (^.4.g)n).w^(Tn-f-( j?-ha ^)n) znq r-i^hic r^^f^ r^rn. 



• ip-^A- mip.i-iq'Ti{m^nq){p^zq)n{m-i.tnq) ^^' tUlUb UpC prU< 



innumerabilibus integralibus exprefliones per continuos fador 

 rcs in infinitum excurrentes inueniri poflimt ; eo faltem? 

 cafiii quo a:=i j quippe qui plerumque potifiimum defi* 



