128 DE EXPRFSSION E 



__P P-+-q p-+-n p-hj_q _____ _p __ p_ 



P-hq ' P-+-*q • p-+-zq • p-t-t~q • ■ • • p-4-lq iq 



r-j-s r -+- 1 s r-+- ?' r +• ^s r-+- is i j 



r * r_j_j • r-_-zS • r-t-js ' ■ • — " r r 



multiplicando has duas fbrraas habebimus 



, — 11 P (r-hs) (P-+-q)(r-t-2$) ( p -+■ z q ) (r-+- t s) 



*■— fs • r(f4-j) • (r -+-*)(£-*. 2 g) • (r^^sJ^-Hs^' CtC ' 



Coroll. 3. 



21. Si ergo valor formulae integralis inuentus 

 per hanc expreffionem =: i multiplicetur , prodibit ex- 

 preffio latius patens eidem aequalis, fcilicet: 



fx m "~dx(l X n ) k ~ J ~~ a (ffH-fe"M?VM) i (m-+-kn-j-n)(p-+-q)( r-t-2S ) z{m-+kn + -2n^p^ 2 q)(r+-is) . 



"vbi pro p,q,r,s numeros quoscunque affumere iicet. 

 Pluribus modis ergo ita accipi poflunt , vt quilibet fa&or 

 ad formam fimpliciorem redigatur. 



Coroll 4. 



22. Sit pzzz:m, et qzzzn, eritque : 



r Y m-_J.J x v n,k-i—JL i(m-+-kn(r-+ -s) _(m-+ k n-t-n) (r-4-2s) 3(m-±.kn-+.7 n')(r-+is < } 

 JX aX[l-X ) - mks- (m-j t -n)(k-+-<)r (mr+.2n)i}.-+-i)(r-+s)' (m-+-in]k-t-z)(r-+. 2 s) • Clv "» 



fi porro ponatur rzzzzk. et szzzi. er;t 3 



f v m-i / } v { T v n\k-i —_l_ \(m-4-kn) _ (m-*-kn-+-n ^^'__+___ r }_) ~ f 

 _ JA U.n.i-* ) — m' (m^-v)k- (m-+. 2 n)(k-+i)'(m-+.ui)(k-+-2)' CLL * 



quae efl; expreflio primum inuenta. Sin autem fit 

 rzz-' m-i-kn, et szzzn, erit, 



Lm-iJ v /j n\h-t— V'-+-kn t(m^-kn -+.n) _ (m-+. kv -+-2n) z (m-+.kn-+-_n) 

 JX u^i.-ji j - mkn \v l -+n)(k^i)'^ml+T2n)(k+-2) m (m-+.zn)(k-^-i,y CLC * 



CorolJ. 5. 



23. Si ponatur/> = fc--}-i, et qzzit, erit : 



fffm-iJ.J. r n^,fe-f— r i(m r +-kn) !r-i-s ) _(m+kn+-n)( r-+.2S ) ,(m^ kn -i-in) ( r~i-_s) 



JX UX\l X ) -^fc^jns- m~r(k<+.2) \m^+.n)(r-+-s)(k+. s ) (m-+. i n).r-+-2S)(k-i-+) 



flt 



