Novi commentari Academiae Scientiarum Imperialis Petropolitanae . m ^p conllante ob dH - ^-^y ^{^-^PP) __ PJ^JXSlI^^I^ dV{2-h5pp)^ — df~ ^ ^p __ ppdd? (i-{-pp) pd?[i-\-2pp) ^ __ pdd?{i-^ppY ^dVji-^-pp^^ — dp ^ dp ^ IV. IN ANALVSl INFINITORrM. 135 IV. Ponatur dy— i^-p^l erit ^ z — ^^^L±i> ?Hinc fit z -^y^jq d X et .=;—/—/--; duae ergohae formulae integrabiks funt reddendae. Ponaturfq d X zn qx —Jxdq z=iqx -M J q ~- q -r-J qq q -\^ ^^ Tt fit X -- j^ — -^ ; ergo q — ^^ Sint iam M et N fundiones quaecunque ipfius u^ et ob j dNddM—i MddN « ^ = -TdNTT^ >nN— erit : . —!idN ^ , • . d M
Novi commentari Academiae Scientiarum Imperialis Petropolitanae . m ^p conllante ob dH - ^-^y ^{^-^PP) __ PJ^JXSlI^^I^ dV{2-h5pp)^ — df~ ^ ^p __ ppdd? (i-{-pp) pd?[i-\-2pp) ^ __ pdd?{i-^ppY ^dVji-^-pp^^ — dp ^ dp ^ IV. IN ANALVSl INFINITORrM. 135 IV. Ponatur dy— i^-p^l erit ^ z — ^^^L±i> ?Hinc fit z -^y^jq d X et .=;—/—/--; duae ergohae formulae integrabiks funt reddendae. Ponaturfq d X zn qx —Jxdq z=iqx -M J q ~- q -r-J qq q -\^ ^^ Tt fit X -- j^ — -^ ; ergo q — ^^ Sint iam M et N fundiones quaecunque ipfius u^ et ob j dNddM—i MddN « ^ = -TdNTT^ >nN— erit : . —!idN ^ , • . d M d N f. - -t- y dNjJM—JMddN ~ •^^ ^ _ _, ivT ^—7 dNddM — iMddN -T- i^ d M d -J ( j M — :iN) _ M —N ergo j— dividjM-jMddN 1 dM dN ) M-+-N eC C—dNddM—dMddN ^ pontis fiat Jxdq ~ /VI, vt fit //^^a — qx lam fit /^—?- =r Q_, ideoque M c:::: ^-JT •> 90 valoreper ^ inuanto, cum Q_ fit fundio ipfius </, erit x—\^\z H-/ ^qx-m tt z-y—~ -\-li -^ ^(^, feu ob^M = q:p4-3^^^Q,erit liiiic-. ^6T)E METHOW BlOTHJKTEJE ANJWCA hiDcqiie propterea — OddCt , qlQq- VL Vel fiat /*^ rr N, vt habeatur x-^^tr. fxd^^ JqqdN — qqN — ^Jlsi qdq. lam ponatutJNq d q-Q^ exiftente Q^ fundione quacunque ipfius q^«que erit N r= i^. ,iN=: f^^J - f^^ vnde fiet j+^ = 2|^-•-2||S--(-2 qQuamobrem nancifcemur has formulas: gddCL dQ. * dg* * d q „ (^*?—OdaQ- i^^ O J 7dq*- ? dl -T- Vi ^ {qq-+->)ddQ,__ ai^ * rdq* dq ~r-\i. VII. Ad alias formulas inoeniendas ponamus:Jx=z tipdu j dy -zz duipp-x) tt dz -^z du{pp-^-i) eritque: xz^ ^Jpdu^y-^-z — z fppdu; z-yzz^u ergo quaeftio ad has duas formulas reducitur:Jpdu=zpu -Judp \ Jppdu — ppu- vijupdp. Sit nunc Judp — M, et fupdp — N, erit: dn dN . 1 dH i^ dMddfi — dyidin U^Tp= pfp^ ideoque p-^€tdp=z aK , dHl . z»-j> Tuae u — iti^dd^dHddn. — • Porro J^ AKALTSl INFINirORVM, 137 Porro eft fp(fii = r ~ d^^^^d^n - M, etJpp c/u =: -^^ —? ^^j^j loJyi - 2 N ^ ergo TJW
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