Pagina:Werkecarlf03gausrich.djvu/209

VII. Termini septem, ${\textstyle n=6.}$

${\textstyle {\begin{array}{rl}U^{\phantom {\prime }}=&u^{7}-{\frac {21}{13}}u^{5}+{\frac {105}{143}}u^{3}-{\frac {35}{429}}u\\U^{\prime }=&u^{6}-{\frac {50}{39}}u^{4}+{\frac {283}{715}}uu-{\frac {256}{15015}}\\T^{\phantom {\prime }}=&t^{7}-{\frac {7}{2}}t^{6}+{\frac {63}{13}}t^{5}-{\frac {175}{52}}t^{4}+{\frac {175}{143}}t^{3}-{\frac {63}{286}}tt+{\frac {7}{429}}t-{\frac {1}{3432}}\\T^{\prime }=&t^{6}-3t^{5}+{\frac {535}{156}}t^{4}-{\frac {145}{78}}t^{3}+{\frac {1377}{2860}}tt-{\frac {223}{4290}}t+{\frac {323}{240240}}\\&a^{\phantom {\prime \prime \prime \prime \prime \prime }}=0{,}0254460438\;\;286202\\&a^{\prime {\phantom {\prime \prime \prime \prime \prime }}}=0{,}1292344072\;\;003028\\&a^{\prime \prime {\phantom {\prime \prime \prime \prime }}}=0{,}2970774243\;\;113015\\&a^{\prime \prime \prime {\phantom {\prime \prime \prime }}}=0{,}5\\&a^{\prime \prime \prime \prime {\phantom {\prime \prime }}}=0{,}7029225756\;\;886985\\&a^{\prime \prime \prime \prime \prime {\phantom {\prime }}}=0{,}8707655927\;\;996972\\&a^{\prime \prime \prime \prime \prime \prime }=0{,}9745539561\;\;713798\\R^{\phantom {\prime \prime \prime }}=&R^{\prime \prime \prime \prime \prime \prime }=0{,}0647424830\;\;844348\quad \log .=8{,}8111893529\\R^{\prime {\phantom {\prime \prime }}}=&R^{\prime \prime \prime \prime \prime {\phantom {\prime }}}=0{,}1398526957\;\;446384\quad {\phantom {\log .=.}}9{,}1456708421\\R^{\prime \prime {\phantom {\prime }}}=&R^{\prime \prime \prime \prime {\phantom {\prime \prime }}}=0{,}1909150252\;\;525595\quad {\phantom {\log .=.}}9{,}2808401093\\R^{\prime \prime \prime }=&{\frac {256}{1225}}\,\;=0{,}2089795918\;\;367347\quad {\phantom {\log .=.}}9{,}3201038766\end{array}}}$

Horum coëfficientium, ${\textstyle R^{\prime \prime \prime }}$ excluso, expressio generalis

${\textstyle -{\frac {1859}{16800}}u^{4}-{\frac {1573}{29400}}uu+{\frac {7947}{39200}}}$

Correctio proxime ${\textstyle ={\frac {1}{176679360}}L^{\scriptscriptstyle XIV}}$

23.

Coronidis loco methodi nostrae efficaciam ob oculos ponemus computando valorem integralis

$$\int {\frac {dx}{\log x}}$$

ab ${\textstyle x=100000}$ usque ad ${\textstyle x=200000.}$

I. Ex termino uno habemus ${\textstyle \Delta RA=8390{,}394608}$

II. Ex terminis duobus fit ${\textstyle \ldots \left\{{\begin{array}{ll}\Delta RA&=4271{,}810097\\\Delta R^{\prime }A^{\prime }&=4134{,}144502\\\hline {\text{Summa}}&=8405{,}954599\end{array}}\right..}$

III.Ex terminis tribus ${\textstyle \ldots \ldots \left\{{\begin{array}{ll}\Delta RA&=2390{,}572772\\\Delta R^{\prime }A^{\prime }&=3729{,}064270\\\Delta R^{\prime \prime }A^{\prime \prime }&=2286{,}599733\\\hline {\text{Summa}}&=8406{,}236775\end{array}}\right.}$