Page:Joseph Louis de Lagrange - Œuvres, Tome 6.djvu/606

${\begin{aligned}\log 1{,}01805=&0{,}0077692,\\\log 0{,}98195=&9{,}9920894,\\\log {\frac {p}{2}}=\log 386=&{\underline {2{,}5865873}},\\\log \mathrm {F} =&2{,}5943565,\\\log \mathrm {G} =&2{,}5786767.\end{aligned}}$

Donc

$\mathrm {F} =392{,}97,\quad \mathrm {G} =379{,}03.$

Employant maintenant les valeurs trouvées d’après la seconde série, on aura

${\begin{alignedat}{3}q+q'\quad =&\qquad \,0{,}84420,\\q-q'\quad =&\quad \ \ \ 13{,}47096,\qquad &\log =&1{,}1293986,\qquad &2\log =&2{,}2587972,\\(q-q')^{2}=&\quad \ 181{,}46720,\\-4p'=&-{\underline {176{,}53576}},\\&4{,}93144&\log =&0{,}6929746,&{\frac {1}{2}}\log =&0{,}3464872,\end{alignedat}}$

${\begin{aligned}{\sqrt {(q-q')^{2}-4p'}}=&2{,}22069,\\q+q'=&{\underline {0{,}84420}}.\\\mathrm {Somme} \ldots \ldots \ldots \ \ &3{,}06489.\\\mathrm {Diff{\acute {e}}rence} \ldots \ldots \ \ &1{,}37649.\\\end{aligned}}$

Donc

$\varpi =0{,}68824,\quad \rho =-1{,}53244.$

Ensuite

${\begin{alignedat}{2}\log(q-q')=&1{,}1293986,\\\log {\sqrt {(q-q')^{2}-4p'}}=&{\underline {0{,}3464873}}.\\\mathrm {Diff{\acute {e}}rence} \ldots \ldots \ \ &0{,}7829113.\qquad &\mathrm {Nombre\ corr} .=6{,}06612.\end{alignedat}}$

${\begin{aligned}\log 5{,}06612=&0{,}7046755,\\\log 7{,}06612=&0{,}8491800,\\\log -{\frac {p}{2}}=\log 82{,}5=&{\underline {1{,}9164539}},\\\log(\mathrm {F} )=&2{,}6211294,\\\log(\mathrm {G} )=&2{,}7656339.\end{aligned}}$