Page:Joseph Louis de Lagrange - Œuvres, Tome 6.djvu/165

ensuite,

${\begin{aligned}&{\overset {\backsim }{\Gamma }}(a_{2},a_{1})=\mathrm {A} +{\breve {\Gamma }}(a_{2},a_{1}),\\&{\overset {\backsim }{\Gamma }}(a_{3},a_{1})=\mathrm {A} +{\breve {\Gamma }}(a_{3},a_{1}),\\&\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots ,\end{aligned}}$

ce qui donne (Article XLVII)

${\begin{array}{|c|c|c|c|c|c|c|}\hline &(a_{1},a_{2})&(a_{1},a_{3})&(a_{1},a_{4})&(a_{2},a_{3})&(a_{2},a_{4})&(a_{3},a_{4})\\\hline \ {\breve {\Gamma }}\ &0{,}981&0{,}126&0{,}018&0{,}942&0{,}087&0{,}576\\\hline \end{array}}$

${\begin{array}{|c|c|c|c|c|c|c|}\hline &(a_{2},a_{1})&(a_{3},a_{1})&(a_{4},a_{1})&(a_{3},a_{2})&(a_{4},a_{2})&(a_{4},a_{3})\\\hline \ {\breve {\Gamma }}\ &1{,}558&0{,}320&0{,}083&1{,}506&0{,}245&1{,}013\\\hline \end{array}}$

LXXXVI.

Donc, faisant ces substitutions, et remettant ${\frac {{\mathfrak {S}}_{1}}{\mathbb {Z} \!^{\upsilon }}},{\frac {{\mathfrak {S}}_{2}}{\mathbb {Z} \!^{\upsilon }}},\ldots ,$ au lieu de $n\chi _{1},n\chi _{2},\ldots ,$ on aura

${\begin{aligned}n\varpi _{1}=&0{,}981{\frac {{\mathfrak {S}}_{2}}{\mathbb {Z} \!^{\upsilon }}}+0{,}126{\frac {{\mathfrak {S}}_{3}}{\mathbb {Z} \!^{\upsilon }}}+0{,}018{\frac {{\mathfrak {S}}_{4}}{\mathbb {Z} \!^{\upsilon }}}+0{,}018660\nu +0{,}0000003,\\n\varpi _{2}=&1{,}558{\frac {{\mathfrak {S}}_{1}}{\mathbb {Z} \!^{\upsilon }}}+0{,}942{\frac {{\mathfrak {S}}_{3}}{\mathbb {Z} \!^{\upsilon }}}+0{,}087{\frac {{\mathfrak {S}}_{4}}{\mathbb {Z} \!^{\upsilon }}}+0{,}007404\nu +0{,}0000010,\\n\varpi _{3}=&0{,}320{\frac {{\mathfrak {S}}_{1}}{\mathbb {Z} \!^{\upsilon }}}+1{,}506{\frac {{\mathfrak {S}}_{2}}{\mathbb {Z} \!^{\upsilon }}}+0{,}576{\frac {{\mathfrak {S}}_{4}}{\mathbb {Z} \!^{\upsilon }}}+0{,}002904\nu +0{,}0000040,\\n\varpi _{4}=&0{,}083{\frac {{\mathfrak {S}}_{1}}{\mathbb {Z} \!^{\upsilon }}}+0{,}245{\frac {{\mathfrak {S}}_{2}}{\mathbb {Z} \!^{\upsilon }}}+1{,}013{\frac {{\mathfrak {S}}_{3}}{\mathbb {Z} \!^{\upsilon }}}+0{,}000936\nu +0{,}0000222.\end{aligned}}$