Page:Joseph Louis de Lagrange - Œuvres, Tome 5.djvu/334

$\mathrm {C} ''\cos \gamma +\mathrm {D} ''\cos \delta +\mathrm {E} ''\cos \varepsilon +\mathrm {F} ''\cos \varpi -0{,}03437=0,$

$-2{,}5693\mathrm {C} ''\cos \gamma +0{,}0383\mathrm {D} ''\cos \delta +4{,}1127\mathrm {E} ''\cos \varepsilon +4{,}5591\mathrm {F} ''\cos \varpi$

$-0{,}00895=0,$

$1{,}8631\mathrm {C} ''\cos \gamma -0{,}0698\mathrm {D} ''\cos \delta +4{,}4481\mathrm {E} ''\cos \varepsilon +5{,}9063\mathrm {F} ''\cos \varpi$

$-0{,}02314=0,$

$-0{,}3993\mathrm {C} ''\cos \gamma +0{,}0205\mathrm {D} ''\cos \delta -24{,}2205\mathrm {E} ''\cos \varepsilon +17{,}7634\mathrm {F} ''\cos \varpi$

$-0{,}09422=0\,;$

d’où l’on tire

${\begin{alignedat}{2}\mathrm {C} ''\sin \gamma \ =&0{,}01251&\mathrm {C} ''\cos \gamma \ =&0{,}00273\\&8{,}0973614,\qquad \qquad &&7{,}4353346,\\\mathrm {D} ''\sin \delta \ =&0{,}02526&\mathrm {D} ''\cos \delta \ =&0{,}02848\\&8{,}4024162,&&8{,}4545400,\\\mathrm {E} ''\sin \varepsilon \ =&-0{,}00139&\mathrm {E} ''\cos \varepsilon \ =&-0{,}00092\\&\quad \ 7{,}1412930,&&\quad \ 6{,}9615682,\\\mathrm {F} ''\sin \varpi =&0{,}00167&\mathrm {F} ''\cos \varpi =&0{,}00409\\&7{,}2227479,&&7{,}6111361,\end{alignedat}}$

et de là

${\begin{aligned}\gamma =&77^{\circ }43'0'',\\\delta =&360^{\circ }-41^{\circ }34'10'',\\\varepsilon =&180^{\circ }+56^{\circ }31'50'',\\\varpi =&22^{\circ }14'20'',\end{aligned}}$

${\begin{alignedat}{4}\mathrm {C} ''=&0{,}01281&\mathrm {D} ''=&0{,}03807&\mathrm {E} ''=&0,00166&\mathrm {F} ''=&0,00441\\&8{,}1074203,\ \ &&8{,}5805533,\ \ &&7{,}2200506,\ \ &&7{,}6447084\,;\end{alignedat}}$

enfin, multipliant ces dernières valeurs respectivement par celles du n^o 70, on aura

${\begin{alignedat}{4}\mathrm {C} '''=&-0{,}03290&\mathrm {D} '''=&0{,}00146&\mathrm {E} '''=&0{,}00683&\mathrm {F} '''=&0{,}02012\\&\quad \ 8{,}5172283,&&7{,}1641374,&&7{,}8341818,&&8{,}3035884,\\\mathrm {C} ^{\scriptscriptstyle {\text{IV}}}=&0{,}02386&\mathrm {D} ^{\scriptscriptstyle {\text{IV}}}=&-0{,}00266&\mathrm {E} ^{\scriptscriptstyle {\text{IV}}}=&0{,}00738&\mathrm {F} ^{\scriptscriptstyle {\text{IV}}}=&0{,}02606\\&8{,}3376495,&&\quad \ 7{,}4245580,&&7{,}8682242,&&8{,}4160224,\\\mathrm {C} ^{\scriptscriptstyle {\text{V}}}\ =&-0{,}00511&\mathrm {D} ^{\scriptscriptstyle {\text{V}}}\ =&0{,}00078&\mathrm {E} ^{\scriptscriptstyle {\text{V}}}\ =&-0{,}04020&\mathrm {F} ^{\scriptscriptstyle {\text{V}}}\ =&0{,}07839\\&\quad \ 7{,}7087403,&&6{,}8913180,&&\quad \ 8{,}6042337,&&8{,}8942337.\end{alignedat}}$