Page:Joseph Louis de Lagrange - Œuvres, Tome 6.djvu/592

EXEMPLE I. N^o 41.

FORMATION DES TABLES DES PLANÈTES.

${\begin{array}{|l|l|}\hline &\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \mathrm {QUATRI{\grave {E}}ME\ CASE} .\\\hline \mathrm {Premier\ quotient} &{\underline {\ \ \ 1+x^{2}+0{,}51428x}}\\\mathrm {Premier\ diviseur} &\ \ \ 1-1{,}51428x\ \ +1{,}01000x^{2}-1{,}27000x^{3}+0{,}38714x^{4}+1{,}54286x^{5}-1{,}59143x^{6}+0{,}82714x^{7}-0{,}89286x^{8}-0{,}22857x^{9}\\\mathrm {Premier\ dividende} &\ \ \ 1-x\\&-1+1{,}51428x\ \ -2{,}01000x^{2}+9{,}78428x^{3}-1{,}39714x^{4}-0{,}27286x^{5}+1{,}20429x^{6}-2{,}37000x^{7}+2{,}48429x^{8}-0{,}59857x^{9}\\&\ \quad -1{,}51428\quad +0{,}77877\quad \,-0{,}51943\quad \,+0{,}65314\quad -0{,}19910\quad -0{,}79346\quad +0{,}81844\quad -0{,}42539\quad +0{,}45918\\\mathrm {Premier\ reste} &\ \ \ {\text{★}}\qquad {\text{★}}\ \qquad -1{,}23123x^{2}+2{,}26485x^{3}-0{,}74400x^{4}-0{,}47196x^{5}-0{,}41083x^{6}-1{,}55156x^{7}+2{,}05890x^{8}-0{,}13939x^{9}\\\hline \mathrm {Deuxi{\grave {e}}me\ quotient} &{\underline {\ \ \ 1+x^{2}+0{,}32522x}}\\\mathrm {Deuxi{\grave {e}}me\ diviseur} &\ \ \ 1-1{,}83950x\ \ +0{,}60427x^{2}+0{,}38332x^{3}+0{,}33367x^{4}+1{,}26017x^{5}-1{,}67223x^{6}+0{,}11295x^{7}\\\mathrm {Deuxi{\grave {e}}me\ dividende} &\ \ \ 1-1{,}51428x\ \ +1{,}01000x^{2}-1{,}27000x^{3}+0{,}38714x^{4}+1{,}54286x^{5}-1{,}59143x^{6}+0{,}82714x^{7}\\&-1+1{,}83950\quad -1{,}60427\quad +1{,}45618\quad -0{,}27060\quad -1{,}64349\quad +2{,}00590\quad -1{,}37312\\&\ \ \ {\text{★}}\ \ \ 0{,}32522x\ \ -0{,}59427x^{2}+0{,}18618x^{3}+0{,}11654x^{4}-0{,}10063x^{5}+0{,}41447x^{6}-0{,}54598x^{7}\\&\ \quad -0{,}32522\quad +0{,}59824\quad -0{,}19652\quad -0{,}12466\quad +0{,}10853\quad -0{,}40983\quad +0{,}54384\\\mathrm {Deuxi{\grave {e}}me\ reste} &\ \ \ {\text{★}}\qquad {\text{★}}\ \qquad \quad 0{,}00397x^{2}-0{,}01034x^{3}-0{,}00812x^{4}+0{,}00790x^{5}-0{,}00464x^{6}-0{,}00214x^{7}\\\hline \end{array}}$

${\begin{array}{|l|l|}\hline &\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \mathrm {CINQUI{\grave {E}}ME\ CASE} .\\\hline \mathrm {Premier\ quotient} &{\underline {\ \ \ 1+x^{2}+0{,}30569x}}\\\mathrm {Premier\ diviseur} &\ \ \ 1+0{,}69431x\ \ +0{,}01066x^{2}-0{,}50355x^{3}+1{,}17417x^{4}+0{,}75829x^{5}+0{,}89100x^{6}+0{,}03673x^{7}-0{,}34242x^{8}-1{,}27014x^{9}\\\mathrm {Premier\ dividende} &\ \ \ 1+x\\&-1-0{,}69431x\ \ -1{,}01066x^{2}-0{,}19086x^{3}+1{,}16351x^{4}-0{,}25474x^{5}+0{,}28317x^{6}-0{,}79502x^{7}-0{,}54858x^{8}+1{,}23341x^{9}\\&\ \quad -0{,}30569\quad -0{,}21224\quad -0{,}00326\quad \ +0{,}15393\quad +0{,}35893\quad -0{,}23180\quad -0{,}27237\quad -0{,}01123\quad +0{,}10467\\\mathrm {Premier\ reste} &\ \ \ {\text{★}}\qquad {\text{★}}\ \qquad -1{,}22290x^{2}-0{,}19402x^{3}+1{,}31744x^{4}+0{,}10419x^{5}+0{,}05137x^{6}-1{,}06739x^{7}-0{,}55981x^{8}+1{,}33808x^{9}\\\hline \mathrm {Deuxi{\grave {e}}me\ quotient} &{\underline {\ \ \ 1+x^{2}+0{,}53566x}}\\\mathrm {Deuxi{\grave {e}}me\ diviseur} &\ \ \ 1+0{,}15865x\ \ -1{,}07730x^{2}-0{,}08519x^{3}-0{,}04201x^{4}+0{,}87284x^{5}+0{,}45777x^{6}-1{,}09416x^{7}\\\mathrm {Deuxi{\grave {e}}me\ dividende} &\ \ \ 1+0{,}69431x\ \ +0{,}01066x^{2}-0{,}50355x^{3}-1{,}17417x^{4}+0{,}75829x^{5}+0{,}89100x^{6}+0{,}03673x^{7}\\&-1-0{,}15865\quad +0{,}07730\quad -0{,}07346\quad +1{,}11931\quad -0{,}78765\quad -0{,}41576\quad +0{,}22132\\&\ \ \ {\text{★}}\ \ \ 0{,}53566x\ \ +0{,}08796x^{2}-0{,}57701x^{3}-0{,}05486x^{4}-0{,}02936x^{5}+0{,}47524x^{6}+0{,}25805x^{7}\\&\ \quad -0{,}53566\quad -0{,}08498\quad +0{,}57706\quad +0{,}04563\quad +0{,}02250\quad -0{,}46755\quad -0{,}24521\\\mathrm {Deuxi{\grave {e}}me\ reste} &\ \ \ {\text{★}}\qquad {\text{★}}\ \qquad \quad 0{,}00298x^{2}+0{,}00005x^{3}-0{,}00923x^{4}-0{,}00686x^{5}+0{,}00769x^{6}+0{,}01284x^{7}\\\hline \end{array}}$