Page:Joseph Louis de Lagrange - Œuvres, Tome 6.djvu/604

EXEMPLE II. N^o 42.

FORMATION DES TABLES DES PLANÈTES.

${\begin{array}{|l|l|}\hline &\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \mathrm {QUATRI{\grave {E}}ME\ CASE} .\\\hline \mathrm {Premier\ quotient} &{\underline {\ \ \ 1+x^{2}+0{,}40026x}}\\\mathrm {Premier\ diviseur} &\ \ \ 1-0,40026x-0,60233x^{2}-0,39896x^{3}-0,76684x^{4}+1,93135x^{5}+0,05051x^{6}-0,81340x^{7}-0,23705x^{8}-1,01554x^{9}+1,73186x^{10}\\\mathrm {Premier\ dividende} &\ \ \ 1\qquad \quad {\text{★}}\ \ \ \qquad \qquad -x^{2}\\&-1+0,40026x-0,39767x^{2}+0,79922x^{3}+1,36917x^{4}-1,53239x^{5}+0,71633x^{6}-1,11795x^{7}+0,18624x^{8}+1,82894x^{9}-1,49481x^{10}\\&\ \quad -0,40026\ \ \ +0,16021\quad +0,24109\quad +0,15969\quad +0,30693\quad -0,77304\quad -0,02022\quad -0,32560\quad +0,09488\quad +0,40648\\\mathrm {Premier\ reste} &\ \ \ {\text{★}}\qquad {\text{★}}\qquad -1,23746x^{2}+1,04031x^{3}+1,52886x^{4}-1,22546x^{5}-0,05671x^{6}-1,13817x^{7}+0,51214x^{8}+1,92382x^{9}-1,08833x^{10}\\\hline \mathrm {Deuxi{\grave {e}}me\ quotient} &{\underline {\ \ \ 1+x^{2}+0{,}44043x}}\\\mathrm {Deuxi{\grave {e}}me\ diviseur} &\ \ \ 1-0,84069x-1,23543x^{2}+0,99030x^{3}+0,04582x^{4}+0,91976x^{5}-0,41386x^{6}-1,55465x^{6}+0,87948x^{8}\\\mathrm {Deuxi{\grave {e}}me\ dividende} &\ \ \ 1-0,40026x-0,60233x^{2}-0,39896x^{3}-0,76684x^{4}+1,93135x^{5}-0,05051x^{6}-0,81340x^{7}-0,23705x^{8}\\&-1+0,84069\ \ +0,23543\quad -0,14961\quad +1,18961\,\quad -1,91106\quad +0,36804\quad +0,63489\quad -0,46562\\&\ \ \ {\text{★}}\ \ \ 0,44043x-0,36690x^{2}-0,54857x^{3}+0,42277x^{4}+0,02029x^{5}+0,41855x^{6}-0,17851x^{7}-0,70267x^{8}\\&\ \quad -0,44043\ \ +0,37026\quad +0,54414\quad -0,43616\,\quad -0,02018\quad -0,40509\quad +0,18228\quad +0,68472\\\mathrm {Deuxi{\grave {e}}me\ reste} &\ \ \ {\text{★}}\qquad {\text{★}}\qquad \quad 0,00336x^{2}+0,00443x^{3}-0,01339x^{4}+0,00011x^{5}+0,01346x^{6}+0,00377x^{7}-0,01795x^{8}\\\hline \end{array}}$

${\begin{array}{|l|l|}\hline &\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \mathrm {CINQUI{\grave {E}}ME\ CASE} .\\\hline \mathrm {Premier\ quotient} &{\underline {\ \ \ 1+x^{2}+7{,}15758x}}\\\mathrm {Premier\ diviseur} &\ \ \ 1-7,15758x+\ \ 6,09697x^{2}+\ \ 0,77576x^{3}-\ \ 1,38788x^{4}+2,43030x^{5}-\ \ 7,50303x^{6}+\ \ 4,45030x^{7}+\ \ 2,71515x^{8}-\ \ 2,57575x^{9}\\\mathrm {Premier\ dividende} &\ \ \ 1\qquad {\text{★}}\qquad \qquad \quad {\text{★}}\\&-1+7,15758x-\ \ 7,09697x^{2}+\ \ 6,38182x^{3}-\ \ 4,70909x^{4}-3,20606x^{5}+\ \ 8,89091x^{6}-\ \ 6,86060x^{7}+\ \ 4,78788x^{8}-\ \ 1,85455x^{9}\\&\ \quad -7,15758\ \ \,+51,23091\quad -43,63954\quad -\ \ 5,55254\quad +9,93385\quad -17,39509\quad +53,70353\quad -31,71025\quad -19,43390\\\mathrm {Premier\ reste} &\ \ \ {\text{★}}\quad \qquad {\text{★}}\qquad \,44,13394x^{2}-37,25772x^{3}-10,26163x^{4}+6,72779x^{5}-\ \ 8,50418x^{6}+46,84293x^{7}-26,92237x^{8}-21,28845x^{9}\\\hline \mathrm {Deuxi{\grave {e}}me\ quotient} &{\underline {\ \ \ 1+x^{2}+6{,}31338x}}\\\mathrm {Deuxi{\grave {e}}me\ diviseur} &\ \ \ 1-0,84420x-0,23951x^{2}+0,15244x^{3}-0,18830x^{4}+1,06138x^{5}-0,61002x^{6}-0,48125x^{7}\\\mathrm {Deuxi{\grave {e}}me\ dividende} &\ \ \ 1-7,15758x+6,09697x^{2}+0,77576x^{3}-1,38788x^{4}+2,43030x^{5}-7,50303x^{6}+4,43030x^{7}\\&-1+0,84420\ \ -0,76749\quad +0,69176\quad \,+0,42081\quad -1,21382\quad +0,79832\quad -0,58013\\&\ {\text{★}}-6,31338x\,+5,32948x^{2}+1,46752x^{3}-0,96707x^{4}+1,21648x^{5}-6,70471x^{6}+3,85017x^{7}\\&\ \quad +6,31338\ \ \ -5,32973\quad -1,46793\quad +0,96241\quad -1,18884\quad +6,70090\quad -3,85135\\\mathrm {Deuxi{\grave {e}}me\ reste} &\ \ \ {\text{★}}\quad \qquad {\text{★}}\quad -0,00025x^{2}-0,00041x^{3}-0,00466x^{4}+0,02764x^{5}-0,00381x^{6}-0,00118x^{7}\\\hline \end{array}}$