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Joseph Louis de Lagrange - Œuvres, Tome 6.djvu/611
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Remarque
I, N
o
43.
D’APRÈS LES OBSERVATIONS.
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+
456
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168
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274
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933
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220
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631
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274
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168
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456
−
933
+
494
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463
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224
{\displaystyle {\begin{array}{|c|}\hline \mathrm {PREMI{\grave {E}}RE\ CASE} .\\\hline {\begin{array}{lllllll}\ \ +456\quad &-168\quad &+274\quad &-933\quad &+220\quad &+631\quad &-232\ \ \ \\&&&&+274&-168&+456\\&&&-933&+494&+463&+224\end{array}}\\\hline \end{array}}}
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933
2.9698816
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494
2.6937269
9.7238453
0
,
52948
9.4476906
0
,
28034
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463
2.6655810
9.6956994
0
,
49625
9.4195447
0
,
26275
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224
2.3502480
9.3803664
0
,
24008
−
1
,
22341
0.0875722
1
,
03231
0.0138101
9.9262379
0
,
84380
{\displaystyle {\begin{array}{|c|}\hline \mathrm {DEUXI{\grave {E}}ME\ CASE} .\\\hline {\begin{array}{llllll}-933&2.9698816&\quad {\text{––––}}\\+494&2.6937269&9.7238453&0,52948&9.4476906&0,28034\\+463&2.6655810&9.6956994&0,49625&9.4195447&0,26275\\+224&2.3502480&9.3803664&0,24008\\\hline -1,22341&0.0875722\\1,03231&0.0138101&9.9262379&0,84380\\\end{array}}\\\hline \end{array}}}
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28034
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26275
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03231
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x
★
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31332
x
{\displaystyle {\begin{array}{|c|}\hline \mathrm {TROISI{\grave {E}}ME\ CASE} .\\\hline {\begin{array}{l|l}\mathrm {Premier\ quotient} \quad \ldots &{\underline {\ \ \ 1+x^{2}+0,52948x}}\\\mathrm {Premier\ diviseur} \ldots \ldots &\ \ \ 1-0,52948x-0,49625x^{2}-0,24008x^{3}\\\mathrm {Premier\ dividende} \ \ \ldots &\ \ \ 1\quad \qquad {\text{★}}\qquad \qquad \ \ \ -x^{2}\\&-1+0,52948x-0,50375x^{2}+0,76956x^{3}\\&\quad \ -0,52948\ \ \ +0,28034\quad +0,26275\\\mathrm {Premier\ reste} \ldots \ldots \ldots &\ \ {\text{★}}\ \qquad \quad {\text{★}}\quad -1,22341x^{2}+1,03231x^{3}\\\\\hline \\\mathrm {Deuxi{\grave {e}}me\ quotient} \ldots &{\underline {\ \ \ 1+x^{2}+0,31332x}}\\\mathrm {Deuxi{\grave {e}}me\ diviseur} \ \ldots &\ \ \ 1-0,84380x\\\mathrm {Deuxi{\grave {e}}me\ dividende} &\ \ \ 1-0,52948x\\&-1+0,84380x\\&\ \ \ {\text{★}}\quad 0,31332x\\\end{array}}\\\hline \end{array}}}
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+
358
−
657
−
360
+
860
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181
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305
−
457
−
360
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657
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358
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860
−
541
−
352
−
99
{\displaystyle {\begin{array}{|c|}\hline \mathrm {QUATRI{\grave {E}}ME\ CASE} .\\\hline {\begin{array}{lllllll}\quad +358\quad &-657\quad &-360\quad &+860\quad &-181\quad &+305\quad &-457\quad \\&&&&-360&-657&+358\\&&&+860&-541&-352&-\ \ 99\\\end{array}}\\\hline \end{array}}}
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+
860
2.9344985
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541
2.7331973
9.7986988
0
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62907
9
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5973976
0
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39573
−
352
2.5465427
9.610442
0
,
40930
9
,
4107430
0
,
25748
−
99
1.9956352
9.0611367
0
,
11512
1
,
19493
0.0773425
1
,
00167
0.0007245
9.9233820
0
,
83827
{\displaystyle {\begin{array}{|c|}\hline \mathrm {CINQUI{\grave {E}}ME\ CASE} .\\\hline {\begin{array}{llllll}+860&2.9344985\\-541&2.7331973&9.7986988&0,62907&9,5973976&0,39573\\-352&2.5465427&9.610442&0,40930&9,4107430&0,25748\\-99&&1.9956352&9.0611367&0,11512\\\hline 1,19493&0.0773425\\1,00167&0.0007245&9.9233820&0,83827\\\end{array}}\\\hline \end{array}}}
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00167
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209207
{\displaystyle {\begin{array}{|c|}\hline \mathrm {SIXI{\grave {E}}ME\ CASE} .\\\hline {\begin{array}{l|l}\mathrm {Premier\ quotient} \quad \ \ldots &{\underline {\ \ \ 1+x^{2}+0,62907x}}\\\mathrm {Premier\ diviseur} \ldots \ldots &\ \ \ 1-0,62907x-0,40930x^{2}-0,11512x^{3}\\\mathrm {Premier\ dividende} \ \ \ldots &\ \ \ 1\quad \qquad {\text{★}}\qquad \qquad \ \ \ -x^{2}\\&-1+0,62907x-0,59070x^{2}+0,74419x^{3}\\&\quad \ -0,62907\,\ \ +0,39573\quad +0,25748\\\mathrm {Premier\ reste} \ \ldots \ldots \ldots &\ \ {\text{★}}\,\qquad \quad {\text{★}}\quad -1,19497x^{2}+1,00167x^{3}\\\\\hline \\\mathrm {Deuxi{\grave {e}}me\ quotient} \ \ \ldots &{\underline {\ \ \ 1+x^{2}+0,20920x}}\\\mathrm {Deuxi{\grave {e}}me\ diviseur} \ \ \ \ldots &\ \ \ 1-0,83827x\\\mathrm {Deuxi{\grave {e}}me\ dividende} \ldots &\ \ \ 1-0,62907x\\&-1+0,83827\\&\ \ \ {\text{★}}\quad 0,209207\\\end{array}}\\\hline \end{array}}}