Page:Annales de mathématiques pures et appliquées, 1812-1813, Tome 3.djvu/158

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ANALISE INDÉTERMINÉE

${\begin{aligned}(bc'-cb')a-(ac'-ca')b+(ab'-ba')c+od+\ldots &=0,\\(bd'-db')a-(ad'-da')b+oc+(ab'-ba')d+\ldots &=0,\\(cd'-dc')a+ob-(ad'-da')c+(ac'-ca')d+\ldots &=0,\\oa+(cd'-dc')b-(bd'-db')c+(bc'-cb')d+\ldots &=0,\\\ldots \ldots \ldots \ldots \ldots \ldots \ldots &\ldots ,\\(bc'-cb')a'-(ac'-ca')b'+(ab'-ba')c'+od'+\ldots &=0,\\(bd'-db')a'-(ad'-da')b'+oc'+(ab'-ba')d'+\ldots &=0,\\(cd'-dc')a'+ob'-(ad'-da')c'+(ac'-ca')d'+\ldots &=0,\\oa'+(cd'-dc')b'-(bd'-db')c'+(bc'-cb')d'+\ldots &=0,\\\ldots \ldots \ldots \ldots \ldots \ldots \ldots &\ldots ,\\\end{aligned}}$

3.^o dans le cas de trois équations

$\left.{\begin{aligned}&(bc'd''-bd'c''+db'c''-cb'd''+cd'b''-dc'b'')a\\-&(ac'd''-ad'c''+da'c''-ca'd''+cd'a''-dc'a'')b\\+&(ab'd''-ad'b''+da'b''-ba'd''+bd'a''-db'a'')c\\-&(ab'c''-ac'b''+ca'b''-ba'c''+bc'a''-cb'a'')d\\+&\ldots \ldots \ldots \ldots \ldots \ldots \ldots \\\end{aligned}}\right\}=0,$

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$\left.{\begin{aligned}&(bc'd''-bd'c''+db'c''-cb'd''+cd'b''-dc'b'')a'\\-&(ac'd''-ad'c''+da'c''-ca'd''+cd'a''-dc'a'')b'\\+&(ab'd''-ad'b''+da'b''-ba'd''+bd'a''-db'a'')c'\\-&(ab'c''-ac'b''+ca'b''-ba'c''+bc'a''-cb'a'')d'\\+&\ldots \ldots \ldots \ldots \ldots \ldots \ldots \\\end{aligned}}\right\}=0,$

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