Let be a locally Euclidean coordinate system. Then
(1)
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Now plug in
(2)
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(3)
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to obtain
(4)
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Reading off the coefficients from
(5)
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gives
(6)
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(7)
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(8)
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Making a change of coordinates gives
(9)
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(10)
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(11)
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(12)
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(13)
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(14)
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