What was the original purpose of the Cauchy-Schwartz inequality?

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The first discovery of the Cauchy-Schwartz inequality is attributed to Cauchy.

What was the original reason why Cauchy came up with this inequality? What did he use it for?

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Cauchy wrote:

"can be used with good advantage in the theory of radii of curvature of curves traced on any surfaces, thus in several questions of Mechanics."

This comment appears on page 305 in Bradley-Sandifer translation of the Cours d'Analyse.