Cauchy's Inequality

Theorem

 * $\displaystyle \sum {r_i^2} \sum {s_i^2} \ge \left({\sum {r_i s_i}}\right)^2$

where all of $r_i, s_i \in \R$.

Proof 2
He first published this result in 1821.

It is a special case of the Cauchy-Bunyakovsky-Schwarz Inequality.