Cauchy Schwarz Inequality Original Reference

Question

The inequality is well known to experts in linear algebra and computational geometry. However, I want to know the original source of the inequality (in the form of a published journal article, if exists) which I can cite in my report. I am insisting on it since a lot of people in my field (telecommunication engineering) may not be familiar with it and a citation will make it more credible when I use it.

Answer 1

Please read the following website. You may find your answer there. http://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality

Answer 2

In the case of ${\mathbb R}^3$, it seems you can go back to J.L. Lagrange in 1773 (Oeuvres, t. 3. Gauthier-Villars, Paris, 1869, page 662/3).