I am currently preparing a talk that revolves around the triangle inequality.

Because this inequality is so well-established, I do not want to (in my talk) belabor too much upon the importance it enjoys. For example, I learned some useful views [here][1]. But, these concerns are currently too advanced---for my purposes, I am seeking first some historical background; specifically,

> Approximately when, where, and how did the concept of a *triangle inequality* get formalized, and its importance recognized?


  [1]: http://mathoverflow.net/questions/65513/why-the-triangle-inequality