[pixelbill]

These terms were coined before the Americas were discovered by Europeans.

Europe was the West, then you have the Middle East, then the Far East (China, Japan). That was the whole world to them pretty much. When the Americas were discovered they were known as the New World, and eventually became known as the West as well (Due to the fact that most of our culture comes from Europe, eg. Western Culture).

[Symbiote]

Also the Near East, which was roughly the Ottoman Empire -- countries around the Mediterranean, Black and Red Seas. ("Mediterranean": middle of land.)

I suspect Rome (or some other city in Italy) is the centre of these terms, but I haven't looked for evidence of that.