We've heard a lot lately about great athletic rivalries, most notably between Olympic swimmers Michael Phelps and Ryan Lochte. So it's worth noting the source of this watery word.
In ancient Rome, the word rivus meant "a small stream," and its derivative, rivalis, meant "of or belonging to a small stream or brook." Later, rivalis came to refer literally to "someone who lives on the opposite side of a small stream from another." It's easy to see how this idea of neighbors who have to share something important could lead to the idea of rivalry in other kinds of competition, such as love, business, politics, or athletics.
Although it's tempting to see a direct connection between rival and river, it seems the latter derives from Latin ripa, "riverbank or shore," the source also of riparian, "having to do with riverbanks." There's also a trace of ripa in the English word arrive; in its earliest sense, arrive had to do with the idea of "reaching shore, coming into port." It derives from Latin ad, "to," and ripa, "shore."
Incidentally, the words derive and derivation are themselves etymologically downstream from Latin rivus. Both derive from Latin derivare, literally, "to lead, turn or draw off" a stream of water.
Any further comments about small streams and Olympic pools are best left to the experts.
Photo by Melissa Wiese. Used under a Creative Commons license.