Those ancient Greeks also believed the Earth was round two millennia before Columbus or Magellan sailed. Some argued against geocentrism, too -- just not always for the right reasons.
Take the Pythagoreans, the semimystical group founded by famed mathematician Pythagoras in sixth century B.C.E. that removed Earth from the center of the universe for various reasons. To them, Earth circled a Central Fire, as did the sun, moon, planets, stars and a made-up counter-Earth (aka antichthon). At the time, setting the Earth in motion represented a radical shift in thought, but then the Pythagoreans -- who avoided beans, picking up fallen objects or touching white roosters -- waltzed to their own tune: the music of the spheres [sources: Allen; Burnet; Lewis and Chasles; Toulmin and Goodfield].
If anything, attempts to salvage geocentrism in light of contrary observations were just as wacky and far more byzantine. Mercury and Venus, whose travels appeared tangled with the sun's, were moved inward or set in orbits around it, even as it orbited us. In the second century, Claudius Ptolemy explained retrograde motion, the apparent backing and looping of planets caused by differing orbital speeds, by resorting to orbits-within-orbits called epicycles. This Aristotelian-Ptolemaic cosmology dominated until Nicolaus Copernicus put the sun back in the center where it belonged, and Galileo proved him right [sources: Encyclopaedia Britannica; Gagarin and Cohen; Toulmin and Goodfield; Yost and Daunt].