Aristotle, in De Caelo 2.13, claims that Anaximander believed that the earth stays where it is due to “indifference” and equidistance from everything else. The author claims that Aristotle derived this theory from his reading of Plato’s Phaedo and Timaeus. It is much more likely that Anaximander believed the earth to be supported by the vortex, or δίνη, as held by other thinkers of his time, and noticed by Simplicius in his commentary on De Caelo.
Robinson, John, "Anaximander and the Problem of the Earth's Immobility" (1953). The Society for Ancient Greek Philosophy Newsletter. 263.