Philosophers of ancient Athens did not visualize a "flat earth." For them, circles and spheres were the most perfect of geometric figures because of their symmetry, and they envisioned a universe of concentric spheres.
If you have only seen the night sky from the confines of a brightly lit area like a city, it might be hard to envision what the stars look like out in the country today, or in the ancient world. If you stand out in a field and look up, you see what appears to be a dome, absolutely studded with stars.
The ancients looked up and observed. They saw how the constellations moved, in fixed positions relative to one another. They saw stars set in the west and then saw the same stars rise in the east the next evening. They concluded that they were watching the motions of a sphere onto which the stars were affixed, and that the earth was a sphere at the center of that larger sphere.
But certain heavenly bodies moved in a way that seemed detached from that sphere of stars. The sun and moon were the obvious ones, but they spotted a few other "wanderers" (in Greek, "planets"). So they imagined each of these wanderers attached to its own sphere, and these concentric spheres moved at different rates as they rotated about the earth in the center. (Interestingly, they could see that the motions of Mercury and Venus were different from the rest, and their model placed those two inside the sphere of the sun.)
And they saw a great unity in all this, when they reflected upon in through the lens of their philosophical viewpoint, as follows.
The traditional "Liberal Arts" were divided into two sets: the Trivium (grammar, dialectic or logic, and rhetoric) and the Quadrivium:
Arithmetic (Number theory): the study of quantities at rest. Music: the study of quantities in motion Geometry: the study of form at rest Astronomy: the study of form in motion.
The motto of the Pythagorean school was "all is number." Thus music was about "harmonious" ratios of numbers. And the ratios of the various speeds of motion of the heavenly spheres produced what they called "the music of the spheres." Centuries later, the poet Alexander Pope would write "Oh Harmony! Heavenly Harmony!" in reference to this.
The four elements of the Quadrivium all came together in this view of the universe. To the Greek mind, this would have been very pleasing.
