Features:

1. The Presocratic philosopher Parmenides was probably the first proposer in recorded history of the spherical Earth theory (see, e.g., David Furley (1922--2010), The Greek Cosmologists, 1987, p. 41, 56).

2. Actually, for almost any ancient discovery, it just understood that there may have been unrecorded discoverers before the recorded ones. Since this is just understood, it usually goes without saying.

3. Parmenides' stated reasoning for a spherical Earth, insofar as he tells us, was philosophical: the spherical shape would allow perfect balance and this sustained the spherical Earth at the center of the cosmos which he probably thought of as spherically symmetric and centered on the spherical Earth.

4. But Parmenides may have had empirical reasons for proposing a spherical Earth that were known to later classical writers (see Wikipedia: Spherical Earth: Antiquity). Yours truly actually believes this must be so.

5. For a spherically symmetric cosmos centered on the spherical Earth, the order of Parmenides' thinking may have been as follows.
   1. Empirical evidence suggests the Earth's surface is curved.
   2. Since everywhere perpendicular to the surface is downward due to gravity, there may be a center of curvature and the known Earth may be part of a sphere.
   3. Extrapolating from the known Earth and as the simplest hypothesis, the Earth is a sphere---ignoring little perturbations like mountains. Thus, there is a spherical Earth.
   4. Now the astronomical objects seem to circle either the Earth or an axis through the Earth (i.e., the celestial axis).
   5. Therefore, the whole universe is spherically symmetric, more or less, and centered/balanced on the center of the Earth.
   6. To summarize, the universe is a spherically-symmetric geocentric universe.

6. The empirical reasons for the spherical Earth theory in classical antiquity are discussed in Wikipedia: Spherical Earth: Antiquity. Here we will just briefly mention 4 empirical reasons:
   1. In partial lunar eclipses, the Earth's shadow (i.e., its umbra) on the Moon always has a round edge which is hard to arrange unless the Earth is spherical. Of course, you have to believe that the Earth's shadow causes lunar eclipses in order to believe this reason for the spherical Earth. However, Parmenides did believe the Earth's shadow causes lunar eclipses and is, in fact, the first person in recorded history to note this fact (see, e.g., David Furley (1922--2010), The Greek Cosmologists, 1987, p. 41, 56).

   2. Ships and mountains rise and sink below the horizon as seen over the sea. Yours truly thinks seeing this effect requires sharp-eyed sailors under the ultra-clear skys of the Mediterranean Sea.

   3. As you move north and south some stars become blocked or unblocked from sight by the Earth just as if the Earth were curved.

   4. If the sky were a big dome over a flat Earth, why did no one seem ever get closer to the point where the dome passed below the flat Earth. A spherical Earth explains this.

      Another perspective on the same point is that the horizon is always on average the same distance away no matter where you are on Earth. It moves with you. Again a spherical Earth explains this.