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 below Empirical Evidence for the Spherical Earth Theory and 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 that the Earth's surface is curved (see below Empirical Evidence for the Spherical Earth Theory).
   2. Gravity everywhere on Earth's surface points perpendicular to the Earth's surface (ignoring small local features like mountains).
   3. Points 1 and 2 imply that there is NO single direction of gravity. The simplest viable theory then is that there is a center of gravitation and gravity always points toward that center.
   4. Given points 1 and 3, every local region on the Earth's surface must form a plane perpendicular to the local gravity direction. The set of these local planes CANNOT have gaps without regions on Earth's surface NOT being perpendicular to the local gravity direction. Ergo there are NO gaps and the set of local planes must form a spherical region. Thus, the known Earth is part of a sphere.
   5. Extrapolating from the known Earth and as the simplest hypothesis, the Earth is a sphere (ignoring small local features like mountains). Thus, there is a spherical Earth.
   6. Now the astronomical objects seem to circle either the Earth or an axis through the Earth (i.e., the celestial axis).
   7. Therefore, the whole universe is spherically symmetric, more or less, and centered/balanced on the center of the Earth.
   8. To summarize, the universe is a spherically-symmetric geocentric universe.

6. Empirical Evidence for the Spherical Earth Theory:

   Empirical evidence for the spherical Earth theory in classical antiquity is discussed in Wikipedia: Spherical Earth: Antiquity. Here we will just briefly mention 4 empirical evidences:

   1. In partial lunar eclipses, the Earth's shadow (i.e., its umbra) on the Moon has a round edge. This is true whatever the orientation of the Sun and Moon are to the horizon and whatever path the Moon takes through the umbra. Unless the Earth were round, the roundness of its shadow would be hard to arrange. This argument was presented by Aristotle (384--322 BCE) without claiming originality (see Wikipedia: Spherical Earth: Classical Greece). 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. For example, seen at 10 km, the bottom 10 m of ship is below the horizon. The sinking-below-the-horizon argument was presented by Strabo (64/63 BCE--c.24 CE) without claiming originality (see Wikipedia: Spherical Earth: Roman Empire). Yours truly thinks seeing the sinking-below-the-horizon effect requires sharp-eyed sailors under the ultra-clear skys of the Mediterranean Sea. For a discussion of the distance to the horizon, see Celestial sphere file: horizon_types_formula.html

   3. As you move north and south, that astronomical phenomena shift consistently with spherical Earth theory. In particular, the stars that are circumpolar change. To explicate, in the Northern Hemisphere as you move north, more stars are never in the sky (they become south celestial pole (SCP) circumpolar) and more stars are always in the sky though invisible in the daytime (they become north celestial pole (NCP) circumpolar). In the Southern Hemisphere as you move south, it's the same mutatis mutandis. Of course, few if any ancient Greeks reached the Southern Hemisphere.

      This change in circumpolar stars is consistent with the spherical Earth theory.

      The behavior of the Sun on the celestial sphere in the course of the solar year = 365.2421897 days (J2000) as function of latitude is also consistent with thte spherical Earth theory.

   4. There were two evidences that the flat Earth theory could NOT explain simultaneously. It could explain one or the other, but NOT both. To explicate:
      1. No one had ever reached edge of the flat Earth, where you could see the Sun, Moon, and stars go down into underworld.

         Furthermore, no one had ever reached a point where those astronomical objects were seen as larger than in the Mediterranean Basin.

         Another perspective on the same points is that the horizon is always on average seen at the same distance away no matter where you are on known Earth and astronomical objects always seem the same size no matter where you are on known Earth. Note that sailors may have had this perspective from their voyages to the eastern or western ends of the Mediterranean Sea.

         The flat Earth theory had to posit that the edge of the flat Earth and the astronomical objects were so remote from the Mediterranean Basin that no one from Mediterranean Basin had ever been able to get noticeably closer to them.

      2. The ancient Greek astronomers eventually knew the stages of lunar eclipses happen at different solar times at different locations even though the stages happen, of course, at the same absolute time. To accommodate lunar eclipses in the flat Earth theory, you had to posit the horizon and the astronomical objects were rather close.

      The spherical Earth theory could explain both evidences. The astronomical objects were very far away and the spherical Earth was relatively small and the horizon was always necessarily the same distance away on average wherever you were on the spherical Earth.

Credit/Permission: © David Jeffery, 2003 / Own work.
Image link: Itself.
Local file: local link: parmenides_earth.html.
File: Ancient Astronomy file: parmenides_earth.html.