There are really only three proofs the ancient Greeks gave for the rotundity of the earth. They are:
1. Ships appear to sink into the horizon as they recede far from the observer
2. The shadow on the moon during a Lunar Eclipse is round
3. The southern constellations of the night sky appear to rise as you travel Southwards
Samuel Birley Rowbotham and the authors of the Flat Earth Literature deal with these proofs nearly exclusively. On the sinking ship, Rowbotham describes a mechanism by which the hull is hidden by the angular limits of the human eye - the ship will appear to intersect with the vanishing point and become lost to human perception as the hull's increasingly shallow path creates a tangent beyond the resolution of the human eye. The vanishing point is created when the perspective lines are angled less than one minute of a degree. Hence, this effectively places the vanishing point a finite distance away from the observer.
Usually it is taught in art schools that the vanishing point is an infinite distance away from the observer, as so:

However, since man cannot perceive infinity due to human limitations, the perspective lines are modified and placed a finite distance away from the observer as so:

This finite distance to the vanishing point is what allows ships to ascend into horizon and disappear as their hulls intersect with the vanishing point. Every receding star and celestial body in the night sky likewise disappears after intersecting with the vanishing point.
We know that this explanation is true because it's a fact that a half sunken ship can be restored by the aid of a telescope.
As a ship recedes into the ocean's horizon, distant from the observer, it will appear to the naked eye to sink from the bottom up into the sea after it touches the horizon line. It has been found that this effect is purely perceptual, that a good telescope with sufficient zoom will change the observer's perspective and bring the ship's hull back in full view. This is not possible if the ship were really behind a "hill of water." Hence, the effect which is usually thought to prove the earth as a globe really proves it to be a plane.
It's one of the first and primary proofs of a Flat Earth. The fact that a telescope can restore a half-sunken ship demonstrates that the ship is not traveling behind a convex sea.
From
Zetetic Cosmogony by Thomas Winship we read:




