The evidence for a flat earth is derived from many different facets of science and philosophy. The simplest is by relying on ones own senses to discern the true nature of the world around us. The world looks flat, the bottoms of clouds are flat, the movement of the Sun; these are all examples of your senses telling you that we do not live on a spherical heliocentric world. This is using what's called an empirical approach, or an approach that relies on information from your senses. Alternatively, when using Descartes' method of Cartesian doubt to skeptically view the world around us, one quickly finds that the notion of a spherical world is the theory which has the burden of proof and not flat earth theory.
It is often said that the predictions of eclipses prove astronomers to be right in their theories. But it is not seen that this proves too much. It is well known that Ptolemy predicted eclipses for six-hundred years, on the basis of a plane Earth, with as much accuracy as they are predicted by modern observers. If, then, the predictions prove the truth of the particular theories current at the time, they just as well prove one side of the question as the other, and enable us to lay claim to a proof that the Earth is not a globe.
35) If the Earth were truly a globe, then every line of latitude south of the equator would have to measure a gradually smaller and smaller circumference the farther South travelled. If, however, the Earth is an extended plane, then every line of latitude south of the equator should measure a gradually larger and larger circumference the farther South travelled. The fact that many captains navigating south of the equator assuming the globular theory have found themselves drastically out of reckoning, moreso the farther South travelled, testifies to the fact that the Earth is not a ball.
78) From Anchorage, Alaska at an elevation of 102 feet, on clear days Mount Foraker can be seen with the naked eye 120 miles away. If Earth were a ball 25,000 miles in circumference, Mount Foraker’s 17,400 summit should be leaning back away from the observer covered by 7,719 feet of curved Earth. In reality, however, the entire mountain can be quite easily seen standing straight from base to summit.