The ancient Greeks knew that the Earth was spherical. Aristotle gave some convincing arguments for the spherical Earth, including ships sailing over the horizon. When ships sail away over the horizon the mast disappears after the lower part of the ship has disappeared. Similarly the mast appears before the lower part of the ship when a ship sails towards us over the horizon. This is consistent with the Earth being spherical. During lunar eclipses the Earth's shadow is always round. Eratosthenes used geometry and a hired pace man to estimate its circumference to within a few percent. 
Medieval Europeans knew this, and had correctly warned Christopher Columbus that he would never get to India with his limited supplies. Columbus relied on a fallacious argument that the Earth was much smaller than the Greeks estimated.
Some writers have presented the mistaken idea that medieval Europeans used a literal reading of the Bible to conclude that the Earth was flat.  They supposedly tried to convince Christopher Columbus that he would fall off the edge of the Earth, the story goes, but Columbus discovered America and Ferdinand Magellan proved that the Earth was round. 
- The Sum of Existence, by A.R. Barnes, Jr. - contains an account of how Eratosthenes estimated the circumference of the Earth.
- Flattening the Earth Sep-Oct 2002, Mercury Magazine, pp. 34-38. by Jeffrey Burton Russell
- "Among various rude tribes we find survivals of a primitive idea that the earth is a flat table or disk, ceiled, domed, or canopied by the sky, and that the sky rests upon the mountains as pillars."
- "Eratosthenes concluded the Earth to be 40,000 kilometers in circumference, or approximately 25,000 miles. Within a few percentage points, this is correct.." The Sum of Existence], by A.R. Barnes, Jr.
- 'In the time of Columbus, did educated Christians believe the earth was flat? The correct answer is NO, but most modern people will say YES. Why? This wrong idea is due to a fascinating abuse of history that began around 1830 when two writers (a sloppy novelist and an atheist scholar) invented a false story about "belief in a flat earth" that, in the 1870s, was popularized by Draper.' (Craig Rusbult)
- Saying "to the ends of the earth", "the four corners of the world" or "the sun sank into the sea" does not make you a flat Earther.The Myth of the Flat Earth (Bede's Library)
- "The flat earth remained clearly in the realm of fiction until after Darwin published his Origin of Species in 1859. Two of Darwin’s followers then elevated it to a historical claim in books defending Darwinism and attacking Christianity: John Draper’s The History of the Conflict Between Religion and Science (1874), and Andrew Dickson White’s A History of the Warfare of Science with Theology in Christendom (1896).
So defenders of Darwinism who ridicule their critics for being like believers in a flat earth are being misled by a myth that Darwinists themselves helped to create."
- "Christianity did not invent or promote the myth of the flat Earth." Who invented the flat Earth? (ChristianAnswers.net)
- 'The reason for promoting both the specific lie about the sphericity of the earth and the general lie that religion and science are in natural and eternal conflict in Western society, is to defend Darwinism. The answer is really only slightly more complicated than that bald statement. The flat-earth lie was ammunition against the creationists. The argument was simple and powerful, if not elegant: "Look how stupid these Christians are. They are always getting in the way of science and progress. These people who deny evolution today are exactly the same sort of people as those idiots who for at least a thousand years denied that the earth was round. How stupid can you get?"'The Myth of the Flat Earth, by Jeffrey Burton Russell.