As noted several times in responses above, educated people in the western world generally understood that the world was round starting at least with the Age of Pericles.
Years ago in an astronomy class I learned four arguments given by ancient Greeks for believing that the world is round:
1.) Travelers who go far to the north or south find that familiar stars disappear over the horizon behind them and new stars rise up in the direction in which they are headed. This suggests that our view of the sky is obstructed from being on a round surface.
2.) When a ship sails off in the distance it does not merely get smaller and smaller until it disappears from view. Rather, it appears to sink into the ocean, suggesting that it is passing over a curved surface which “rises up” to block our view.
3.) Observations of the earth’s shadow as it is cast on the moon demonstrate that it is a curved surface. Similarly, observations of the moon’s phases show that it is not a flat disc, but a sphere.
4.) About the farthest anyone had ever traveled west and brought back reliable information is the northwestern coast of Africa. There is a peculiar species of animal found there called (in English) “the elephant”. About the farthest east anyone had ever traveled who has brought back reliable information is India. There are elephants there too. Conclusion? India is right around the corner from northwest Africa.
Well, three out of four ain’t bad. This forth argument points up a misunderstanding educated people did have: although attempts by ancient Greeks to estimate the circumference of the earth appear to have come within a few hundred miles of the correct measurement (there are some arguments about how to interpret the units of measurement that were employed), educated people commonly misjudged just how big around the earth was. Sometimes they thought it was way bigger than it was, and sometimes they thought it was way smaller.
As alluded to before, Columbus differed with prevailing opininion of his time primarily as to how big the earth was. And he was wrong; hence his mistaken belief that he had reached the East Indies.
The Greeks had further believed that there was a land mass around the south pole, as this permitted the earth to remain stable and not roll around. This belief in a southernmost continent was accepted on faith for centuries. It may account for why Antarctica is called “Antarctica”
“Arctic” derives from the Latina for north. And “Antarctic”? It means opposite of the north.
Why not call it after the Latin word for south?
Because Captain Cook–who was the first westerner to see Antarctica–had already used it. He had used the name “Australia” (“southland”) to refer to…Australia. He is said to have mistakenly supposed that the land mass he saw was the northern protrusion of the great south pole continent which he already assumed existed. Hence maps of the late 1700s showing Australia and Antarctica as parts of one vast undefined continent.
Biblical references to the flatness of the earth are generally taken to have been meant literally. St. Augustine, for one, argued that the earth had to be flat because the Bible says so. As late at the 19th Century Biblical literalists (or people who claim to be such) were still greatly bothered by the idea that the world might be round. Alfred Ward Russell, the co-developer of the Theory of Evolution, was harassed for decades by Biblical literalists who demanded he “admit” that his experiment to show the curvature of the earth had failed. Since then Biblical “literalists” have, in the main, become choosier about wht arguments to pick.