Notice how the map is curved upwards at the ends. That tells me that they KNEW the world was round, even before Columbus.........
They knew it for a couple of millennia before Columbus.
Actually the roundness of the earth was well known long before Columbus. Eratosthenes (276 BC - 194 BC), a Greek mathematician, not only knew the earth was a sphere, but measured its diameter about 200 BC. His calculation was within a few percent of the correct value.
It is a myth that people once believed the Earth was flat. Well before the time of Eratosthenes, educated people knew it was round.
The objection to Columbus's proposed voyage was not that "he'd sail off the edge," but that he had seriously underestimated the length of the voyage. It appears that he had fudged the numbers to make the voyage appear more feasible, knowing that the voyage would really be longer than he claimed in his proposals. This is a practice not unheard of among today's scientists when writing grant proposals.