Galileo is not credited with discovering that the world is round. The idea that the Earth is round is traced back to ancient Greece in the 6th century B.C.
According to How It Works Daily, Pythagoras from the 6th century B.C. is credited with coming up with the idea that the Earth is spherical. According to NASA's StarChild website, at around 350 B.C., Aristotle declared the Earth to be a sphere based on constellation observations as one travelled further away from the equator. Within the next hundred years after Aristotle, Aristarchus and Eratosthenes measured the size of the Earth. In 1522 A.D., an expedition led by the Portuguese explorer Ferdinand Magellan circumnavigated the globe.