According to the professor, what were, the beliefs of the Greek philosophers based upon?

In ancient times, many people believed the earth was a flat disc. Well over 2,000 years ago, the ancient Greek philosophers were able to put forward two good arguments proving that it was not.  Direct observation Of heavenly bodies was the basis of both these arguments. First, the Greeks knew that during eclipses of the moon, the earth was between the sun and the moon, and they saw that during these eclipses, the earth’s shadow on the moon was always round, they realized that this could be true only if the earth was spherical. If the earth were a flat disc, then its shadow during eclipses would not be a perfect circle, it would be stretched out into a long ellipse. The second argument was based on what the Greeks saw during their travels. They noticed that the North Star, or Polaris, appeared lower in the sky when they traveled south, in more northerly regions, the North Star appeared to them to be much higher in the sky. By the way, it was also from this difference in the apparent position of the North Star that the Greeks first calculated the approximate distance around the circumference of the earth, a figure recorded in ancient documents says 400,000 stadia, that’s the plural of the word stadium. Today, it’s not known exactly what length one stadium represents, but let’s say it was about 200 meters, the length of many athletic stadiums. This would make the Greek’s estimate about twice the figure accepted today, a very good estimate for those writing so long before even the fast telescope was invented.