How eratosthenes calculated the size of the earth?

Answer 1

At noon, on the summer solstice, there is a well in Syene where the sunlight shines straight down to the bottom. Upon witnessing this, Eratosthenes waited until the solstice came again and measured the angle of the shadow cast into a well in Alexandria. This told him the difference in angle between the two cities along a curve, and he already knew the distance (in stadia). Associating the two, he multiplied the distance enough to equal 360 degrees. This was the circumference of the Earth. He was actually slightly off, because the Earth isn't a perfect sphere and Alexandria isn't perfectly north of Syene, but he was amazingly close.

Answer 2

He didn't discuss it with me at the time, but I think I can guess: He wanted the answer to a question that had
often bugged him and others with similar levels of intellectual curiosity. The answer, or some close estimate,
would add to the sum total of human knowledge, even though it wouldn't make a bit of difference in the
day-to-day life of a single individual on earth. In that way, Eratosthenes' pursuit was similar to the modern
investigation of the questions of how the sun shines, why the sky is blue, and why we are here.

Answer 3

Because the question kept gnawing at his guts: "If the earth is a sphere, what size is it ?"
He could know no peace . . . have no rest . . . until he found an answer to his question.
That's the way it is for people who go around thinking.

Answer 4

because he wanted to see the answer