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...wait, really? I know back then it was probably anyone's guess, but that sounds like one of those oddly specific things that makes the moon being made of cheese sound like a down-to-earth conclusion.
I checked, and it looks like I oversimplified: Anaxagoras estimated that the moon was the size of the Peloponnesus and the sun was somewhat larger—but how much larger depended on how much further away it was, which he had no means of guessing.
His estimate of the moon’s size was derived from observations of a solar eclipse, in which the path of totality was about the size of the Peloponnesus—but he probably missed a lot of places that experienced a partial eclipse and didn’t make note of it.
I mean his train of thought deserves credit, just not for factoring in everything. A good Greek philosopher was like the Sherlock Holmes of their day; I recall reading Aristotle saw the Earth's shadow on the moon and how it curved and he was like "ah, so the Earth isn't flat, it's a ball" (though then he'd go on to say stuff like "other cultures are less prone to revolution, so they must be natural slave cultures", which would be more like Half-Life 3's hypothetical version of Sherlock Holmes).