What did Epicurus Say about the size of the sun and whether the Earth was round or flat?

In the letter to Pythocles, Epicurus specifically makes clear before he starts discussing astronomy that: "But this is not the case with celestial phenomena: these at any rate admit of manifold causes for their occurrence and manifold accounts, none of them contradictory of sensation, of their nature. For in the study of nature we must not conform to empty assumptions and arbitrary laws, but follow the promptings of the facts; for our life has no need now of unreason and false opinion; our one need is untroubled existence. All things go on uninterruptedly, if all be explained by the method of plurality of c__auses in conformity with the facts, so soon as we duly understand what may be plausibly alleged respecting them. But when we pick and choose__among them, rejecting one equally consistent with the phenomena, we clearly fall away from the study of nature altogether and tumble into myth. Some phenomena within our experience afford evidence by which we may interpret what goes on in the heavens. We see bow the former really take place, but not how the celestial phenomena take place, for theiroccurrence may possibly be due to a variety of causes. However, we must observe each fact as presented, and further separate from it all the facts presented along with it, the occurrence of which from various causes is not contradicted by facts within our experience."

Then when he addresses the size of the sun, he says "The size of the sun and the remaining stars relatively to us is just as great as it appears. But in itself and actually it maybe a little larger or a little smaller, or precisely as great as it is seen to be. For so too fires of which we have experience are seen by sense when we see them at a distance. And every objection brought against this part of the theory will easily be met by anyone who attends to plain facts, as I show in my work On Nature. "

Now his reason for this conclusion is clear from this — he says that on earth, things that give off light do not appear to recede in the distance as much as those things that don't. So applying that rule here, there's no reason to think that the sun is a huge distance away, any further than the moon, so no reason to think it is huge in size. Of course a major reason he leaned toward this conclusion is that he was battling the platonists, who said they were gods, and who were trying to reduce nature down to a series of calculations. He chose incorrectly, but he was motivated by good reasons. I believe much the same explanation goes to the earth as well, which I gather they did think was round, but that since everything falls down you would fall off thebottom if you were on the other side. So there were good solid reasons the Epicureans chose the positions they did, and definitely not go along just because Epicurus said so.

Also (Credit to Joshua for this):

It's important to consider the whole proposition. Epicurus thought that the sun was;

1. Wholly material
2. In constant but not uniform motion
3. In a centerless cosmos
4. Governed by the same laws as things on Earth
5. Arose out of matter, and has a finite period of existence
6. But its matter will recombine into other things
7. About as big as it seems.

Compare Aristotle's sun;

1. Made of aether, an element that didn't exist on earth
2. In constant and uniform motion (because aetherial)
3. Set in motion by unmoved mover (god)
4. Orbiting a stationary earth that was the center of everything
5. Governed by different laws than Earth (the laws of the aether)
6. Exists in perpetuity (because aetherial)
7. Size uncertain (not mentioned, as far as I can tell)

Discussion of this issue is here.