If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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So, you just have an argument from silence that heliocentrism was not clearly rejected?
I just read through the bits of Sand Reckoner referring to Aristarchus (Mendell's translation), and throughout Archimedes seems to be at pains to distance himself from Aristarchus's model, treating it as a minority view (emphasis added):
Not language which suggests he takes it particularly seriously, much less endorses it.
In fact, it seems that the only reason Archimedes brings up Aristarchus at all is as a form of 'worst-case analysis': some fools doubt the power of mathematics and numbers, but Archimedes will show that even under the most ludicrously inflated estimate of the size of the universe (one implied by Aristarchus's heliocentric model), he can still calculate & count the number of grains of sands it would take to fill it up; hence, he can certainly calculate & count the number for something smaller like the Earth. From the same chapter:
And he triumphantly concludes in ch4:
All I have ever said is that you should stop telling fairy tales about why the Greeks rejected heliocenrism. If the Sandreckoner convinces you that Archimedes rejected heliocentrism, fine, whatever, but it sure doesn't talk about parallax.
I listed several pieces of positive evidence, but I'm not interested in the argument.