On 2015-04-19 10:04, Warren D Smith wrote:

MStay> I don't get it. How do you get any indication of the Sun's size

...

relative to the moon?<MStay

--Aristarchus's input data were the following (from which you should be able to see how he did it).

1. He knew the size of the Earth based on two latitude measurements at two places (Alexandria & Syene) a known distance apart along a Meridian. 2. When the moon is exactly half full, the angle between sun & moon is 87 degrees. (Except that really, it is 89.85 degrees. A difficult measurement to make, since judging "half full" by eye.) 3. During a total eclipse, moon & sun are essentially the same angular diameter. (True.) 4. The Earth's shadow at the location of the moon is about twice as wide as the moon. (Actually, 3.67.) 5. The moon subtends an angle of 2 degrees. (Actually, 0.52 degrees, it is hard to understand how Aristarchus could have been so far off on this. Archimedes gave 0.5 degrees.)

I don't think Aristarchus had good measuring equipment, he could have been a lot more accurate.

Conjecture: The ratio 400 seemed ridiculously large, and he was fudging to get a more plausible result. --rwg