Yes, RWG has a very good point that Aristarchus could have used Moon-Earth-Sun triangles of other angles than right by using other crescents than "half full." PUZZLE: And what angle would have been the best, in the sense of returning the most accuracy despite measurement errors? M | alpha | | | theta E-----------------S Another brilliant measurement was by Ole Roemer who in 1676 deduced the speed of light by observing Jupiter's moons. You need a telescope or at least good binoculars for this, plus excellent clocks, so the ancient Greeks could not have done it. A sketch of how he presumably did it is here: http://www.amnh.org/education/resources/rfl/web/essaybooks/cosmic/p_roemer.h... Roemer actually never published his method because the great experts all told him he was an idiot, and him doing this was some kind of insult or something. But I think it was really fantastic, I very much doubt I ever would have thought of his technique.