Historical determination of the astronomical unit (again)

[DrArthurCarlson]

Aristarchus of Samos (?310-230BC) used the shadow line of the moon to estimate the distance to the sun. According to http://www-astronomy.mps.ohio-state.edu/~pogge/Ast161/Unit3/greek.html, he "Showed geometrically that the Sun was at least 20x further than the Moon. Really 400x further: sound method, poor data." According to http://www-astronomy.mps.ohio-state.edu/~pogge/Ast161/Unit4/venussun.html, this corresponds to 8 million kilometers, compared to the true value of 150 million.   The second web site above also refers to an estimate of 87 million km by Copernicus in 1543 and one of 111 million km by Edmund Halley in 1716. All of this before measurements of the transit of Venus. And as far as I can figure out, the transit of Mercury was too difficult to be of any use.   Did Copernicus and Halley use the method of Aristarchus, but with more careful observations, or is there some other method that can be applied without a telescope but which is more accurate?   --Art Carlson