Dr. Carlson,
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."
This is an inaccurate summary of Aristarchus. (I would not
known that, but I happen to have Aristarchus' complete work on my
desk, Greek with a facing English translation, forming an appendix
to
Aristarchus of Samos, the Ancient Copernicus
by Sir Thomas Heath
Clarendon Press, Oxford, 1913
Dover reprint 1981
ISBN 0-486-24188-2
LC Catalog Card Number: 81-66916)
Anyway, Hipparchus opens his book with a paragraph of 6 axioms,
then immediately follows them with (tr. Heath), p353:
We are now in a position to prove the following
propositions:-
1. The distance of the sun from the earth is greater than
eighteen times, but less than twenty times, the distance of the moon
(from the earth); this follows from the hypothesis of halved
moon.
The halved moon refers to axiom 4:
"That, when the moon appears to us halved, its distance from
the sun is then less than a quadrant by one-thirtieth of a quadrant."
(i.e., 87 degrees).
Aristarchus' proof of the 18 < D < 20
is in "Proposition 7", and runs about 3pp of text, plus
of course 3pp of translation. It's out of copyright, e-mail me if you
want me to scan them for you.
--
Bill Thayer
http://tinyurl.com/iquh
http://tinyurl.com/iquh
