Does anyone know where I can find an English translation, preferably online or in a book the library of a small liberal arts college would be likely to have, of the original proof of Pappus' hexagon theorem from projective geometry?
3 Answers
It is in book 7 of Pappus's Collection. There is an English translation published by Springer. It's an expensive book, so I'll reproduce the proof & figure here:
It relies on earlier lemmas; there's an explanation that includes them on Wikipedia.
This is available in the Loeb Classics Library, Greek Mathematical Works, Vol II (edited by Ivor Thomas), page 600.The Loeb CL can probably be found in its entirety in many liberal arts college libraries. For your convenience, you can find the book here.

$\begingroup$ Igor, although the book does seem to have a lot, neither page 600 nor the rest of the book has the particular theorem and proof I'm looking for. Thanks, though. $\endgroup$ Jan 12, 2012 at 23:22

$\begingroup$ Hmm, may have been a slight delusion on my part. I will investigate further... $\endgroup$ Jan 12, 2012 at 23:54
Stumbled by coincidence today over the book "Sir Thomas Heath: A History of Greek Mathematics, II". Chapter XIX (pp. 355439) is devoted to Pappus and contains a lot of (mathematical) stuff. Perhaps you can find there what you are looking for.
You can find the book at the Internet Archive (PDF link on the left, download may take a while).

$\begingroup$ I love the link, and I'm definitely going to show it to my professor. However, the author spends exactly one sentence on the hexagon theorem, mentioning that it's based on some lemma's from Euclid's Porisms. Oh, well. $\endgroup$ Jan 19, 2012 at 20:34