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Does anyone know where I can find an english translation, preferrably 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?

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Well, I managed to find a proof using only Euclidean Geometry at Cut-the-Knot: . I have no idea whether this is the original proof, though. – Avi Steiner Jan 19 '12 at 20:48
up vote 6 down vote accepted

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: enter image description here enter image description here

It relies on earlier lemmas; there's an explanation that includes them on Wikipedia.

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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.

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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. – Avi Steiner Jan 12 '12 at 23:22
Hmm, may have been a slight delusion on my part. I will investigate further... – Igor Rivin Jan 12 '12 at 23:54

Stumbled by coincidence today over the book "Sir Thomas Heath: A History of Greek Mathematics, II". Chapter XIX (pp. 355-439) is devoted to Papus and contains a lot of (mathematical) stuff. Perhaps you can find there what you are looking for.

You can find the book online at the page


(PDF on the left, download may take a while).

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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. – Avi Steiner Jan 19 '12 at 20:34

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