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It should be in the public domain (obviously), so I'd thought I could find the English text on the web somewhere. Apparently not?

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There is: archive.org/details/diophantusofalex00heatiala for Diophantus of Alexandria; a study in the history of Greek algebra by Sir Thomas L Heath (1910). –  Did Aug 24 '11 at 12:45
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Look at this text by Norbert Schappacher for some interesting history. –  t.b. Aug 24 '11 at 12:48
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@Didier, that comment could be an answer. –  lhf Aug 24 '11 at 13:31
    
The fact that Diophantus' writings are in the public domain does not automatically mean that a translation into English would be in the public domain. –  Michael Hardy Aug 24 '11 at 16:20
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If you want a physical copy, some print-on-demand companies offer copies of the Heath book (e.g. on amazon) for not too much money. There is a Dover edition too: ISBN 1443730238. –  mt_ Aug 24 '11 at 23:33
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2 Answers 2

up vote 6 down vote accepted

There is one such translation (freely available), included in the book Diophantus of Alexandria; a study in the history of Greek algebra by Sir Thomas L. Heath (1910).

For some interesting history, user @t.b. recommended (and I fully concur) to look at the paper Diophantus of Alexandria: a text and its history (2005) by Norbert Schappacher (this paper is freely available as well).

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http://www.amazon.com/Books-VII-Diophantus-Arithmetica-Indo-European/dp/0387906908

this says there exists a book, but the cost seems a bit high

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This is a translation into English by Sesiano of an Arabic translation of what may be some of the "lost" books of Arithmetica. (The manuscript was found not that many years ago in a shrine library.) The text is probably substantially modified from the original. Any decent university library will have it. Yes, the cost is high, but the profit margin is undoubtedly much less than on a routine calculus book. –  André Nicolas Aug 24 '11 at 15:35
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