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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?

Mihai
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3 Answers3

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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).

Frédéric Grosshans
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Did
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  • Obviously, the translation by Sir Thomas L. Heath does not include the four books discovered in an Arabic translation in 1968, and even less the three books which are still missing – Frédéric Grosshans Nov 24 '22 at 14:55
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Context

Diophantus' Arithmetica consists of 13 books written originally in Greek circa in ~270 CE. The original Greek text is lost to us. The earliest surviving texts are from copies in Arabic transmitted through the Islamic world, before returning to Western Europe in the 1600s via translations from Arabic back into Greek or Latin.

In 1621 CE, Bachet published in Latin the standard text which Fermat read and annotated with his observations. This makes available 6 of the 13 books. In 1968, an Arabic text was discovered in Iran containing Books 4-7 of the Arithmetica. This means 10 of the 13 original books are extent, and the current scholarly view is that Bachet's text has the original Books 1-3, Books 4-7 are from the Arabic text, and the other three books from Bachet are from 8-13, but we don't know which three, and with three books still lost.

Translations to English

Thomas Heath (1910) made an English translation of Bachet's version, but using the text of Tannery (1893, 1895), available freely here: https://archive.org/details/diophantusofalex00heatiala It has Books 1-3 & "4-6".

The Tannery text (Greek and Latin) is available here: Vol 1 (1893) and Vol 2 (1895)

The English translation (1982) by Jacques Sesiasno of Books 4-7 can be found here: https://www.amazon.com/dp/0387906908/

Historical References

The history of Diophantus's Arithmetica here: www-irma.u-strasbg.fr/~schappa/NSch/Publications_files/1998cBis_Dioph.pdf

A review of Sesiano's translation, with its history, is here: http://www.jphogendijk.nl/reviews/sesiano.html

Assad Ebrahim
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  • Is Heath's book really a translation? It seems more like a book ABOUT Diophantus's "Arithmetica", not the translation of the actual book. There's just an "abstract" from the books, mostly an abbreviated description of the problems and their solutions which doesn't seem to be a 1:1 translation from Bachet's Latin version or the original Greek one. Unless I'm stupid and I can't find the actual translation in the book? – SasQ Jul 17 '19 at 21:56
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    @SasQ: Yes, this really is a translation :) Looking at the contents, the first third of the book is the usual scholarly introduction (128pp), the second third is a TRANSLATION of The Arithmetica (pp.129-266, Books I-VI), and the last third (pp.267-387) is a supplement containing Fermat's margin notes, Heath's notes, and some hard solutions by Euler. The translation starts "Knowing, my most esteemed friend Dionysius, that you are anxious to learn how to investigate problems in numbers..." (p.129). The translation is of original text edition of Tannery (1893), which Heath prefers to Bachet's. – Assad Ebrahim Jan 09 '20 at 02:30
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This link says there exists a book, but the cost seems a bit high.

Aaron Maroja
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Bhargav
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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