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From what I've read, in 1975, Jacques Sesiano in his Ph.D. thesis managed to translate four 'new' books from Diophantus' Arithmetica. This brings the total number of books of Arithmetica salvaged to 10 distinct books, if we include the 6 from Heath's Greek translation.

Does anyone know if any of the 6 Greek version of the books were found in Arabic? Has there been other major progress in finding the last 3 books?

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    $\begingroup$ I don't think there is universal agreement that the four 'newly' discovered Arabic books are in fact by Diophantus. In fact, the problems treated in these books seem to be slightly more repetitive and elementary, so I would advocate a sceptical attitude myself. $\endgroup$
    – R.P.
    Commented May 9, 2017 at 21:56
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    $\begingroup$ "seem to be slightly more repetitive and elementary" By that logic, surely Book I couldn't be Diophantus' either... However I can understand a healthy amount of skepticism. It would be good to hear how others weigh in on this. $\endgroup$
    – CAB
    Commented May 9, 2017 at 22:39
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    $\begingroup$ You're right, but Book I is somewhat exceptional as well. Remember that Diophantus' Arithmetica has been described as a collection so varied that, even after having read the solutions to a hundred problems, it is still hardly easier to solve the 101st problem. This is simply not true for the four 'new' books, for example the problems (and solutions) in the Arabic book known as 'Book IV' are all very similar to each other. It isn't true for Book I either, but this is after all the first book, and Diophantus has consciously arranged the work so as to progress from the easy to the difficult. $\endgroup$
    – R.P.
    Commented May 9, 2017 at 23:00
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    $\begingroup$ Perhaps then we have the order wrong? Though Sesiano seems convinced the order is Greek I-III and then Arabic IV-VII and then the other three Greek books. Of course perhaps this just isn't Diophantus' work but rather someone after Diophantus; perhaps a disciple/student? Anyway I can't keep speculating but hopefully more historians out there mention what is 'widely accepted'. $\endgroup$
    – CAB
    Commented May 9, 2017 at 23:15
  • $\begingroup$ You might be interested in the article of Norbert Schappacher here: www-irma.u-strasbg.fr/~schappa/NSch/Publications_files/…. Starting at p.16, it describes some relevant details about the document history. $\endgroup$
    – Marty
    Commented May 10, 2017 at 4:28

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As Sesiano writes in his book, the first three books that once existed in Arabic translation (by Qusta ibn Luqa) are lost. But al-Karaji quoted extensively from Diophantus Book III (and gives almost all of Book IV) in his work Fahri, which proves that the Books I-III must have been known in Arabic times.

The situation has not changed since the publication of the Arabic books by Rashed and Sesiano: Rashed and Houzel do not mention any new discoveries in their book Les Arithmétiques de Diophante from 2013.

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