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While reading the book My Numbers, My Friends by Paulo Ribenboim, I came across a reference to a paper on page 42 :

"1657 Frénicle de Bessy. Solutio duorum problematum circa numeros cubos et quadratos. Bibliothèque Nationale de Paris."

I'm looking for the above paper, either downloadable or purchasable copy.

Any help will be greatly appreciated.

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A quick Google search shows that the French National Library has this paper: http://catalogue.bnf.fr/ark:/12148/cb336077500. They do sell reproductions.

Edit. By now (Oct 2018), you can also view/download a scanned copy for free.

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    Maybe the "Bibliothèque Nationale de Paris" was a nice hint in that direction :) – 2017-01-27
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    I also had a look at the BnF (https://espacepersonnel.bnf.fr/views/vel/mon_panier.jsf#). The numerization of the document costs 45 euros. (2 months delay) – 2017-01-27
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This German site claims to have that paper. It also shows up on Google Books, maybe there is a way to buy from there too.