Of or belonging to Descartes

A fascinating paper my daughter brought home from school raised a question in our household, one which I direct to the savants of the group in hopes of receiving a definitive answer. The fascinating element of the paper was its several uses of the possessive form of Descartes. The paper contained at least three distinct spellings, though perhaps one was a typo:
Descartes' the most frequent occurrence
Descarte's only a single occurence
Descartes's two occurrences
Not a one really looks entirely plausible to me, although I believe I'd use the last. The second is most likely a typo, I think, but the first is the form I found the most interesting. It seems utterly impossible, even if there might be stylistic reasons to accept, say, Moses' as a possessive.
How would "Descartes'" be pronounced, do you suppose? Why not exactly like "Descartes"? The maybe-typo evidence suggests that the author was thinking something like "day-carts". Perhaps the third choice would have sounded to her ear like "day-cartzez", leaving only the first alternative. I see that other authors on the Internet use that same spelling, so I suppose there may be a reason for it, but how say you all?

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