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There is certainly more than one mathematician called Dionysodorus and this does make it a little difficult in deciding exactly what was studied by each.
Dionysodorus is believed to have invented a conical sundial. The report fails to make it clear which Dionysodorus this is, but the fact that the Dionysodorus described here worked on conic sections makes it likely that he is also the person to have studied a conical sundial.
References (2 books/articles)