"woman supposed to possess powers of prophecy, female soothsayer," c. 1200, from Old French sibile, from Latin Sibylla, from Greek Sibylla, name for any of several prophetesses consulted by ancient Greeks and Romans, of uncertain origin. Said to be from Doric Siobolla, from Attic Theoboule "divine wish."
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Definitions of sibylline from WordNet
resembling or characteristic of a prophet or prophecy;
a kind of sibylline book with ready and infallible answers to questions