See Madelyn Gutwirth (pp. 172-82; 239) for the importance of this famous painting to Staël, who actually had her own portrait painted as the Sibyl.
By the nineteenth-century, Sibyls were popular cultural icons, and the term had become a commonplace way to refer to an inspired or prophetic woman author.
Mary Shelley opens the frame narrative of The Last Man with the discovery of "Sibylline leaves."
Romantic Circles / Electronic Editions / The Last Man / Note: Domenichino's Sibyl