The Collaborative International Dictionary
Rhapsodomancy \Rhap"so*do*man`cy\, n. [Rhapsody + -mancy.] Divination by means of verses.
Douglas Harper's Etymology Dictionary
"divination by means of verses," 1727, from French rhapsodomancie, from Greek rhapsodos "a rhapsodist" (see rhapsody) + -manteia (see -mancy).\n\nThere were various methods of practicing this rhapsodomancy. Sometimes they wrote several verses or sentences of a poet on so many pieces of wood, paper, or the like; shook them together in an urn; and drew out one, which was accounted the lot. Sometimes they cast dice on a table, on which verses were written; and that on which the die lodged, contained the prediction.
[Rees' "Cyclopedia," London, 1819]
Wiktionary
n. divination by reading a random passage from a poem.
Wikipedia
Rhapsodomancy is an ancient form of divination performed by choosing through some method a specific passage or poem from which to ascertain information.
There were various methods for practicing rhapsodomancy. Sometimes, individuals would write several verses or sentences from a poet on multiple pieces of wood, paper, or similar material, shake them together in an urn, and pick one at random. Sometimes, they cast dice on a table that was covered with verses; the one on which the die landed was said to contain the prediction.
In ancient Rome, the method of sortes involved opening a book and choosing some verse at first sight. This method was particularly called the sortes Praenestinae; and afterwards, according to the poet who was used, sortes Homerica, sortes Virgilianae, etc.