vague (adj.)

"action of wandering," 1650s, from French évagation, from Latin evagationem (nominative evagatio), noun of action from past participle stem of evagari, from assimilated form of ex "out, out of" (see ex-) + vagari, from vagus "roving, wandering" (see vague).

late 14c., in constituciouns extravagaunt, a term in Canon Law for papal decrees not originally included or codified in the Decretals, from Medieval Latin extravagantem (nominative extravagans), present participle of extravagari "wander outside or beyond," from Latin extra "outside of" (see extra-) + vagari "wander, roam" (see vague).

In 15c. it also could mean "rambling, irrelevant; extraordinary, unusual." Extended sense of "excessive, extreme, exceeding reasonable limits" first recorded 1590s, probably via French; that of "wasteful, lavish, exceeding prudence in expenditure" is from 1711. Related: Extravagantly. Wordsworth ("Prelude") used extravagate (v.).