Extravagant
late Middle English (in the sense ‘unusual, unsuitable’): from medieval Latin extravagant- ‘diverging greatly’, from the verb extravagari, from Latin extra- ‘outside’ + vagari ‘wander’.
wiktionary
From Old French and French extravagant, from Medieval Latin extravagans, past participle of extravagor(“to wander beyond”), from Latin extra(“beyond”) + vagor(“to wander, stray”).
etymonline
extravagant (adj.)
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.).