peripateticyoudaoicibaDictYouDict
peripatetic: [16] Peripatetic means literally ‘walking round’. It comes via Old French peripatetique and Latin peripatēticus from Greek peripatētikós. This was a derivative of peripatein, a compound verb formed from the prefix perí- ‘round’ and patein ‘walk’. But the Greeks used it not simply for ‘walk around’, but specifically for ‘teach while walking around’ – an allusion to the teaching methods of Aristotle, who discussed and argued with his pupils and followers while walking about in the Lyceum, a garden near the temple of Apollo in Athens.

Hence adherents of Aristotle’s school of philosophy are known as Peripatetics. The more general use of the adjective for ‘itinerant’ represents a relatively modern (17th-century) return to its etymological meaning.
peripatetic (n.)youdaoicibaDictYouDict
c. 1400, "disciple of Aristotle," from Old French perypatetique (14c.), from Latin peripateticus "pertaining to the disciples or philosophy of Aristotle," from Greek peripatetikos "given to walking about" (especially while teaching), from peripatein "walk up and down, walk about," from peri- "around" (see peri-) + patein "to walk, tread" (see find (v.)). Aristotle's custom was to teach while strolling through the Lyceum in Athens. In English, the philosophical meaning is older than that of "person who wanders about" (1610s).
peripatetic (adj.)youdaoicibaDictYouDict
1560s in the philosophical sense, 1640s in the literal sense; see peripatetic (n.).