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 etymology, peripatetic origin, 英语词源]