'peripteral' originates from Modern Latin 'peripteralus', specifically the Greek word 'perípteron' (περίπτερον), where 'peri-' meant 'around' and 'pteron' meant 'wing' (used figuratively for a row or range, here a row of columns).

'peripteral' changed from the Greek 'perípteron' into late Latin/Medieval Latin forms such as 'peripterum'/'peripteralus' and then entered English (via scholarly architectural Latin and French usage) as 'peripteral' in descriptions of classical temples.

Initially it referred specifically to a building 'with a surrounding row (wing) of columns' and it has retained that architectural sense into modern English.