'arch' has multiple historical roots: the architectural sense originates from Latin, specifically the word 'arcus', where 'arc-' meant 'bow'; the sense meaning 'chief' or 'extreme' comes from Greek, specifically the word 'arkhos', where 'arkh-' meant 'ruler' or 'chief'.

'arch' (architectural) came into English via Old French 'arche' from Latin 'arcus', and the 'chief/extreme' sense arrived via Greek 'arkhos' into Late Latin/Old French forms, eventually yielding the modern English 'arch'.

Initially it meant 'bow' or 'curve' (from Latin) and separately 'ruler/chief' (from Greek); over time these distinct origins produced the modern senses 'curved structure' and 'chief/extreme/knowingly superior'.