'approximator' originates from Latin, specifically from the Late Latin verb 'approximare', where the prefix 'ad-' (toward) combined with 'proximus' (nearest) to form the sense 'to make near' or 'to come near'.

'approximator' developed from Late Latin 'approximatus' (past participle of 'approximare'), passed into Middle English/learned English as 'approximate', and later formed the agent noun with the suffix '-or' to denote 'one who approximates'.

Initially it meant 'to make near' or 'bring close'; over time the sense shifted toward 'to estimate roughly' or 'to give an approximate value', and 'approximator' came to mean an agent (person, device, or method) that produces such estimates.