'approximate' originates from Latin, specifically the word 'approximatus' (past participle of 'approximare'), where 'ad-/ap-' meant 'to' and 'proximus' meant 'nearest'.

'approximate' changed from Latin 'approximare' / 'approximatus' into Late Latin and Old French forms (e.g. 'aproximer'), and entered Middle English before becoming the modern English 'approximate'.

Initially, it meant 'to bring near' or 'make near' (physically or figuratively), but over time it evolved to the current senses of 'be close to' and 'estimate roughly'.