'approximation' originates from Latin, specifically the verb 'approximare' (a combination of 'ad-' meaning 'to' and 'proximus' meaning 'nearest'), where the sense was 'to bring near.'

'approximare' in Late Latin passed into Middle French and Late Latinized forms and then entered Middle English as 'approximacioun' or similar spellings, eventually becoming the modern English 'approximation.'

Initially it meant 'to bring or make near' (physical proximity); over time it shifted toward senses of 'nearly equal' or 'an estimate close to the true value,' which is its primary modern meaning.