'approximative' originates from Latin, specifically the verb 'approximare' (past participle 'approximatus'), where 'ad-/ap-' meant 'to/toward' and 'proximus' meant 'nearest' or 'close'.

'approximare' passed into Late Latin as 'approximativus', influenced Old French (e.g. 'approximatif'), and then entered English as the adjective 'approximative'; the adverb 'approximatively' is formed by adding the suffix '-ly' to the adjective.

Initially related to 'bringing near' or 'nearness' (physical or figurative), the sense shifted to indicate nearness in value or degree — i.e. 'not exact but close,' which is the modern usage.