'augmentatively' originates from Latin, specifically from the adjective-forming element based on the verb 'augmentare' (from 'augēre'), where 'aug-' / 'augēre' meant 'to increase'.

'augmentatively' developed via Late Latin and Old French formations: Latin 'augmentare' (to increase) > Old French 'augmenter'/'augmentatif' > Middle English/early Modern English 'augment' and the adjective 'augmentative', with the adverbial suffix '-ly' producing 'augmentatively'.

Initially derived forms centered on the action 'to increase' (Latin 'augēre' = 'to increase'); over time the derived adjective and adverb came to mean 'serving to increase' or 'in a manner that increases', which is the modern sense.