'gradually-narrowed' originates from a combination of the adverb 'gradually' and the past-participle/adjective 'narrowed'. 'gradually' ultimately comes from Latin, specifically the word 'gradualis' (from 'gradus'), where 'gradus' meant 'step' and the suffix '-alis' formed adjectives; 'narrow' originates from Old English, specifically the word 'nearwe', where the root meant 'tight' or 'confined'.

'gradually' passed into English via Medieval Latin/Old French as 'gradualis' and Middle English 'gradual' with the adverbial suffix '-ly' forming 'gradually'. 'narrow' evolved from Old English 'nearwe' to Middle English 'narwe' and then to modern English 'narrow'. The compound adjective 'gradually-narrowed' is a modern English combination used to describe a process of becoming narrower over time.

Initially the components meant 'step-like' or 'by steps' (from Latin 'gradus') and 'tight/confined' (from Old English 'nearwe'); over time these became 'by degrees' (gradually) and 'not wide' (narrow). Together, the phrase came to mean 'made narrower over time' with that single combined sense.