'assonant' originates from Latin, specifically the verb 'assonare' (formed from 'ad-' + 'sonare'), where 'ad-' meant 'toward' and 'sonare' meant 'to sound'.

'assonare' passed into Old French as 'assoner' / 'assonance' and then into Middle English, eventually yielding the modern English adjective and noun 'assonant' (and the noun 'assonance').

Initially it meant 'to make a sound like' or 'to sound toward (another)', and over time it narrowed to the modern sense of 'showing similarity of vowel sounds' (i.e., assonance).