'arcuate' originates from Latin, specifically the word 'arcuatus', where 'arcus' meant 'bow'.

'arcuatus' in Late Latin passed into medieval Latin and Middle English as 'arcuate', and the adverbial form 'arcuately' developed in English from that adjective.

Initially, it meant 'bowed or curved', and over time it retained that sense, evolving into the modern meaning of 'curved' or 'in a curved manner'.