'terete' originates from Latin, specifically the word 'teres', where the root meant 'rounded, smooth'.

'terete' changed from the Latin adjective 'teres, teretis' and was used in Neo-Latin/botanical Latin as 'teret-' or 'teretus', and was borrowed into English (chiefly in botanical contexts) as 'terete'.

Initially, it meant 'rounded, smooth' in Latin, but over time it evolved into the specialized botanical sense of 'cylindrical and often tapering, with a circular cross-section' in modern English.