The word nervine comes from the Latin nervinus, belonging to a sinew. Nervine travelled across the Channel from France to 17th-century England. There it was first applied to the sinews. That is not illogical because the Latin nervinus derives from nervus meaning "a sinew, tendon, thong, string (as a bowstring), or wire." In ancient anatomy the Romans (and Greeks) did not distinguish between and tendons and nerves. The name "nervus" referred to any white cordlike structure, whether it be a band of connective tissue or a fiber in the nervous system.
(I must admit I did not know the word "nervine" myself. I came upon it in a diabolically difficult Saturday New York Times crossword -- they get progressively harder fro Monday to Saturday. The clue was "Soothing medicine." There were 7 spaces to be filled. The answer proved to be NERVINE. I found it was not in most standard desktop dictionaries nor in many medical dictionaries. -- Editor)