rheumatic: [14] Greek rheuma meant literally ‘flow, stream’ (it came ultimately from the same Indo-European base as produced English stream, and was a close relative of the Greek verb rhein ‘flow’, which provides the second halves of English catarrh and diarrhoea). It was used for a ‘watery discharge from the body’, and was borrowed into English (via late Latin rheuma and Old French reume) as rheum [14] in the sense ‘mucous discharge from the eyes or nose’.
Pains in the joints were in former times thought to be caused by watery secretions within the body, and so towards the end of the 17th century the term rheumatism was applied to them. => catarrh, diarrhoea, rhyme, rhythm
late 14c., from Old French reumatique (Modern French rhumatique), from Latin rheumaticus "troubled with rheum," from Greek rheumatikos, from rheuma "discharge from the body" (see rheum).