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catarrh: catarrh: [16] Etymologically, catarrh is ‘something that flows down’. It comes via French catarrhe and late Latin catarrhus from Greek katárrhous, a derivative of the verb katarrhein, a compound formed from the prefix katá- ‘down’ (as in cataract) and the verb rhein ‘flow’ (a relative of English rheumatism and stream).
=> diarrhoea, rheumatism, stream
diarrhoea: diarrhoea: [16] Diarrhoea means literally ‘through-flow’ (and hence semantically is a parallel formation to diabetes). It comes via late Latin diarrhoea from Greek diárrhoia, a term coined by the physician Hippocrates for ‘abnormally frequent defecation’. It was formed from the prefix dia- ‘through’ and rhein ‘flow’ (a relative of English rheumatism and stream).

Of other -rrhoea formations (or -rrhea, as it is generally spelled in American English), pyorrhoea ‘inflammation of the tooth sockets’ was coined in the early 19th century, and logorrhoea at around the turn of the 20th, originally as a clinical term in psychology (although subsequently hijacked as a facetious synonym for ‘talkativeness’).
=> rheumatism, stream
rheumatic: 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
rhythm: rhythm: [16] Rhythm goes back ultimately to Greek rhuthmós. This originally meant ‘recurring motion’, and was related to the verb rhein ‘flow’ (source of English catarrh and diarrhoea). It was subsequently applied to ‘recurrent accents in verse’, in which sense it passed into English via Latin rhythmus. (Later Old French alteration of the word led to English rhyme.)
=> catarrh, diarrhoea, rheumatic, rhyme
amenorrhea (n.): 1804, Modern Latin, from Greek privative prefix a- "not" (see a- (3)) + men "month" (see moon (n.)) + rhein "to flow" (see rheum). Related: amenorrheal.
catarrh (n.): late 14c., from Medieval Latin catarrus, from Late Latin catarrhus, from Greek katarrhous "a catarrh, a head cold," literally "a flowing down," earlier kata rrhoos, ultimately from kata- "down" (see cata-) + rhein "to flow" (see rheum). Related: Catarrhalcatarrhous.
diarrhea (n.): late 14c., from Old French diarrie, from Late Latin diarrhoea, from Greek diarrhoia "diarrhea" (coined by Hippocrates), literally "a flowing through," from diarrhein "to flow through," from dia- "through" (see dia-) + rhein "to flow" (see rheum). Respelled 16c. from diarria on Latin model.
Douai: or Douay, name of town in northern France, used elliptically in reference to the English translation of the Bible begun there late 16c., sanctioned by Roman Catholic Church. [Also called Rheims-Douai translation because it was published in Rheims in 1582]. It uses more Latinate words than the KJV.
gonorrhea (n.): also gonorrhoea, 1520s, from Late Latin gonorrhoia, from Greek gonos "seed" (see gonad) + rhoe "flow," from rhein "to flow" (see rheum). Mucus discharge was mistaken for semen. In early records often Gomoria, etc., from folk etymology association with biblical Gomorrah. Related: Gonorrheal; gonorrhoeal.
hemorrhoids (n.): plural of hemorrhoid; late 14c., emeroudis, from Old French emorroides (13c.), from Latin hæmorrhoidae, from Greek haimorrhoides (phlebes) "(veins) liable to discharge blood," plural of haimorrhois, from haima "blood" (see -emia) + rhoos "a stream, a flowing," from rhein "to flow" (see rheum). Related: Hemmorhoidal.
Rhemish (adj.): "of or pertaining to Rheims (earlier English Rhemes), city in northeastern France (see Reims), 1580s; specifically in reference to an English translation of the New Testament by Roman Catholics at the English college there, published 1582.
rheum (n.): "mucous discharge," late 14c., from Old French reume "a cold" (13c., Modern French rhume), from Latin rheuma, from Greek rheuma "discharge from the body, flux; a stream, current, flood, a flowing," literally "that which flows," from rhein "to flow," from PIE root *sreu- "to flow" (cognates: Sanskrit sravati "flows," srotah "stream;" Avestan thraotah- "stream, river," Old Persian rauta "river;" Greek rheos "a flowing, stream," rhythmos "rhythm," rhytos "fluid, liquid;" Old Irish sruaim, Irish sruth "stream, river;" Welsh ffrwd "stream;" Old Norse straumr, Old English stream, Old High German strom (second element in maelstrom); Lettish strauma "stream, river;" Lithuanian sraveti "to trickle, ooze;" Old Church Slavonic struja "river," o-strovu "island," literally "that which is surrounded by a river;" Polish strumień "brook").
Rhine: principal river in western Germany, from German Rhein, from Middle High German Rin, ultimately from Gaulish Renos, literally "that which flows," from PIE root *reie- "to move, flow, run" (cognates: Sanskrit rinati "causes to flow," ritih "stream, course;" Latin rivus "stream;" Old Church Slavonic reka "river;" Middle Irish rian "river, way;" Gothic rinnan "run, flow," rinno "brook;" Middle Low German ride "brook;" Old English riþ "stream;" Old English rinnan, Old Norse rinna "to run," Dutch ril "running stream"). The spelling with -h- (also in Latin Rhenus; French Rhin) is from influence of the Greek form of the name, Rhenos.
Rhineland: 1670s, from German Rheinland; see Rhine + land (n.). Related: Rheinlander.
rhythm (n.): 1550s, "rhymed verse, metrical movement," from Latin rhythmus "movement in time," from Greek rhythmos "measured flow or movement, rhythm; proportion, symmetry; arrangement, order; form, shape, wise, manner; soul, disposition," related to rhein "to flow," from PIE root *sreu- "to flow" (see rheum). Rhythm method of birth control attested from 1936. Rhythm and blues, U.S. music style, is from 1949 (first in "Billboard").
seborrhea (n.): also seborrhoea, "discharge of sebaceous matter, especially as a scalp condition," 1849, coined in Modern Latin as a hybrid, from sebo-, used as comb. form of Latin sebum "tallow, suet, grease" (see sebum) + Greek hroia "flow, flux," from rhein "to flow" (see rheum)
haemorrhoid: "A swollen vein or group of veins in the region of the anus", Late Middle English: via Old French and Latin from Greek haimorrhoides (phlebes) 'bleeding (veins)', from haima 'blood' + an element related to rhein 'to flow'.