thereunder (adv.)

Old English þær "in or at that place, so far as, provided that, in that respect," from Proto-Germanic *thær (source also of Old Saxon thar, Old Frisian ther, Middle Low German dar, Middle Dutch daer, Dutch daar, Old High German dar, German da, Gothic þar, Old Norse þar), from PIE *tar- "there" (source also of Sanskrit tar-hi "then"), from root *to- (see the) + adverbial suffix -r.

Interjectional use is recorded from 1530s, used variously to emphasize certainty, encouragement, or consolation. To have been there "had previous experience of some activity" is recorded from 1877.

Old English under (prep.) "beneath, among, before, in the presence of, in subjection to, under the rule of, by means of," also, as an adverb, "beneath, below, underneath," expressing position with reference to that which is above, from Proto-Germanic *under- (source also of Old Frisian under, Dutch onder, Old High German untar, German unter, Old Norse undir, Gothic undar), from PIE *ndher- "under" (source also of Sanskrit adhah "below;" Avestan athara- "lower;" Latin infernus "lower," infra "below").

Productive as a prefix in Old English, as in German and Scandinavian (often forming words modeled on Latin ones in sub-). Notion of "inferior in rank, position, etc." was present in Old English. With reference to standards, "less than in age, price, value," etc., late 14c. As an adjective, "lower in position; lower in rank or degree" from 13c. Also used in Old English as a preposition meaning "between, among," as still in under these circumstances, etc. (though this may be an entirely separate root; see understand).

Under the weather "indisposed" is from 1810. Under the table is from 1913 in the sense of "very drunk," 1940s in sense of "illegal" (under-board "dishonest" is from c. 1600). To keep something under (one's) hat "secret" is from 1885; to have something under (one's) nose "in plain sight" is from 1540s; to speak under (one's) breath "in a low voice" is attested from 1832.