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amidst (prep.): a variant of amid (q.v.) with adverbial genitive -s and parasitic -t. Amidde became amyddes (13c.) and acquired a -t by 1560s, probably by association with superlatives in -st.
There is a tendency to use amidst more distributively than amid, e.g. of things scattered about, or a thing moving, in the midst of others. [OED]
in medias res: Latin, literally "in the midst of things" (see medium).
inter-: Latin inter (prep., adv.) "among, between, betwixt, in the midst of," from PIE *enter "between, among" (cognates: Sanskrit antar, Old Persian antar "among, between," Greek entera (plural) "intestines," Old Irish eter, Old Welsh ithr "among, between," Gothic undar, Old English under "under"), a comparative of *en "in" (see in). Also in certain Latin phrases in English, such as inter alia "among other things." A living prefix in English from 15c. Spelled entre- in French, most words borrowed into English in that form were re-spelled 16c. to conform with Latin except entertain, enterprise.
interim (n.): 1540s, from Latin interim (adv.) "in the meantime, meanwhile," originally "in the midst of that," from inter- "between" (see inter-) + im, ancient adverb from stem of pronoun is "this, that."
meta-: word-forming element meaning 1. "after, behind," 2. "changed, altered," 3. "higher, beyond;" from Greek meta (prep.) "in the midst of, in common with, by means of, in pursuit or quest of," from PIE *me- "in the middle" (cognates: German mit, Gothic miþ, Old English mið "with, together with, among;" see mid). Notion of "changing places with" probably led to senses "change of place, order, or nature," which was a principal meaning of the Greek word when used as a prefix (but also denoting "community, participation; in common with; pursuing").

Third sense, "higher than, transcending, overarching, dealing with the most fundamental matters of," is due to misinterpretation of metaphysics as "science of that which transcends the physical." This has led to a prodigious erroneous extension in modern usage, with meta- affixed to the names of other sciences and disciplines, especially in the academic jargon of literary criticism.
ring (n.1): "circular band," Old English hring "small circlet, especially one of metal for wearing on the finger or as part of a mail coat; anything circular," from Proto-Germanic *hringaz "something curved, circle" (cognates: Old Norse hringr, Old Frisian hring, Danish, Swedish, Dutch ring, Old High German hring, German Ring), from PIE *(s)kregh- nasalized form of (s)kregh-, from root *(s)ker- (3) "to turn, bend," with wide-ranging derivative senses (cognates: Latin curvus "bent, curved," crispus "curly;" Old Church Slavonic kragu "circle," and perhaps Greek kirkos "ring," koronos "curved").

Other Old English senses were "circular group of persons," also "horizon." Meaning "place for prize fight and wrestling bouts" (early 14c.) is from the space in a circle of bystanders in the midst of which such contests once were held, "... a circle formed for boxers, wrestlers, and cudgel players, by a man styled Vinegar; who, with his hat before his eyes, goes round the circle, striking at random with his whip to prevent the populace from crowding in" [Grose, 1785]. Meaning "combination of interested persons" is from 1829. Of trees, from 1670s; fairy ring is from 1620s. Ring finger is Old English hringfingr, a compound found in other Germanic languages. To run rings round (someone) "be superior to" is from 1891.

Nursery rhyme ring a ring a rosie is attested in an American form (with a different ending) from c. 1790. "The belief that the rhyme originated with the Great Plague is now almost universal, but has no evidence to support it and is almost certainly nonsense" ["Oxford Dictionary of English Folklore"]. This proposal of connection dates only to the late 1960s.
salamander (n.): mid-14c., "legendary lizard-like creature that can live in fire," from Old French salamandre "legendary fiery beast," also "cricket" (12c.), from Latin salamandra, from Greek salamandra, probably of eastern origin.

The application in zoology to a tailed amphibian (known natively as an eft or newt) is first recorded 1610s. Aristotle, and especially Pliny, are responsible for the fiction of an animal that thrives in and extinguishes fires. The eft lives in damp logs and secretes a milky substance when threatened, but there is no obvious natural explanation its connection with the myth.

Also used 18c. for "a woman who lives chastely in the midst of temptations" (after Addison), and "a soldier who exposes himself to fire in battle." To rub someone a salamander was a 19c. form of German student drinking toast (einem einen salamander reiben). Related: Salamandrine; salamandroid.
understand (v.): Old English understandan "comprehend, grasp the idea of," probably literally "stand in the midst of," from under + standan "to stand" (see stand (v.)). If this is the meaning, the under is not the usual word meaning "beneath," but from Old English under, from PIE *nter- "between, among" (cognates: Sanskrit antar "among, between," Latin inter "between, among," Greek entera "intestines;" see inter-). Related: Understood; understanding.

That is the suggestion in Barnhart, but other sources regard the "among, between, before, in the presence of" sense of Old English prefix and preposition under as other meanings of the same word. "Among" seems to be the sense in many Old English compounds that resemble understand, such as underniman "to receive," undersecan "examine, investigate, scrutinize" (literally "underseek"), underðencan "consider, change one's mind," underginnan "to begin." It also seems to be the sense still in expressions such as under such circumstances.

Perhaps the ultimate sense is "be close to;" compare Greek epistamai "I know how, I know," literally "I stand upon." Similar formations are found in Old Frisian (understonda), Middle Danish (understande), while other Germanic languages use compounds meaning "stand before" (German verstehen, represented in Old English by forstanden "understand," also "oppose, withstand"). For this concept, most Indo-European languages use figurative extensions of compounds that literally mean "put together," or "separate," or "take, grasp" (see comprehend). Old English oferstandan, Middle English overstonden, literally "over-stand" seem to have been used only in literal senses. For "to stand under" in a physical sense, Old English had undergestandan.