but (adv., prep.)

Old English be- (unstressed) or bi (stressed) "near, in, by, during, about," from Proto-Germanic *bi "around, about," in compounds often merely intensive (source also of Old Saxon and Old Frisian bi "by, near," Middle Dutch bie, Dutch bij, German bei "by, at, near," Gothic bi "about"), from PIE *bhi, reduced form of root *ambhi- "around."

As an adverb by c. 1300, "near, close at hand."

OED (2nd ed. print) has 38 distinct definitions of it as a preposition. Originally an adverbial particle of place, which sense survives in place names (Whitby, Grimsby, etc., also compare rudesby). Elliptical use for "secondary course" was in Old English (opposed to main, as in byway, also compare by-blow "illegitimate child," 1590s, Middle English loteby "a concubine," from obsolete lote "to lurk, lie hidden"). This also is the sense of the second by in the phrase by the by (1610s).

By the way literally means "along the way" (c. 1200), hence "in passing by," used figuratively to introduce a tangential observation ("incidentally") by 1540s. To swear by something or someone is in Old English, perhaps originally "in the presence of." Phrase by and by (early 14c.) originally meant "one by one," with by apparently denoting succession; modern sense of "before long" is from 1520s.

By and large "in all its length and breadth" (1660s) originally was nautical, "sailing to the wind and off it," hence "in one direction then another;" from nautical expression large wind, one that crosses the ship's line in a favorable direction.

expressing motion or direction from within or from a central point, also removal from proper place or position, Old English ut "out, without, outside," from Proto-Germanic *ūt- (Old Norse, Old Frisian, Old Saxon, Gothic ut, Middle Dutch uut, Dutch uit, Old High German uz, German aus), from PIE root *uidh- "up, out, up away, on high" (source also of Sanskrit ut "up, out," uttarah "higher, upper, later, northern;" Avestan uz- "up, out," Old Irish ud- "out," Latin usque "all the way to, continuously, without interruption," Greek hysteros "the latter," Russian vy- "out").

Sense of "to a full end, completely, to a conclusion or finish" is from c. 1300. Meaning "so as to be no longer burning or alight; into darkness" is from c. 1400. Of position or situation, "beyond the bounds of, not within," early 15c. Meaning "into public notice" is from 1540s; that of "away from one's place of residence," c. 1600. The political sense of "not in office, removed or ejected from a position" is from c. 1600. Meaning "come into sight, become visible" (of stars, etc.) is by 1610s. In radio communication, a word indicating that the speaker has finished speaking, by 1950.

As a preposition, "out of; from, away from; outside of, beyond; except; without, lacking;" mid-13c., from the adverb.

Meaning "from harmonious relations, into quarreling" (as in to fall out) is from 1520s. Meaning "from one's normal state of mind" (as in put out) is from 1580s; out to lunch "insane" is student slang from 1955. Adjectival phrase out-of-the-way "remote, secluded" is attested from late 15c. Out-of-towner "one not from a certain place" is from 1911. Out of this world "excellent" is from 1938; out of sight "excellent, superior" is from 1891. To (verb) it out "bring to a finish" is from 1580s. Expression from here on out "henceforward" is by 1942. Out upon, expressing abhorrence or reproach, is from early 15c.

also *mbhi-, Proto-Indo-European root meaning "around;" probably derived from *ant-bhi "from both sides," from root *ant- "front, forehead."

It forms all or part of: abaft; about; alley (n.1) "open passage between buildings;" ambagious; ambassador; ambi-; ambidexterity; ambidextrous; ambience; ambient; ambiguous; ambit; ambition; ambitious; amble; ambulance; ambulant; ambulate; ambulation; ambulatory; amphi-; amphibian; Amphictyonic; amphisbaena; Amphiscians; amphitheater; amphora; amputate; amputation; ancillary; andante; anfractuous; be-; begin; beleaguer; between; bivouac; but; by; circumambulate; embassy; ember-days; funambulist; ombudsman; perambulate; perambulation; preamble; somnambulate; somnambulism; umlaut.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit abhitah "on both sides," abhi "toward, to;" Avestan aibi; Greek amphi "round about;" Latin ambi- "around, round about;" Gaulish ambi-, Old Irish imb- "round about, about;" Old Church Slavonic oba; Lithuanian abu "both;" Old English ymbe, German um "around."