Etymology
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Words related to *bheue-

Bauhaus (n.)
1923, from German Bauhaus, literally "architecture-house;" name of a school of design founded in Weimar, Germany, 1919 by Walter Gropius (1883-1969), later extended to the principles it embodied. First element is bau "building, construction, structure," from Old High German buan "to dwell" (from PIE root *bheue- "to be, exist, grow"). For second element, see house (n.).
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be (v.)

Old English beon, beom, bion "be, exist, come to be, become, happen," from Proto-Germanic *biju- "I am, I will be." This "b-root" is from PIE root *bheue- "to be, exist, grow," and in addition to the words in English it yielded German present first and second person singular (bin, bist, from Old High German bim "I am," bist "thou art"), Latin perfective tenses of esse (fui "I was," etc.), Old Church Slavonic byti "be," Greek phu- "become," Old Irish bi'u "I am," Lithuanian būti "to be," Russian byt' "to be," etc.

The modern verb to be in its entirety represents the merger of two once-distinct verbs, the "b-root" represented by be and the am/was verb, which was itself a conglomerate. Roger Lass ("Old English") describes the verb as "a collection of semantically related paradigm fragments," while Weekley calls it "an accidental conglomeration from the different Old English dial[ect]s." It is the most irregular verb in Modern English and the most common. Collective in all Germanic languages, it has eight different forms in Modern English:

BE (infinitive, subjunctive, imperative); AM (present 1st person singular); ARE (present 2nd person singular and all plural); IS (present 3rd person singular); WAS (past 1st and 3rd persons singular); WERE (past 2nd person singular, all plural; subjunctive); BEING (progressive & present participle; gerund); BEEN (perfect participle).

The paradigm in Old English was: eom, beo (present 1st person singular); eart, bist (present 2nd person singular); is, bið (present 3rd person singular);  sind, sindon, beoð (present plural in all persons); wæs (past 1st and 3rd person singular); wære (past 2nd person singular); wæron (past plural in all persons); wære (singular subjunctive preterit); wæren (plural subjunctive preterit).

The "b-root" had no past tense in Old English, but often served as future tense of am/was. In 13c. it took the place of the infinitive, participle and imperative forms of am/was. Later its plural forms (we beth, ye ben, they be) became standard in Middle English and it made inroads into the singular (I be, thou beest, he beth), but forms of are claimed this turf in the 1500s and replaced be in the plural. For the origin and evolution of the am/was branches of this tangle, see am and was.

That but this blow Might be the be all, and the end all. ["Macbeth" I.vii.5]
beam (n.)

Old English beam originally "living tree," but by late 10c. also "rafter, post, ship's timber," from Proto-Germanic *baumaz "tree" (source also of Old Frisian bam "tree, gallows, beam," Middle Dutch boom, Old High German boum, German Baum "tree," and perhaps also (with unexplained sound changes) Old Norse baðmr, Gothic bagms), which is of uncertain etymology (according to Boutkan probably a substrate word). The shift from *-au- to -ea- is regular in Old English.

Meaning "ray of light" developed in Old English, probably because beam was used by Bede to render Latin columna (lucis), the Biblical "pillar of fire." Meaning "directed flow of radiation" is from 1906. To be on the beam "going in the right direction" (1941) originally was an aviator's term for "to follow the course indicated by a radio beam." Nautical sense of "one of the horizontal transverse timbers holding a ship together" is from early 13c., hence "greatest breadth of a ship," and slang broad in the beam, by 1894 of ships, of persons, "wide-hipped," by 1938.

Boer (n.)
"Dutch colonist in South Africa," 1824, from Dutch boer "farmer," from Middle Dutch, cognate with Old English gebur "dweller, farmer, peasant," and thus related to bower, German Bauer, and the final syllable of neighbor; from PIE root *bheue- "to be, exist, grow."

The Boer War (1899-1902), in which Great Britain defeated the South African Republic of Transvaal and Orange Free State, was technically the Second Boer War, there having been a brief preview 1880-1881.
bondage (n.)

c. 1300, "legal condition of a serf or slave," from Middle English bond "a serf, tenant farmer," from Old English bonda "householder," from or cognate with Old Norse boandi "free-born farmer," noun use of present participle of boa "dwell, prepare, inhabit," from PIE *bhow-, from root *bheue- "to be, exist, grow." For sense evolution, see bond (adj.). The sexual sado-masochism sense is recorded by 1963 (in a New York law against publications portraying it).

boodle (n.)
1833, "crowd;" 1858, "phony money," especially "graft money," actual or potential (1883), both American English slang, either or both based on bundle (n.), or from Dutch boedel "property, riches," which is from Proto-Germanic *bothla, from PIE root *bheue- "to be, exist, grow."
boom (n.1)
"long pole," 1640s, specifically, "long spar run out from a ship" (1660s), from Scottish boun, borrowed from Dutch boom "tree, pole, beam," from a Middle Dutch word analogous to German Baum, English beam (n.). As "movable bar for a microphone or camera," 1931.
boor (n.)
early 14c., "country-man, peasant farmer, rustic," from Old French bovier "herdsman," from Latin bovis, genitive of bos "cow, ox." This was reinforced by or merged with native Old English gebur "dweller, farmer, peasant" (unrelated but similar in sound and sense), and 16c. by its Dutch cognate boer, from Middle Dutch gheboer "fellow dweller," from Proto-Germanic *buram "dweller," especially "farmer" (compare German Bauer), from PIE root *bheue- "to be, exist, grow."

"A word of involved history in and out of English, though the ultimate etymology is clear enough" [OED]. In English it often was applied to agricultural laborers in or from other lands, as opposed to the native yeoman; negative transferred sense "one who is rude in manners" attested by 1560s (in boorish), from notion of clownish rustics. Related: Boorishness.
booth (n.)
c. 1200, mid-12c. in place-names, "temporary structure of boards, etc.," especially a stall for the sale of goods or food or entertainment, at a fair, etc., from Old Danish boþ "temporary dwelling," from East Norse *boa "to dwell," from Proto-Germanic *bowan-, from PIE root *bheue- "to be, exist, grow." See also bower, and compare German Bude "booth, stall," Middle Dutch boode, Lithuanian butas "house," Old Irish both "hut," Bohemian bouda, Polish buda, some of which probably were borrowed from East Norse, some independently formed from the PIE root.
bound (adj.2)
c. 1200, boun, "ready to go;" hence "going or intending to go" (c. 1400), from Old Norse buinn past participle of bua "to prepare," also "to dwell, to live," from Proto-Germanic *bowan (source also of Old High German buan "to dwell," Old Danish both "dwelling, stall"), from PIE root *bheue- "to be, exist, grow." Final -d is presumably through association with bound (adj.1).