Etymology
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Words related to *bheid-

abet (v.)
late 14c., "urge on, incite" (implied in abetting), from Old French abeter "to bait, to harass with dogs," literally "to cause to bite," from a- "to" (see ad-) + beter "to bait." This verb is probably from Frankish or some other Germanic source (perhaps Low Franconian betan "incite," or Old Norse beita "cause to bite"); ultimately from Proto-Germanic *baitjan, from PIE root *bheid- "to split," with derivatives in Germanic referring to biting. Sense of "encourage by aid or approval" is from 1779. Related: Abetted; abetting.
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bait (n.)
"food put on a hook or trap to attract prey," c. 1300, from Old Norse beita "food, bait," especially for fish, from beita "cause to bite," from Proto-Germanic *baitjan, causative of *bitan, from PIE root *bheid- "to split," with derivatives in Germanic referring to biting. The noun is cognate with Old Norse beit "pasture, pasturage," Old English bat "food." Figurative sense "means of enticement" is from c. 1400.
bateau (n.)
"light, long boat for river navigation," 1711, from Canadian French bateau, from Old French batel, from Germanic *bait- "a boat" (see boat (n.)).
beetle (n.1)
insect of the order Coleoptera, Old English bitela "beetle," apparently originally meaning "little biter, biting insect," from bitel "biting," from Proto-Germanic *bitan, from PIE root *bheid- "to split," with derivatives in Germanic referring to biting.

By normal evolution it would be *bittle, but it seems to have been influenced by beetle (n.2). Sometimes applied to soft insects, as black beetle, an old name for the cockroach. As a nickname for the original Volkswagen car, 1946, translating German Käfer.
bit (n.1)

"small piece," c. 1200; related Old English bite "act of biting," and bita "piece bitten off," which probably are the source of the modern words meaning "boring-piece of a drill" (the "biting" part, 1590s), "mouthpiece of a horse's bridle" (mid-14c.), and "a piece (of food) bitten off, morsel" (c. 1000). All from Proto-Germanic *biton (source also of Old Saxon biti, Old Norse bit, Old Frisian bite, Middle Dutch bete, Old High German bizzo "biting," German Bissen "a bite, morsel"), from PIE root *bheid- "to split."

Meaning "small piece, fragment" of anything is from c. 1600. Sense of "short space of time" is 1650s. Theatrical bit part is from 1909. Money sense "small coin" in two bits, etc. is originally from the U.S. South and the West Indies, in reference to silver wedges cut or stamped from Spanish dollars (later Mexican reals); transferred to "eighth of a dollar."

bite (v.)

Old English bitan "to pierce or cut with the teeth" (class I strong verb; past tense bat, past participle biten), from Proto-Germanic *beitanan (source also of Old Saxon bitan, Old Norse and Old Frisian bita "cut, pierce, penetrate," Middle Dutch biten, Dutch bijten, German beissen, Gothic beitan "to bite"), from PIE root *bheid- "to split," with derivatives in Germanic referring to biting.

To bite the bullet is said to be 1700s military slang, from old medical custom of having the patient bite a lead bullet during an operation to divert attention from pain and reduce screaming. Figurative use from 1891; the custom itself attested from 1840s. To bite (one's) tongue "refrain from speaking" is 1590s; to bite (one's) lip to repress signs of some emotion or reaction is from early 14c. To bite off more than one can chew (c. 1880) is U.S. slang, from plug tobacco.

To bite the dust "be thrown or struck down," hence "be vanquished, die, be slain, perish in battle" is from 1750, earlier bite the ground (1670s), lick the dust (late 14c.), which OED identifies as "a Hebraism," but Latin had the same image; compare Virgil's procubuit moriens et humum semel ore momordit.

bitter (adj.)
Old English biter "having a harsh taste, sharp, cutting; angry, full of animosity; cruel," from Proto-Germanic *bitras- (source also of Old Saxon bittar, Old Norse bitr, Dutch bitter, Old High German bittar, German bitter, Gothic baitrs "bitter"), from suffixed form of PIE root *bheid- "to split" (source also of Old English bitan "to bite;" see bite (v.)). Evidently the meaning drifted in prehistoric times from "biting, of pungent taste," to "acrid-tasting." Used figuratively in Old English of states of mind and words. Related: Bitterly.
bitter end (n.)

In lexicons of sea language going back to 1759, the bitter end is the part of a cable which is round about the bitts (the two great timbers used to belay cables) when the ship is at anchor (see bitt).

Bitter end of the Cable, the End which is wound about the Bitts. ["The News-Readers Pocket-Book: Or, a Military Dictionary," London, 1759]

So, when a cable is played out to the bitter end, there is no more left to play. The term began to be used c. 1835 in non-nautical use and with probable influence of or merger with bitter (adj.).

boat (n.)

"small open vessel (smaller than a ship) used to cross waters, propelled by oars, a sail, or (later) an engine," Old English bat, from Proto-Germanic *bait- (source also of Old Norse batr, Dutch boot, German Boot), possibly from PIE root *bheid- "to split," if the notion is of making a boat by hollowing out a tree trunk or from split planking. Or it may be an extension of the name for some part of a ship.

French bateau "boat" is from Old English or Norse. Spanish batel, Italian battello, Medieval Latin batellus likewise probably are from Germanic. Of serving vessels resembling a boat, by 1680s. The image of being in the same boat "subject to similar challenges and difficulties" is by 1580s; to rock the boat "disturb stability" is from 1914.

boatswain (n.)

mid-15c., from late Old English batswegen, from bat "boat" (see boat (n.)) + Old Norse sveinn "boy" (see swain).

BOATSWAIN. The warrant officer who in the old Navy was responsible for all the gear that set the ship in motion and all the tackle that kept her at rest. [Sir Geoffrey Callender, "Sea Passages," 1943]

He also summons the hands to their duties with a silver whistle. Phonetic spelling bo'sun/bosun is attested from 1840. Fowler [1926] writes, "The nautical pronunciation (bō'sn) has become so general that to avoid it is more affected than to use it."