Etymology
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shiver (n.2)

"small piece, broken bit, splinter, fragment, chip," c. 1200, perhaps from an unrecorded Old English word related to Middle Low German schever, schiver "splinter," Old High German scivero, from Proto-Germanic *skif- "split" (source also of Old High German skivaro "splinter," German Schiefer "splinter, slate"), from PIE root *skei- "to cut, split."

Surviving, if at all, in phrases such as break to shivers "break into bits" (mid-15c.). Also, shiver is said to be still dialectal for "a splinter" in Norfolk and Lincolnshire.

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shred (n.)

Middle English shrede "scrap or fragment; strip hanging from a garment," from Old English screade "piece cut off, cutting, scrap," from Proto-Germanic *skraudōn- (source also of Old Frisian skred "a cutting, clipping," Middle Dutch schroode "shred," Middle Low German schrot "piece cut off," Old High German scrot, "scrap, shred, a cutting, piece cut off," German Schrot "log, block, small shot," Old Norse skrydda "shriveled skin"), from PIE *skreu- "to cut; cutting tool," extension of root *sker- (1) "to cut."

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piece (n.1)

c. 1200, pece, "fixed amount, measure, portion;" c. 1300, "fragment of an object, bit of a whole, slice of meat; separate fragment, section, or part," from Old French piece "piece, bit portion; item; coin" (12c.), from Vulgar Latin *pettia, probably from Gaulish *pettsi (compare Welsh peth "thing," Breton pez "piece, a little"), perhaps from an Old Celtic base *kwezd-i-, from PIE root *kwezd- "a part, piece" (source also of Russian chast' "part"). Related: Pieces.

Meaning "separate article forming part of a class or group" is from c. 1400; that of "specimen, instance, example" is from 1560s. Sense of "portable firearm" is from 1580s, earlier "artillery weapon" (1540s). The meaning "chessman" is from 1560s. Meaning "a period of time" is from early 14c.; that of "a portion of a distance" is from 1610s; that of "literary composition" dates from 1530s.

Piece of (one's) mind "one's opinion expressed bluntly" is from 1570s. Piece of work "remarkable person" echoes Hamlet. Piece as "a coin" is attested in English from c. 1400, hence piece of eight, old name for the Spanish dollar (c. 1600) of the value of 8 reals and bearing a numeral 8. Adverbial phrase in one piece "whole, undivided, without loss or injury" is by 1580s; of a piece "as of the same piece or whole" is from 1610s.

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scarf (n.2)

[connecting joint in carpentry, the ends being cut or notched so as to fit into each other], late 13c. (implied in scarf-nail), probably from a Scandinavian source, such as Old Norse skarfr "nail for fastening a joint; diagonally cut end of a board," Swedish skarf, Norwegian skarv, from Proto-Germanic *skarfaz, source also of Dutch scherf, Old English scearfe "a fragment, piece"(from PIE root *sker- (1) "to cut"). Also used as a verb, "unite by means of a scarf" (1620s). Also borrowed into Romanic (French écart, Spanish escarba).

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*plak- (1)

also *plāk-, Proto-Indo-European root meaning "to be flat;" extension of root *pele- (2) "flat; to spread."

It forms all or part of: flag (n.2) "flat stone for paving;" flagstone; flake (n.) "thin flat piece,; flaw; floe; fluke (n.3) "flatfish;" placenta; plagal; plagiarism; plagio-; planchet; plank.

It is the hypothetical source of/evidence for its existence is provided by: Greek plakoeis "flat," plax "level surface, anything flat;" Lettish plakt "to become flat;" Old Norse flaga "layer of earth," Norwegian flag "open sea," Old English floh "piece of stone, fragment," Old High German fluoh "cliff."

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scrap (n.1)

[small piece, fragment] late 14c., scrappe, "piece of food remaining after a meal" (usually plural), from Old Norse skrap "scraps; trifles," from skrapa "to scrape, scratch, cut" (see scrape (v.)).

Hence, "any remnant or small, detached piece" (1580s), typically negative (not a scrap) or in reference to something written or printed. The dismissive term scrap of paper is attested by 1840, made infamous in 1914 by the German chancellor's comment when violating the treaty that guaranteed Belgian neutrality.

The meaning "remains of metal produced or collected after rolling or casting to be reworked" is from 1790. Scrap-iron is attested by 1794.

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crumble (v.)

late 15c., kremelen, "to break into small fragments" (transitive), from Old English *crymelan, presumed frequentative of gecrymman "to break into crumbs," from cruma (see crumb). Intransitive sense of "fall into small pieces" is from 1570s.

The -b- is from 16c., probably on analogy of crumb (where it also is an unetymological intrusion) or of French-derived words like humble, where it belongs. Related: Crumbled; crumbling. Old English gecrymman yielded Middle English crimen "to crumble" (transitive).

As a noun, from 1570s as "a fragment," from 1947 in cookery as dessert dish with a crumb topping, British English. "The technique itself seems to have been a product of Second World War culinary making-do" [Ayto, "Diner's Dictionary"].

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brick (n.)

"rectangular block of artificial stone (usually clay burned in a kiln) used as a building material," early 15c., from Old French briche "brick," which is probably from a Germanic source akin to Middle Dutch bricke "a tile," etymologically "a bit, a fragment, a piece broken off," from the verbal root of break (v.).

Of a brick-shaped loaf by 1735. Meaning "a good, honest fellow" is from 1840, probably on notion of squareness (as in fair and square), though in English brick and square when applied to persons generally are not meant as compliments. Brick wall in the figurative sense of "impenetrable barrier" is from 1886. Brick-and-mortar (adj.) as figurative of "physically real" is from 1865. To do something like a ton of bricks "vigorously" is from 1929 (earlier thousand of bricks, 1836), probably from the notion of how hard such a weight of them falls or hits.

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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."

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*skei- 
Proto-Indo-European root meaning "to cut, split," extension of root *sek- "to cut."

It forms all or part of: abscissa; conscience; conscious; ecu; escudo; escutcheon; esquire; nescience; nescient; nice; omniscience; omniscient; plebiscite; prescience; prescient; rescind; rescission; science; scienter; scilicet; sciolist; scission; schism; schist; schizo-; schizophrenia; scudo; sheath; sheathe; sheave (n.) "grooved wheel to receive a cord, pulley;" shed (v.) "cast off;" shin (n.) "fore part of the lower leg;" shingle (n.1) "thin piece of wood;" shit (v.); shive; shiver (n.1) "small piece, splinter, fragment, chip;" shoddy; shyster; skene; ski; skive (v.1) "split or cut into strips, pare off, grind away;" squire.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit chindhi, chinatti "to break, split up;" Avestan a-sista- "unsplit, unharmed," Greek skhizein "to split, cleave, part, separate;" Latin scindere "to cut, rend, tear asunder, split;" Armenian c'tim "to tear, scratch;" Lithuanian skiesti "to separate, divide;" Old Church Slavonic cediti "to strain;" Old English scitan, Old Norse skita "to defecate;" Old English sceað, Old High German sceida "sheath;" Old Irish sceid "to vomit, spit;" Welsh chwydu "to break open."
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