Etymology
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kerchief (n.)
"square piece of fabric folded and worn about the head," early 13c., kovrechief "piece of cloth used to cover part of the head," especially a woman's head-cloth or veil, from Anglo-French courchief, Old French couvrechief "a kerchief," literally "cover head," from couvrir "to cover" (see cover (v.)) + chief "head" (from Latin caput "head," from PIE root *kaput- "head"). From late 14c. as "piece of cloth used about the person" generally, for purposes other than covering the head; and from c. 1400 as "piece of cloth carried in the hand" to wipe the face, etc. (compare handkerchief).
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trounce (v.)

1550s, "to trouble, afflict, harass," later "to beat, thrash" (1560s), of uncertain origin. Perhaps related to French troncer "to cut, cut off a piece from," from tronce "piece of timber," from Old French tronc (see trunk (n.1)). Related: Trounced; trouncing.

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pane (n.)

mid-13c., "garment, cloak, mantle; a part of a garment;" later "side of a building, section of a wall," from Old French pan "section, piece, panel" (11c.) and directly from Latin pannum (nominative pannus) "piece of cloth, garment," possibly from PIE root *pan- "fabric" (source also of Gothic fana "piece of cloth," Greek pēnos "web," Old English fanna "flag"). De Vaan writes, "If the Gr. and Gm. words listed are related, they probably represent loanwords from an unknown source."

From late 14c. as "section of a wall," also "ornamental hanging, coverlet," and c. 1400 as "a bedspread." The general notion in the word is "distinct part or piece of a surface." Sense of "piece of glass inserted in a window" is attested by mid-15c.

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firebrand (n.)
also fire-brand, c. 1200, "piece of wood kindled at a fire, a piece of something burning," from fire (n.) + brand (n.). Used for spreading fire. Figurative sense of "one who kindles mischief or passions" is from late 14c.
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shred (n.)

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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shard (n.)

also sherd, "piece or fragment," especially "piece of baked clay, piece of broken pottery or tile," from Old English sceard "incision, cleft, gap; potshard, a fragment, broken piece," from Proto-Germanic *skardaz (source also of Middle Dutch schaerde "a fragment, a crack," Dutch schaard "a flaw, a fragment," German Scharte "a notch," Danish skaar "chink, potsherd"), a past participle from PIE root *sker- (1) "to cut."

Meaning "fragment of broken earthenware" developed in late Old English. Also used, by Gower (late 14c.), as "scale of a dragon." French écharde "prickle, splinter" is a Germanic loan-word.

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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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dead-march (n.)

"piece of solemn music played at funerals," c. 1600, from dead + march (n.1).

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flats (n.)
"level tidal tract," 1540s, from flat (n.) in the Middle English "level piece of ground" sense.
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mud-flap (n.)

"piece of rubber behind the wheel of a vehicle to prevent mud from splashing," 1903, from mud (n.) + flap (n.).

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