Etymology
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lath (n.)
"thin strip of wood" used chiefly in roof-building and plastering, late 13c., probably from an unrecorded Old English *læððe, variant of lætt "beam, lath," which is apparently from a Proto-Germanic *laþþo (source also of Old Saxon, Old Norse latta, Middle Dutch, German latte "lath," Dutch lat, Middle High German lade "plank," which is the source of German Laden "counter," hence, "shop"), but there are phonetic difficulties.
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lath (v.)
"to cover or line with laths," 1530s, from lath (n.). Related: Lathed; lathing.
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lattice (n.)
"work with open spaces formed by crossing or interlacing of laths, bars, etc.," c. 1300, from Old French latiz "lattice," from late "lath, board, plank, batten" (Modern French latte), from Frankish or some other Germanic source, such as Old High German latta "lath" (see lath). As a verb from early 15c. Related: Latticed.
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caber (n.)
pole used in housebuilding, especially as an object tossed in the Highland games, 1510s, from Gaelic cabar "pole, spar," cognate with Irish cabar "lath," Welsh ceibr "beam, rafter."
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shingle (n.1)
"thin piece of wood," c. 1200, scincle, from Late Latin scindula (also the source of German Schindel), altered (by influence of Greek schidax "lath" or schindalmos "splinter") from Latin scandula "roof tile," from scindere "to cut, rend, tear asunder, split; split up, part, divide, separate," from PIE *skind-, from root *skei- "to cut, split." Meaning "small signboard" is first attested 1842. Sense of "woman's short haircut" is from 1924; the verb meaning "to cut the hair so as to give the impression of overlapping shingles" is from 1857.
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lather (v.)
from a Middle English variant of letheren (v.), from Old English leþran (late West Saxon lyþran) "become covered with (sweat, blood, etc.)," also transitive, from Proto-Germanic *lauthrjan (source also of Old Norse leyðra "to clean, wash;" see lather (n.)). Meaning "to form in froth, produce suds or foam" is from c. 1600. Related: Lathered; lathering.
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lathe (n.)
"machine for turning wood, etc., so it can be worked by a tool held at rest," early 14c., of uncertain origin, probably from a Scandinavian source. OED compares Danish drejelad "turning-lathe;" other compounds with the element suggest a sense "framework, supporting structure." Others see a possible connection to Old Norse hloeða "to lade, load, saddle (a horse)."
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lather (n.)
Old English leaþr "foam, soap, washing soda," from Proto-Germanic *lauthran (source also of Old Norse lauðr "washing soap, foam"), from PIE *loutro- (source also of Gaulish lautron, Old Irish loathar "bathing tub," Greek louein "to bathe," Latin lavere "to wash"), which is from root *leue- "to wash" + instrumentative suffix *-tro-.

The modern noun might be a 16c. redevelopment from the verb. Meaning "violent perspiration" (especially of horses) is from 1650s; hence the transferred sense "state of agitation" (such as induces sweating), attested from 1839.
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ceiling (n.)

mid-14c., celynge, "act of paneling a room," noun formed (with -ing) from Middle English verb ceil "put a cover or ceiling over," later "cover (walls) with wainscoting, panels, etc." (early 15c.); from Old French celer "to conceal," also "cover with paneling" (12c.), from Latin celare "to hide" (from PIE root *kel- (1) "to cover, conceal, save"). Probably influenced by Latin caelum "heaven, sky" (see celestial).

Extended to the paneling itself from late 14c., then to lath-and-plaster work.  The meaning "interior overhead surface of a room" is attested by 1530s; by late 19c. the meaning "wainscoting" was only in provincial English. Figurative sense "upper limit" is from 1934. Colloquial figurative phrase hit the ceiling "lose one's temper, get explosively angry" attested by 1908; earlier it meant "to fail" (by 1900, originally U.S. college slang). Glass ceiling in the figurative sense of "invisible barrier that prevents women from advancing" in management, etc., is attested from 1988.

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