Etymology
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cutting (n.)

mid-14c., "piece cut off;" late 14c., "act or fact of making incisions, action of cutting," verbal noun from cut (v.). Meaning "shoot or small bough bearing leaf-buds" is from 1660s. Meaning "slip cut from a newspaper or other print publication" is by 1856. Related: Cuttings.  Cutting-board is by 1819.

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undercut (v.)

late 14c., "to cut down or off," from under + cut (v.). In the commercial sense of "sell at lower prices" (or work at lower wages) it is first attested 1884. Figurative sense of "render unstable, undermine" is recorded from 1955, from earlier literal meaning "cut so as to leave the upper portion larger than the lower" (1874).

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sector (n.)

1560s, in geometry, "a section of a circle between two radii," from Late Latin sector "section of a circle," in classical Latin "a cutter, one who cuts," from sectus, past participle of secare "to cut" (from PIE root *sek- "to cut"). Sector translated Greek tomeus in Latin editions of Archimedes.

By 1715 of any figure having the shape of a sector; the meaning "area, division" (without regard to shape) is by 1920, perhaps generalized from a World War I military sense (1916) of "part of a front," based on a circle centered on a headquarters. The meaning "a branch of an economy" is by 1937. As a verb from 1884, "divide into sectors." Related: Sectored; sectoral; sectorial.

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clipping (n.2)

early 14c., "a cutting, act of shearing off," verbal noun from clip (v.1). Sense of "a small piece cut off" is from late 15c. Meaning "an article cut from a newspaper" is from 1857.

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crease (n.)

1660s, "long or thin mark made by doubling or folding," altered from creaste "a ridge," perhaps a variant of crest (n.), via meaning "a fold in a length of cloth" (mid-15c.) which produces a "crest." In sports, first in cricket (1779), where originally it was cut into the ground. As a verb, "to make creases in," from 1580s. Related: Creased; creasing.

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tranche (n.)

c. 1500, from French tranche "a cutting," from trancher, trencher "to cut," Old French trenchier "to cut, carve, slice" (see trench). Economic sense is from 1930.

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tome (n.)

1510s, "a single volume of a multi-volume work," from French tome (16c.) or directly from Latin tomus "section of a book, tome," from Greek tomos "volume, section of a book," originally "a section, piece cut off," from temnein "to cut," from PIE root *tem- "to cut." Sense of "a large book" is attested from 1570s.

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intersection (n.)

1550s, "act or fact of crossing," from French intersection (14c.) and directly from Latin intersectionem (nominative intersectio) "a cutting asunder, intersection," noun of action from past-participle stem of intersecare "intersect, cut asunder," from inter- "between" (see inter-) + secare "to cut" (from PIE root *sek- "to cut"). In English originally a term in geometry; meaning "crossroads, a place of crossing" is from 1864. Related: Intersectional.

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trencher (n.)

"wooden platter on which to cut meat," c. 1300, from Anglo-French trenchour, Old North French trencheor "a trencher," literally "a cutting place," from Old French trenchier "to cut, carve, slice" (see trench).

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match-board (n.)

in carpentry, "a board which has a tongue cut along one edge and a groove in the opposite edge," 1851, from match (n.2) + board (n.1). Matched, of boards so cut, is attested from 1837.

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