Etymology
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testament (n.)
late 13c., "last will disposing of property," from Latin testamentum "a last will, publication of a will," from testari "make a will, be witness to," from testis "witness," from PIE *tri-st-i- "third person standing by," from root *tris- "three" (see three) on the notion of "third person, disinterested witness."

Use in reference to the two divisions of the Bible (early 14c.) is from Late Latin vetus testamentum and novum testamentum, loan-translations of Greek palaia diatheke and kaine diatheke. Late Latin testamentum in this case was a confusion of the two meanings of Greek diatheke, which meant both "covenant, dispensation" and "will, testament," and was used in the former sense in the account of the Last Supper (see testimony) but subsequently was interpreted as Christ's "last will."
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new (adj.)

Middle English neue, from Old English neowe, niowe, earlier niwe "made or established for the first time, fresh, recently made or grown; novel, unheard-of, different from the old; untried, inexperienced, unused," from Proto-Germanic *neuja- (source also of Old Saxon niuwi, Old Frisian nie, Middle Dutch nieuwe, Dutch nieuw, Old High German niuwl, German neu, Danish and Swedish ny, Gothic niujis "new").

This is from PIE *newo- "new" (source also of Sanskrit navah, Persian nau, Hittite newash, Greek neos, Lithuanian naujas, Old Church Slavonic novu, Russian novyi, Latin novus, Old Irish nue, Welsh newydd "new").

From mid-14c. as "novel, modern" (Gower, 1393, has go the new foot "dance the latest style"). In the names of cities and countries named for some other place, c. 1500. Meaning "not habituated, unfamiliar, unaccustomed," 1590s. Of the moon from late Old English. The adverb, "newly, for the first time," is Old English niwe, from the adjective. As a noun, "that which is new," also in Old English. There was a verb form in Old English (niwian, neowian) and Middle English (neuen) "make, invent, create; bring forth, produce, bear fruit; begin or resume (an activity); resupply; substitute," but it seems to have fallen from use.

New Testament is from late 14c. New math in reference to a system of teaching mathematics based on investigation and discovery is from 1958. New World (adj.) to designate phenomena of the Western Hemisphere first attested 1823, in Lord Byron; the noun phrase is recorded from 1550s. New Deal in the FDR sense is attested by 1932. New school in reference to the more advanced or liberal faction of something is from 1806. New Left (1960) was a coinage of U.S. political sociologist C. Wright Mills (1916-1962). New light in reference to religions is from 1640s. New frontier, in U.S. politics, "reform and social betterment," is from 1934 (Henry Wallace) but associated with John F. Kennedy's use of it in 1960.

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New Zealand 
from Dutch Nieuw Zeeland, literally "new sea land," but chiefly a reference to the Dutch province of Zeeland. Discovered 1647 by Dutch explorer Abel Tasman and originally named Staaten Landt; the name was changed the following year by Dutch authorities.
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brand-new (adj.)

"quite new," 1560s, from brand (n.) + new. The notion is "new as a glowing metal fresh from the forge" (Shakespeare has fire-new; Middle English had span-neue "brand new," c. 1300, from Old Norse span-nyr, from span "chip of wood," perhaps as something likely to be new-made). Popularly bran-new.

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New Wave 
1960, of cinema (from French Nouvelle Vague, late 1950s); 1976 as a name for the more restrained and melodic alternative to punk rock.
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New Orleans 

founded 1718 as Nouvelle Orléans, in honor of French regent Philippe, duc d'Orléans (1674–1723). The name was Englished after the place was purchased by the U.S. in 1803.

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new-made (adj.)

"recently made," c. 1400, from new + made. The verb new-make (1610s) probably is a back-formation.

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New Age (adj.)
1971, in reference to a modern spiritual movement, from new + age (n.). It had been used at various times at least since the 1840s.
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New York 

former New Amsterdam (city), New Netherlands (colony), renamed after British acquisition in 1664 in honor of the Duke of York and Albany (1633-1701), the future James II, who had an interest in the territory. See York. Related: New Yorker. Latinized Noveboracensian "of or pertaining to New York" (1890) contains the Medieval Latin name of York, England, Eboracum. New York minute "very short time" attested by 1976.

Some of Mr. [Horace] Gregory's poems have merely appeared in The New Yorker; others are New Yorker poems: the inclusive topicality, the informed and casual smartness, the flat fashionable irony, meaningless because it proceeds from a frame of reference whose amorphous superiority is the most definite thing about it—they are the trademark not simply of a magazine but of a class. [Randall Jarrell, "Town Mouse, Country Mouse," The Nation, Sept. 20, 1941]
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New Jersey 
named 1664 by one of the proprietors, Sir George Carteret, for his home, the Channel island of Jersey. Jersey girl attested from 1770.
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