Etymology
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angle (v.1)
"to fish with a hook," mid-15c., from Old English angel (n.) "angle, hook, fish-hook," related to anga "hook," from Proto-Germanic *angul-, from PIE *ankulo-, suffixed form of root *ang-/*ank- "to bend" (see angle (n.)). Compare Old English angul, Old Norse öngull, Old High German angul, German Angel "fishhook." Figurative sense "catch or elicit by artful wiles" is recorded from 1580s. Related: Angled; angling.
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angle (n.)
"space or difference in direction between intersecting lines," late 14c., from Old French angle "an angle, a corner" (12c.) and directly from Latin angulus "an angle, a corner," a diminutive form from PIE root *ang-/*ank- "to bend" (source also of Greek ankylos "bent, crooked," Latin ang(u)ere "to compress in a bend, fold, strangle;" Old Church Slavonic aglu "corner;" Lithuanian anka "loop;" Sanskrit ankah "hook, bent," angam "limb;" Old English ancleo "ankle;" Old High German ango "hook").

Figurative sense "point or direction from which one approaches something" is from 1872. Angle-bracket is 1781 in carpentry; 1956 in typography.
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Angle 

member of a Teutonic tribe, Old English, from Latin Angli "the Angles," literally "people of Angul" (Old Norse Öngull), a region in what is now Holstein, said to be so-called for its hook-like shape (see angle (n.)). Or the name might refer to fishing (with hooks) as a main activity of the people, and Proto-Germanic *anguz is said also to have meant "narrow," so it might refer to shallow coastal waters.

People from the tribe there founded the kingdoms of Mercia, Northumbia, and East Anglia in 5c. Britain. Their name, rather than that of the Saxons or Jutes, may have become the common one for the whole group of Germanic tribes because their dialect was the first committed to writing.

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angle (v.2)
"to move at an angle, to move diagonally or obliquely," 1741, from angle (n.). Related: Angled; angling.
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Anglist (n.)
"student of English," from German Anglist, from Medieval Latin Angli (see Angle). Related: Anglistics.
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Anglice (adv.)
"in (plain) English," c. 1600, from Medieval Latin Anglice, from Anglicus (see Angle).
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angler (n.)
"fisher with a hook and line," mid-15c. (c. 1300 as a surname); agent noun from angle (v.1).
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English (n.2)
"spin imparted to a ball" (as in billiards), 1860, from French anglé "angled" (see angle (n.)), which is similar to Anglais "English."
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Anglicism (n.)
1640s, "anglicized language, that which is peculiar to England in speech or writing," from Latin Anglicus "of the English" (see Angle) + -ism. As an instance of this, "a word or expression used particularly in England and not in America," from 1781.
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ankylosaurus (n.)
Cretaceous armored dinosaur, 1907, Modern Latin, from Greek ankylos "bent, curved" (see angle (n.)) + -saurus. Said to be a reference to the curved ribs.
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