Etymology
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agonic (adj.)

"having no angle," 1846, from Greek agonos, from a- "not" (see a- (3)) + -gonos "angled," from gōnia "angle, corner" (from PIE root *genu- (1) "knee; angle"). In reference to the imaginary line on the earth's surface connecting points where the magnetic declination is zero.

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goniometer (n.)

instrument for measuring solid angles, 1766, from Greek gōnia "corner, angle" (from PIE root *genu- (1) "knee; angle") + -meter. Related: Goniometry.

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heptagon (n.)

1560s, from French heptagon, from Greek heptagonon, from hepta "seven" (see septi-) + gōnia "angle, corner" (from PIE root *genu- (1) "knee; angle"). Related: Heptagonal.

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trigonometry (n.)

"branch of mathematics that deals with relations between sides and angles of triangles," 1610s, from Modern Latin trigonometria (Barthelemi Pitiscus, 1595), from Greek trigonon "triangle" (from tri- "three" (see tri-) + gōnia "angle, corner" (from PIE root *genu- (1) "knee; angle") + metron "a measure" (from PIE root *me- (2) "to measure").

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hexagon (n.)

1560s, from Latin hexagonum, from Greek hexagonon, neuter of hexagonos "six-cornered, hexagonal," from hex "six" (see hexa-) + gōnia "angle, corner" (from PIE root *genu- (1) "knee; angle").

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decagon (n.)

"plane figure having ten sides and angles," 1630s, from Modern Latin decagonum, from Greek dekagonon, from deka "ten" (from PIE root *dekm- "ten") + gōnia "corner, angle" (from PIE root *genu- (1) "knee; angle"). Related: Decagonal.

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orthogonal (adj.)

"pertaining to or depending upon the use of right angles," 1570s, from French orthogonal, from orthogone, from Late Latin orthogonius, from Greek orthogonios "right-angled," from ortho- "straight" (see ortho-) + gōnia "angle, corner" (from PIE root *genu- (1) "knee; angle"). Related: Orthogonally; orthogonality.

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hypotenuse (n.)
the side of a right triangle that is opposite the right angle, 1570s, from Late Latin hypotenusa, from Greek hypoteinousa "stretching under" (the right angle), fem. present participle of hypoteinein, from hypo- "under" (see hypo-) + teinein "to stretch," from PIE root *ten- "to stretch." Formerly often erroneously hypothenuse. Related: Hypotenusal.
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cotangent (n.)

in trigonometry, "the tangent of the complement of a given angle," a contraction of co. tangent, abbreviation of complement + tangent (n.).

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octagon (n.)

in geometry, "a plane figure having eight angles and eight sides," 1650s, from Latin octagonos, from Greek oktagōnos, literally "eight-angled, eight-cornered," from okta- combining form of okto "eight" (see eight) + gōnia "angle," which is related to gony "knee" (from PIE root *genu- (1) "knee; angle"). Also octogon (1650s), from French octogone.

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