Etymology
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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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radian (n.)
"angle subtended at the center of a circle by an arc equal in length to the radius," 1879, from radius.
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polygon (n.)

in geometry, "a plane figure with numerous angles," 1570s, from Late Latin polygonum, from Greek polygōnon, noun use of neuter of adjective polygōnos "many-angled," from polys "many" (from PIE root *pele- (1) "to fill") + -gōnos "angled," from gōnia "angle, corner" (from PIE root *genu- (1) "knee; angle"). Related: Polygonal.

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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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salient (n.)

"a salient angle or part, a projection," especially as part of a military work, 1828, from salient (adj.).

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canton (n.)

1530s, "corner, angle," from French canton "angle, corner (of a room); piece, portion of a country" (13c.), from Italian (Lombard dialect) cantone "region," especially in the mountains, augmentative of Latin canto "section of a country," literally "corner" (see cant (n.2)).

From 1570s as a term in heraldry and flag descriptions. From c. 1600 as "a subdivision of a country;" applied to the sovereign states of the Swiss republic from 1610s.

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