Etymology
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border (v.)
c. 1400, "to put a border on;" 1530s as "to lie on the border of," from border (n.). Related: Bordered; bordering.
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border (n.)
mid-14c., bordure, in heraldry, "broad, colored band surrounding the shield," from Old French bordeure "seam, edge of a shield, border," from Frankish *bord or a similar Germanic source (compare Old English bord "side;" see board (n.2)). The form of the ending changed after c. 1500. From late 14c. as "edge, side, brink, margin," also "ornamental border along the edge of a dish, garment, etc." Italian and Spanish bordo also are from Germanic.

Sense of "boundary of a city or country" is from late 14c. From c. 1400 as "border region, district lying along the boundary of a country" (replacing earlier march). In U.S. history, "the line between the wild and settled regions of the country" (1827).
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on- 

the preposition and adverb on used as a prefix; Old English on-, an-.

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-on 
subatomic particle suffix, from ion.
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on (prep., adv.)

"in a position above and in contact with; in such a position as to be supported by;" also noting the goal to which some action is or has been directed; "about, concerning, regarding; in a position to cover;" as an adverb, "in or into a position in contact with and supported by the top or upper part of something; in or into place; in place for use or action; into movement or action; in operation," Old English on, unstressed variant of an "in, on, into," from Proto-Germanic *ana "on" (source also of Dutch aan, German an, Gothic ana "on, upon"), from PIE root *an- (1) "on" (source also of Avestan ana "on," Greek ana "on, upon," Latin an-, Old Church Slavonic na, Lithuanian nuo "down from").

Also used in Old English in many places where we now would use in. From 16c.-18c. (and still in northern England dialect) often reduced to o'. Phrase on to "aware" is from 1877.

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clip-on (adj.)

"held on by means of a clip," 1909, from the verbal phrase; see clip (v.2) + on (adv.).

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hang on (v.)
1860, "to remain clinging," 1860, especially "cling fondly to" (1871); see hang (v.) + on (adv.). As a command to be patient, wait a minute, from 1936, originally in telephone conversations.
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hard-on (n.)
"penile erection," 1922, earlier as an adjective (1893), from hard + on.
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