Etymology
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center (n.)

late 14c., "middle point of a circle; point round which something revolves," from Old French centre (14c.), from Latin centrum "center," originally the fixed point of the two points of a drafting compass (hence "the center of a circle"), from Greek kentron "sharp point, goad, sting of a wasp," from kentein "stitch," from PIE root *kent- "to prick" (source also of Breton kentr "a spur," Welsh cethr "nail," Old High German hantag "sharp, pointed").

The spelling with -re was popularized in Britain by Johnson's dictionary (following Bailey's), though -er is older and was used by Shakespeare, Milton, and Pope. Meaning "the middle of anything" attested from 1590s. Figuratively, "point of concentration" (of power, etc.) is from 1680s. Political use, originally in reference to France, "representatives of moderate views" (between left and right) is from 1837. Center of gravity is recorded from 1650s. Center of attention is from 1868.

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center (v.)
1590s, "to concentrate at a center," from center (n.). Meaning "to rest as at a center" is from 1620s. Sports sense of "to hit toward the center" is from 1890. Related: Centered; centering. To be centered on is from 1713. In combinations, -centered is attested by 1958.
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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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dead-center (adj., adv.)

"in the exact middle," 1874, the noun phrase (1836) in reference to lathes or other rotating machinery, meaning the point which does not revolve; see dead (adj.).

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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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center-field (n.)

also centerfield, 1857 in baseball, from center (n.) + field (n.). Related: Center-fielder.

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hard-on (n.)
"penile erection," 1922, earlier as an adjective (1893), from hard + on.
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