Etymology
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sign (n.)

early 13c., signe, "gesture or motion of the hand," especially one meant to express thought or convey an idea, from Old French signe "sign, mark," from Latin signum "identifying mark, token, indication, symbol; proof; military standard, ensign; a signal, an omen; sign in the heavens, constellation."

According to Watkins, literally "standard that one follows," from PIE *sekw-no-, from root *sekw- (1) "to follow." De Vaan has it from PIE *sekh-no- "cut," from PIE root *sek- "to cut" He writes: "The etymological appurtenance to seco 'to cut' implies a semantic shift of *sek-no- 'what is cut out', 'carved out' > 'sign'." But he also also compares Hebrew sakkin, Aramaic sakkin "slaughtering-knife," and mentions a theory that "both words are probably borrowed from an unknown third source."

It has ousted native token. By c. 1300 as "an indication of some coming event." The meaning "a visible mark or device having some special meaning" is recorded from late 13c.; that of "miraculous manifestation, a miracle demonstrating divine power" is from c. 1300. In reference to one of the 12 divisions of the zodiac, from mid-14c.

The sense of "inscribed board with a characteristic device attached to the front of an inn, shop, etc.," to distinguish it from others is recorded from mid-15c. The meaning "indicator, token or signal of some condition" (late 13c.) is behind sign of the times (1520s). The meaning "conventional mark or symbol in place of words" (in music, mathematics, etc., as in plus sign) is by 1550s. In some uses, the word probably is a shortening of ensign

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sign (v.)

early 13c., signen, "to make the sign of the cross," from Old English segnian and Old French signier "to make a sign (to someone); to mark," both of them from Latin signare "to set a mark upon, mark out, designate; mark with a stamp; distinguish, adorn;" figuratively "to point out, signify, indicate," from signum "identifying mark, sign" (see sign (n.)).

The sense of "to mark, stamp" is attested from mid-14c.; that of "affix one's name or signature to" is from late 15c. The meaning "communicate by hand signs, make known by significant motion" is recorded from 1700.

Transitive sense in baseball, "engage (a player) by the signing of an agreement" is by 1889. To sign out (transitive) "secure the release of (someone or something) by signing" is attested by 1963, of library books. The intransitive sense of "record one's departure" is recorded by 1951. Related: Signed; signing.

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-on 

subatomic particle suffix, from ion.

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on- 

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

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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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sign-up (n.)

"action of signing up; number who have signed up," 1940, from the verbal phrase meaning "to enroll, enlist," which is attested by 1903; see sign (v.) + up (adv.).

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sign language (n.)

"system of communication using gestures," especially for communication with and among the deaf, by 1847; see sign (n.). Earlier hand-language (1670s).

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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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