Etymology
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example (n.)

late 14c., "an instance typical of a class; a model, either good or bad, action or conduct as an object of imitation; an example to be avoided; punishment as a warning," partial re-Latinization of earlier essample, asaumple (mid-13c.), from Old French essemple "sample, model, example, precedent, cautionary tale," from Latin exemplum "a sample, specimen; image, portrait; pattern, model, precedent; a warning example, one that serves as a warning," literally "that which is taken out," from eximere "remove, take out, take away; free, release, deliver, make an exception of," from ex "out" (see ex-) + emere "buy," originally "take," from PIE root *em- "to take, distribute." 

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e.g. 

1680s, abbreviation of Latin exempli gratia "for the sake of example;" from genitive of exemplum "example" (see example) + ablative of gratia "sake, favor, grace" (from suffixed form of PIE root *gwere- (2) "to favor").

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exemplary (adj.)

1580s, "fit to be an example," from French exemplaire, from Late Latin exemplaris "that serves as an example, pattern, or motto," from exemplum "example, pattern, model" (see example). Earlier (early 15c.) as a noun meaning "a model of conduct," from Late Latin exemplarium.

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exemplar (n.)

late 14c., "original model of the universe in the mind of God," later (mid-15c.) "model of virtue," from Old French exemplaire (14c.) and directly from Late Latin exemplarium, from Latin exemplum "a copy, pattern, model" (see example). Related: Exemplarily.

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ensample (n.)

"precedent to be followed, illustrative instance; a pattern, model," c. 1300, variant of asaumple, from Old French essample "example" (see example). The survival of this variant form is due to its use in New Testament in KJV (1 Peter v.3). Tyndale (1526) there has insample.

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exemplify (v.)

early 15c., exemplifien, "to illustrate or demonstrate by examples, to instruct by (good) example, be or serve as a model (of conduct)," good or bad, from Medieval Latin exemplificare "to illustrate," from Latin exemplum "example, pattern, model" (see example). Meaning "to serve as an example" is recorded from 1793. Related: Exemplified; exemplifies; exemplifying.

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sampler (n.)

early 14c., "pattern or model to be imitated," from sample (n.) in one of its older senses now found only in its source, example. The meaning "embroidery specimen by a beginner to show skill," (1520s) is probably originally meant as "piece of embroidery serving as an illustrative specimen," or "pattern to be copied or to fix and retain a valuable pattern." As "a collection of samples, a representative selection," from 1912.

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sample (n.)

c. 1300, saumple, "something which confirms a proposition or statement, an instance serving as an illustration" (a sense now obsolete in this word), from Anglo-French saumple, which is a shortening of Old French essample, from Latin exemplum "a sample," or a shortening of Middle English ensaumple (see example (n.)).

The meaning "small quantity (of something) from which the general quality (of the whole) may be inferred" (later usually in a commercial sense) is recorded from early 15c. The sense of "specimen for scientific sampling" is by 1878; the sense in statistics, "a portion drawn from a population for study to make statistical estimates of the whole," is by 1903. As an adjective from 1820.

The word also was used in Middle English in many of the senses now only found in example, such as "an incident that teaches a lesson; a model of action or conduct to be imitated."

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*em- 

Proto-Indo-European root meaning "to take, distribute." 

It forms all or part of: assume; consume; emption; example; exemplar; exemplary; exemplify; exempt; exemption; impromptu; peremptory; pre-emption; premium; presume; presumption; prompt; pronto; ransom; redeem; redemption; resume; sample; sejm; subsume; sumptuary; sumptuous; vintage.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit yamati "holds, subdues;" Latin emere "buy," originally "take," sumere "to take, obtain, buy;" Old Church Slavonic imo "to take;" Lithuanian imu, imti "to take."

For the sense shift from "take" to "buy" in the Latin verbs, compare Old English sellan "to give," source of Modern English sell "to give in exchange for money;" Hebrew laqah "he bought," originally "he took;" and colloquial English I'll take it for "I'll buy it." 

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one-off (n.)

"single example of a manufactured product," by 1927, from one + off. Later given figurative extension.

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