Etymology
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examine (v.)

c. 1300, "put (someone) to question in regard to knowledge, competence, or skill, inquire into qualifications or capabilities;" mid-14c., "inspect or survey (something) carefully, scrutinize, view or observe in all aspects with the purpose of forming a correct opinion or judgment," from Old French examiner "interrogate, question, torture," from Latin examinare "to test or try; consider, ponder," literally "to weigh," from examen "a means of weighing or testing," probably ultimately from exigere "demand, require, enforce," literally "to drive or force out," also "to finish, measure," from ex "out" (see ex-) + agere "to set in motion, drive, drive forward; to do, perform" (from PIE root *ag- "to drive, draw out or forth, move"). Legal sense of "question or hear (a witness in court)" is from early 15c. Related: Examined; examining.

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re-examine (v.)

also reexamine, "examine again, subject to another examination," 1590s, from re- + examine. Related: Re-examined; re-examining; re-examination.

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cross-examine (n.)

"examine a witness (by the other side) to 'check' the effects of previous questioning," 1660s, from cross (adv.) in the sense "proceeding from an adverse party by way of reciprocal contest" + examine. Related: Cross-examination (1746).

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examiner (n.)

early 14c., examinour "one who questions (a witness)," agent noun from examine.

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unexamined (adj.)
late 15c., from un- (1) "not" + past participle of examine (v.).
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examination (n.)

late 14c., "action of testing or judging; judicial inquiry," from Old French examinacion, from Latin examinationem (nominative examinatio), noun of action from past-participle stem of examinare "to weigh; to ponder, consider" (see examine). Sense of "test of knowledge" is attested from 1610s.

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essay (n.)

1590s, "trial, attempt, endeavor," also "short, discursive literary composition" (first attested in writings of Francis Bacon, probably in imitation of Montaigne), from French essai "trial, attempt, essay" (in Old French from 12c.), from Late Latin exagium "a weighing, a weight," from Latin exigere "drive out; require, exact; examine, try, test," from ex "out" (see ex-) + agere "to set in motion, drive" (from PIE root *ag- "to drive, draw out or forth, move") apparently meaning here "to weigh." The suggestion is of unpolished writing. Compare assay, also examine.

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*ag- 

Proto-Indo-European root meaning "to drive, draw out or forth, move."

It forms all or part of: act; action; active; actor; actual; actuary; actuate; agency; agenda; agent; agile; agitation; agony; ambagious; ambassador; ambiguous; anagogical; antagonize; apagoge; assay; Auriga; auto-da-fe; axiom; cache; castigate; coagulate; cogent; cogitation; counteract; demagogue; embassy; epact; essay; exact; exacta; examine; exigency; exiguous; fumigation; glucagon; hypnagogic; interact; intransigent; isagoge; litigate; litigation; mitigate; mystagogue; navigate; objurgate; pedagogue; plutogogue; prodigal; protagonist; purge; react; redact; retroactive; squat; strategy; synagogue; transact; transaction; variegate.

It is the hypothetical source of/evidence for its existence is provided by: Greek agein "to lead, guide, drive, carry off," agon "assembly, contest in the games," agōgos "leader," axios "worth, worthy, weighing as much;" Sanskrit ajati "drives," ajirah "moving, active;" Latin actus "a doing; a driving, impulse, a setting in motion; a part in a play;" agere "to set in motion, drive, drive forward," hence "to do, perform," agilis "nimble, quick;" Old Norse aka "to drive;" Middle Irish ag "battle."

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discuss (v.)

late 14c., discussen, "to examine, investigate," from Latin discuss-, past participle stem of discutere "to dash to pieces, agitate, strike or shake apart," in Late Latin and Medieval Latin also "to discuss, examine, investigate," from dis- "apart" (see dis-) + quatere "to shake" (see quash).

Meaning "examine by argument, debate," the usual modern sense, is from mid-15c. (implied in discussing). Sense evolution in Latin appears to have been from "smash apart" to "scatter, disperse," then in post-classical times (via the mental process involved) to "investigate, examine," then to "debate." Related: Discussed.

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analyze (v.)
c. 1600, of material things, "to dissect, take to pieces," from French analyser, from the noun analyse "analysis" (see analysis). Of literature, "examine critically to get the essence of," from 1610s; meaning in chemistry ("resolve a compound into elements") dates from 1660s. General sense of "to examine closely" dates from 1809; psychological sense is from 1909. Related: Analyzed; analyzing.
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