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unloose (v.)
mid-14c., "relax;" late 14c., "to set free," from un- (2), used here emphatically, + loose (v.). Old English had unliesan "unloose, set free." Related: Unloosed; unloosing.
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analytic (adj.)
"relating to or operating by analogy," c. 1600, from Medieval Latin analyticus, from Greek analytikos "analytical," from analytos "dissolved," from analyein "unloose, release, set free," from ana "up, back, throughout" (see ana-) + lysis "a loosening," from lyein "to unfasten" (from PIE root *leu- "to loosen, divide, cut apart").
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analytics (n.)
the division of logic which distinguishes good from bad arguments, 1590s, from Latin analytica from Greek analytika, from stem of analyein "unloose, release, set free," from ana "up, back, throughout" (see ana-) + lysis "a loosening," from lyein "to unfasten" (from PIE root *leu- "to loosen, divide, cut apart"); also see -ics. Ta Analytika was the name of Aristotle's treatises on logic.
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analytical (adj.)
"employing analytic methods," 1520s, with -al (1) + Medieval Latin analyticus, from Medieval Latin analyticus, from Greek analytikos "analytical," from analytos "dissolved," from analyein "unloose, release, set free," from ana "up, back, throughout" (see ana-) + lysis "a loosening," from lyein "to unfasten" (from PIE root *leu- "to loosen, divide, cut apart").

In linguistics, of languages that use particles and auxiliaries (rather than inflections) to modify meaning and show relations of words, from 1830. Analytical chemistry resolves compounds into elements. Related: Analytically.
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analysis (n.)
1580s, "resolution of anything complex into simple elements" (opposite of synthesis), from Medieval Latin analysis (15c.), from Greek analysis "solution of a problem by analysis," literally "a breaking up, a loosening, releasing," noun of action from analyein "unloose, release, set free; to loose a ship from its moorings," in Aristotle, "to analyze," from ana "up, back, throughout" (see ana-) + lysis "a loosening," from lyein "to unfasten" (from PIE root *leu- "to loosen, divide, cut apart").

Meaning "statement presenting results of an analytic process" is from 1660s. Psychological sense is from 1890. English also formerly had a noun analyse (1630s), from French analyse, from Medieval Latin analysis. Phrase in the final (or last) analysis (1844), translates French en dernière analyse.
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