Etymology
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extreme (adj.)
early 15c., "outermost, farthest;" also "utter, total, in greatest degree" (opposed to moderate), from Old French extreme (13c.), from Latin extremus "outermost, utmost, farthest, last; the last part; extremity, boundary; highest or greatest degree," superlative of exterus (see exterior). In English as in Latin, not always felt as a superlative, hence more extreme, most extreme (which were condemned by Johnson). Extreme unction preserves the otherwise extinct sense of "last, latest" (15c.).
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extreme (n.)
1540s, "utmost point of a thing," from extreme (adj.); originally of the end of life (compare Latin in extremis in reference to the "last stages of life"). Phrase in the extreme "in an extreme degree" attested from c. 1600. Hence extremes "extremities, opposite ends of anything" (1550s); also "extreme measures" (1709).
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extremeness (n.)

"quality of being extreme, tendency to extremes," 1520s; see extreme (adj.) + -ness.

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extremely (adv.)
1530s, from extreme + -ly (2). Originally "with great severity," later more loosely, "in extreme degree" (1570s).
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extremist (n.)
"one who goes to extremes, a supporter of extreme doctrines," 1840, from extreme + -ist.
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in extremis 
"at the point of death," 16c., Latin, literally "in the farthest reaches," from ablative plural of extremus "extreme" (see extreme (adj.)).
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extremism (n.)

"disposition to go to extremes in doctrine or practice," 1848, from extreme + -ism.

I would remind you that extremism in the defense of liberty is no vice! And let me remind you also that moderation in the pursuit of justice is no virtue. [Barry Goldwater (1909-1998), acceptance speech as Republican candidate for President, 1963]
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extremity (n.)
late 14c., "one of two things at the extreme ends of a scale," from Old French estremite (13c.), from Latin extremitatem (nominative extremitas) "the end of a thing," from extremus "outermost;" see extreme (adj.), the etymological sense of which is better preserved in this word. Meaning "utmost point or end" is from c. 1400; meaning "limb or organ of locomotion, appendage" is from early 15c. (compare extremities). Meaning "highest degree" of anything is early 15c. Related: Extremital.
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terminal (adj.)
mid-15c., "relating to or marking boundaries," from Latin terminalis "pertaining to a boundary or end, final," from terminus "end, boundary line" (see terminus). Meaning "fatal" (terminal illness) is first recorded 1891. Sense of "situated at the extreme end" (of something) is from 1805. Slang meaning "extreme" first recorded 1983. Related: Termninally.
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intransigent (adj.)
1874, "uncompromising, refusing to agree or come to understanding," (used of extreme political factions or parties), from French intransigeant (18c.), from Spanish los intransigentes, literally "those not coming to agreement," name for extreme left in the Spanish Cortes and the extreme republicans of the 1870s, from in- "not" (see in- (1)) + transigente "compromising," from Latin transigentem (nominative transigens), present participle of transigere "come to an agreement, accomplish, to carry through" (see transaction). It acquired its generalized sense in French. As a noun in English from 1879.
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