Etymology
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reason (v.)

c. 1400, resounen, "to question (someone)," also "to challenge," from Old French resoner, raisoner "speak, discuss; argue; address; speak to," from Late Latin rationare "to discourse," from Latin ratio "reckoning, understanding, motive, cause," from ratus, past participle of reri "to reckon, think" (from PIE root *re- "to reason, count").

The intransitive sense of "to think in a logical manner, exercise the faculty of reason" is from 1590s; transitive sense of "employ reasoning (with someone)" is from 1680s. Related: Reasoned; reasoning.

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reason (n.)

c. 1200, resoun, "the intellectual faculty that adopts actions to ends," also "statement in an argument, statement of explanation or justification," from Anglo-French resoun, Old French raison "course; matter; subject; language, speech; thought, opinion," from Latin rationem (nominative ratio) "reckoning, understanding, motive, cause," from ratus, past participle of reri "to reckon, think" (from PIE root *re- "to reason, count").

Meaning "sanity; degree of intelligence that distinguishes men from brutes" is recorded from late 13c.; that of "that which recommends itself to enlightened intelligence, a reasonable view of a matter" is from c. 1300.

The sense of "grounds for action, motive, cause of an event" is from c. 1300. The Middle English sense of "meaning, signification" (early 14c.) is preserved in the phrase rhyme or reason. Phrase it stands to (or with) reason is from 1520s. A reason of state (1610s) is a purely political grounds for action.

The Enlightenment gave reason its focused sense of "intelligence considered as having universal validity ... so that it is not something that belongs to any person, but is something partaken of, a sort of light in which every mind must perceive" [Century Dictionary]. Reason itself has long been personified, typically as a woman. Age of Reason "the European Enlightenment" is first recorded 1794 as the title of Tom Paine's book. 

Reason is never a root, neither of act nor desire.
[Robinson Jeffers, "Meditation on Saviors"]
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unreason (n.)
c. 1300, "injustice;" 1827, "absense of reason," from un- (1) "not" + reason (n.).
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reasoning (n.)

late 14c., resouning, "exercise of the power of reason; act or process of thinking logically;" also an instance of this, a presentation of reasons or arguments; verbal noun from reason (v.).

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raison d'etat (n.)

1869, from French raison d'état "reason of state," thus "convenience of the government." See reason (n.) + state (n.2).

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rational (adj.)

late 14c., racional, "pertaining to or springing from reason;" mid-15c., of persons, "endowed with reason, having the power of reasoning," from Old French racionel and directly from Latin rationalis "of or belonging to reason, reasonable," from ratio (genitive rationis) "reckoning, calculation, reason" (see ratio).

In arithmetic, "expressible in finite terms," 1560s. Meaning "conformable to the precepts of practical reason" is from 1630s. Related: Rationally. It is from the same source as ratio and ration; the sense in rational is aligned with that in related reason (n.), which got deformed in French.

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*re- 

*rē-, Proto-Indo-European root meaning "to reason, count;" a variant of PIE root *ar-, also arə-, "to fit together." 

It forms all or part of: Alfred; arraign; arithmetic; Conrad; dread; Eldred; Ethelred; hatred; hundred; kindred; logarithm; Ralph; rate (n.) "estimated value or worth;" rathskeller; ratify; ratio; ration; read; reason; rede; rhyme; riddle (n.1) "word-game;" rite; ritual.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit radh- "to succeed, accomplish;" Greek arithmos "number, amount;" Latin reri "to consider, confirm, ratify," ritus "rite, religious custom;" Old Church Slavonic raditi "to take thought, attend to;" Old Irish im-radim "to deliberate, consider;" Old English rædan "to advise, counsel, persuade; read;" Old English, Old High German rim "number;" Old Irish rim "number," dorimu "I count."

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rhyme (n.)

"agreement in terminal sounds of words or metrical lines," a 16c. attempt to restore a classical spelling to Middle English ryme, rime (c. 1200) "measure, meter, rhythm," later "rhymed verse" (mid-13c.), from Old French rime (fem.), which is related to Old Provençal rim (masc.), earlier *ritme, from Latin rithmus, from Greek rhythmos "measured flow or movement, rhythm; proportion, symmetry; arrangement, order; form, shape, wise, manner; soul, disposition," related to rhein "to flow" (from PIE root *sreu- "to flow").

The persistence of rime, the older form of the word, perhaps is due to popular association with Old English rim "number" (from PIE root *re- "to reason, count"). The intermediate form rhime was frequent until late 18c.

In Medieval Latin, rithmus was used for accentual, as opposed to quantitative, verse, and accentual verse usually was rhymed, hence the sense shift. In prosody, specifically the quality of agreement in end-sounds such that the last stressed vowel, and any sounds after it, are the same, and preceding sounds differ. 

Verse was invented as an aid to memory. Later it was preserved to increase pleasure by the spectacle of difficulty overcome. That it should still survive in dramatic art is a vestige of barbarism. [Stendhal "de l'Amour," 1822]

The sense of "a piece of poetry in which consonance of end-sounds is observed" is from 1610s. From 1650s as "word that rhymes with another." The phrase rhyme or reason "good sense" (chiefly used in the negative) is from late 15c. (see reason (n.)). Rhyme scheme "ordered pattern of end-rhymes in metrical composition" is attested from 1931. Rhyme royal (1841) is a stanza of seven 10-syllable lines rhymed a-b-a-b-b-c-c.

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reasonable (adj.)

c. 1300, resonable, "having sound judgment, endowed with the faculty of reason," from Old French raisonable, from Latin rationabilis, from ratio "reckoning, understanding, motive, cause," from ratus, past participle of reri "to reckon, think" (from PIE root *re- "to reason, count").

Also originally "rational, sane," senses now obsolete. The sense shifted somewhat in Middle English via "due to or resulting from good judgment," then "not exceeding the bounds of common sense."

The meaning "moderate in price" is recorded from 1660s; earlier it meant "moderate in amount" (14c.). Related: Reasonably, which is from late 14c. as "according to reason," c. 1500 as "fairly tolerably;" reasonableness

The adjective reasonable ... denotes a character in which reason, (taking that word in its largest acceptation,) possesses a decided ascendant over the temper and passions: and implies no particular propensity to a display of the discursive power, if indeed it does not exclude the idea of such a propensity. [Dugald Stewart, "Elements of the Philosophy of the Human Mind," 1856]
What the majority of people consider to be 'reasonable' is that about which there is agreement, if not among all, at least among a substantial number of people; 'reasonable' for most people, has nothing to do with reason, but with consensus. [Erich Fromm, "The Heart of Man," 1968]

In law, "befitting a person of reason or sound sense;" reasonable doubt (1670s) is doubt for which a pertinent reason can be assigned and which prevents conviction in the minds of jurors of the truth of the charge.

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logocentric (adj.)
"centered on reason," 1931, from logo- "reason" + -centric.
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