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Origin and history of ratio

ratio(n.)

1630s, in theological writing, "reason, rationale," from Latin ratio "a reckoning, account, a numbering, calculation," hence also "a business affair; course, conduct, procedure," also in a transferred sense, of mental action, "reason, reasoning, judgment, understanding, that faculty of the mind which forms the basis of computation and calculation." This is from rat-, past-participle stem of reri "to reckon, calculate," also "to think, believe" (from PIE root *re- "to think, reason, count").

Latin ratio often was used to represent or translate Greek logos ("computation, account, esteem, reason") in works of philosophy, though the range of senses in the two do not overlap (ratio lacks the key "speech, word, statement" meaning in the Greek word; see Logos).

The mathematical sense of "relation between two similar magnitudes in respect to quantity," measured by the number of times one contains the other, is attested in English from 1650s (it also was a sense in Greek logos). The general or extended sense of "corresponding relationship between things not precisely measurable" is by 1808.

also from 1630s

Entries linking to ratio

Logos(n.)

1580s, "the divine Word, second person of the Christian Trinity," from Greek logos "word, speech, statement, discourse," also "a computation, account," also "reason, judgment, understanding," from PIE *log-o-, suffixed form of root *leg- (1) "to collect, gather," with derivatives meaning "to speak," on notion of "to pick out words." The Greek word was used by Neo-Platonists in metaphysical and theological senses involving notions of both "reason" and "word" and subsequently picked up by New Testament writers.

ratiocination(n.)

"process of reasoning, mental process of passing from the cognition of premises to the cognition of the conclusion," 1520s, from Latin ratiocinationem (nominative ratiocinatio) "a reasoning, calm reasoning," noun of action from past-participle stem of ratiocinari "to reckon, compute, calculate; to deliberate, meditate; to reason, argue, infer." This is a compound of ratio "reckoning, calculation," also "judgment, reason" (see ratio) + -cinari, which probably is related to conari "to endeavor, to try," from PIE *kona-, from root *ken- "to hasten, set oneself in motion" (see deacon).

Most writers make ratiocination synonymous with reasoning. J.S. Mill and others hold that the word is usually limited to necessary reasoning. [Century Dictionary]

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