rational adj.

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.

1550, "the mental process of reasoning," later, "the relation of one number to another" (1660s), then "fixed allowance of food or other means of subsistence for a fixed period of time" (1702, often rations, from French ration in this sense).

All are from Latin rationem (nominative ratio) "reckoning, numbering, calculation; business affair, procedure," also "reason, reasoning, judgment, understanding," in Medieval Latin "a computed share or allowance of food." This is from rat-, past participle stem of reri "to reckon, calculate," also "think" (from PIE root *re- "to reason, count").

The first sense listed for the English word is obsolete; the second has gone with ratio. The military pronunciation (rhymes with fashion) took over in English from the preferred civilian pronunciation (rhymes with nation) during World War I. That war also gave the word a specific sense of "officially limited allowance for civilians in times of war or dearth" (by 1917).