rational

Etymology 1

From Old French rationel, rational, from Latin rationalis (“of or belonging to reason, rational, reasonable; having a ratio”), from ratio (“reason; calculation”).

adj

1. Capable of reasoning.
   Man is a rational creature.
   The utility of valid arguments is a monument to our frailty: to the fact that we are not completely rational beings. 2001, Mark Sainsbury, chapter 1, in Logical Forms — An Introduction to Philosophical Logic, 2nd edition, Blackwell Publishing, §7, page 32
2. Logically sound; not self-contradictory or otherwise absurd.
   His statements were quite rational.
   Prevention for the future is now almost universally allowed to be the only rational plea for the infliction of punishment; but this, when left to the arbitrary discretion of individuals, always has been found, and always will be found, to degenerate into the exercise of revenge for the past. 1812 The Freethinking Christians' Magazine: Volume 2 p. 21
3. (of a person or personal characteristics) Healthy or balanced intellectually; exhibiting reasonableness.
   rational conduct
   Temperature 99.8 degrees. Pulse 104. She was quite conscious and rational at times, at others very noisy. 1867 C. Handfield Jones, Case Of Low Fever: Delirium: Incomplete Dementia. The British Medical Journal Vol. 2, No. 344, Aug. 3
   The [Isaac] Newton that emerges from the [unpublished] manuscripts is far from the popular image of a rational practitioner of cold and pure reason. The architect of modern science was himself not very modern. He was obsessed with alchemy. 2014-06-21, “Magician’s brain”, in The Economist, volume 411, number 8892
4. (mathematics, arithmetic, number theory, not comparable) Of a number, capable of being expressed as the ratio of two integers.
   ¾ is a rational number, but √2 is an irrational number.
5. (mathematics, arithmetic, not comparable) Of an algebraic expression, capable of being expressed as the ratio of two polynomials.
6. (chemistry) Expressing the type, structure, relations, and reactions of a compound; graphic; said of formulae.
7. (physics) Expressing a physical object.
   A rational table is physical, a written table is neither.

noun

1. (mathematics) A rational number: a number that can be expressed as the quotient of two integers.
   The quotient of two rationals is again a rational.

Etymology 2

From Old French rational, from Medieval Latin rationale (“a pontifical stole, a pallium, an ornament worn over the chasuble”), neuter of Latin rationalis (“rational”), for which see the first etymology. Translation of λογεῖον (logeîon) or perhaps λόγιον (lógion, “oracle”) in the Septuagint version of Exodus 28.

noun

1. (historical) The breastplate worn by Israelite high priests.