Part 56

The term ratio is also sometimes applied to the difference of two quantities as well as to their quotient, in which case the former is called arithmetical ratio, the latter, geometrical ratio. The name ratio is sometimes given to the rule of three in arithmetic. See under Rule.

2. Hence, fixed relation of number, quantity, or degree; rate; proportion; as, the ratio of representation in Congress.

Compound ratio, Duplicate ratio, Inverse ratio, etc. See under Compound, Duplicate, etc. -- Ratio of a geometrical progression, the constant quantity by which each term is multiplied to produce the succeeding one.

Ra`ti*oc"i*nate (rsh`*s"*nt), v. i. [L. ratiocinatus, p. p. of ratiocinari, fr. ratio reason. See Ratio.] To reason, esp. deductively; to offer reason or argument.

Ra`ti*oc`i*na"tion (-n"shn), n. [L. ratiocinatio: cf. F. ratiocination.] The process of reasoning, or deducing conclusions from premises; deductive reasoning.

Ra`ti*oc"i*na*tive (- s"*n*tv), a. [L. ratiocinativus.] Characterized by, or addicted to, ratiocination; consisting in the comparison of propositions or facts, and the deduction of inferences from the comparison; argumentative; as, a ratiocinative process.

The ratiocinative meditativeness of his character.

Coleridge.

Ra`ti*oc"i*na*to*ry (-n*t*r), a. Ratiocinative. [R.]

Ra"tion (r"shn or rsh"n), n. [F., fr. L. ratio a reckoning, calculation, relation, reference, LL. ratio ration. See Ratio.] 1. A fixed daily allowance of provisions assigned to a soldier in the army, or a sailor in the navy, for his subsistence.

Officers have several rations, the number varying according to their rank or the number of their attendants.

2. Hence, a certain portion or fixed amount dealt out; an allowance; an allotment.

Ra"tion, v. t. To supply with rations, as a regiment.

Ra"tion*al (rsh"n*al), a. [L. rationalis: cf. F. rationnel. See Ratio, Reason, and cf. Rationale.] 1. Relating to the reason; not physical; mental.

Moral philosophy was his chiefest end; for the rational, the natural, and mathematics . . . were but simple pastimes in comparison of the other.

Sir T. North.

2. Having reason, or the faculty of reasoning; endowed with reason or understanding; reasoning.

It is our glory and happiness to have a rational nature.

Law.

3. Agreeable to reason; not absurd, preposterous, extravagant, foolish, fanciful, or the like; wise; judicious; as, rational conduct; a rational man.

4. (Chem.) Expressing the type, structure, relations, and reactions of a compound; graphic; -- said of formulæ. See under Formula.

Rational horizon. (Astron.) See Horizon, 2 (b). -- Rational quantity (Alg.), one that can be expressed without the use of a radical sign, or in exact parts of unity; -- opposed to irrational or radical quantity. -- Rational symptom (Med.), one elicited by the statements of the patient himself and not as the result of a physical examination.

Syn. -- Sane; sound; intelligent; reasonable; sensible; wise; discreet; judicious. -- Rational, Reasonable. Rational has reference to reason as a faculty of the mind, and is opposed to irrational; as, a rational being, a rational state of mind, rational views, etc. In these cases the speculative reason is more particularly referred to. Reasonable has reference to the exercise of this faculty for practical purposes, and means, governed or directed by reason; as, reasonable desires or plans; a reasonable charge; a reasonable prospect of success.

What higher in her society thou find'st Attractive, human, rational, love still.

Milton.

A law may be reasonable in itself, although a man does not allow it, or does not know the reason of the lawgivers.

Swift.

Ra"tion*al, n. A rational being. Young.