n. [ L., fr. reri, ratus, to reckon, believe, think, judge. See Reason. ] 1. (Math.) The relation which one quantity or magnitude has to another of the same kind. It is expressed by the quotient of the division of the first by the second; thus, the ratio of 3 to 6 is expressed by 3/6 or 1/2; of a to b by a/b; or (less commonly) the second term is made the dividend; as, a:b = b/a. [ 1913 Webster ]

☞ Some writers consider ratio as the quotient itself, making ratio equivalent to a number. [ 1913 Webster ] 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. [ 1913 Webster ]

2. Hence, fixed relation of number, quantity, or degree; rate; proportion; as, the ratio of representation in Congress. [ 1913 Webster ]

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. [ 1913 Webster ]

v. i. [ L. ratiocinatus, p. p. of ratiocinari, fr. ratio reason. See Ratio. ] To reason, esp. deductively; to offer reason or argument. [ 1913 Webster ]

n. [ L. ratiocinatio: cf. F. ratiocination. ] The process of reasoning, or deducing conclusions from premises; deductive reasoning. [ 1913 Webster ]

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. [ 1913 Webster ]

The ratiocinative meditativeness of his character. Coleridge. [ 1913 Webster ]

a. Ratiocinative. [ R. ] [ 1913 Webster ]

v. t. To supply with rations, as a regiment. [ 1913 Webster ]

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. [ 1913 Webster ]

☞ Officers have several rations, the number varying according to their rank or the number of their attendants. [ 1913 Webster ]

2. Hence, a certain portion or fixed amount dealt out; an allowance; an allotment. [ 1913 Webster ]

n. A rational being. Young. [ 1913 Webster ]

a. [ L. rationalis: cf. F. rationnel. See Ratio, Reason, and cf. Rationale. ] 1. Relating to the reason; not physical; mental. [ 1913 Webster ]

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. [ 1913 Webster ]

2. Having reason, or the faculty of reasoning; endowed with reason or understanding; reasoning. [ 1913 Webster ]

It is our glory and happiness to have a rational nature. Law. [ 1913 Webster ]

3. Agreeable to reason; not absurd, preposterous, extravagant, foolish, fanciful, or the like; wise; judicious; as, rational conduct; a rational man. [ 1913 Webster ]

4. (Chem.) Expressing the type, structure, relations, and reactions of a compound; graphic; -- said of formulae. See under Formula. [ 1913 Webster ]

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. [ 1913 Webster ]

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. [ 1913 Webster ]

What higher in her society thou find'st
Attractive, human, rational, love still. Milton. [ 1913 Webster ]

A law may be reasonable in itself, although a man does not allow it, or does not know the reason of the lawgivers. Swift. [ 1913 Webster ]

n. [ L. rationalis, neut. rationale. See Rational, a. ] An explanation or exposition of the principles of some opinion, action, hypothesis, phenomenon, or the like; also, the principles themselves. [ 1913 Webster ]