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

(Ra`ti*oc"i*na*tive) (- os"i*na*tiv), 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.

(Ra`ti*oc"i*na*to*ry) a. Ratiocinative. [R.]

(Ra"tion) 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) 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.

Ratihabition to Rattlings

(Rat`i*ha*bi"tion) n. [L. ratihabitio; ratus fixed, valid + habere to hold.] Confirmation or approbation, as of an act or contract. [Obs.] Jer. Taylor.

(Ra"ti*o) 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 &frac36 or ½; of a to b by a/b; or (less commonly) the second term is made the dividend; as, a:b = b/a.

Some writers consider ratio as the quotient itself, making ratio equivalent to a number.

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.

  By PanEris using Melati.

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