Definify.com
Webster 1913 Edition
Ratio
Ra′tio
(rā′shĭō̍ or rā′shō̍)
, Noun.
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 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 CongressWebster 1828 Edition
Ratio
RA'TIO
,Noun.
Proportion, or the relation of homogeneous things which determines the quantity of one from the quantity of another, without the intervention of a third.
The relation which one quantity has to another of the same kind, as expressed by the quotient of the one divided by the other. Thus the ratio of 4 to 2 is 4/2, or 2; and the ratio of 5 to 6 is 5/6. This is geometrical ratio, which is that signified when the term is used without distinction; but arithmetical ratio is the difference between two quantities. Thus the arithmetical ratio of 2 to 6 is 4.
Ratio respects magnitudes of the same kind only. One line may be compared with another line, but a line cannot be compared with a superficies, and hence between a line and a superficies there can be no ratio.
Definition 2022
Ratio
ratio
ratio
See also: Ratio
English
Noun
ratio (plural ratios)
 A number representing a comparison between two things.
 (arithmetic) The relative magnitudes of two quantities (usually expressed as a quotient).
 (law) Short for ratio decidendi.
Derived terms
Derived terms


Related terms
Translations
number representing comparison


arithmetics: relative magnitude of two quantities expressed as quotient
ratio decidendi — see ratio decidendi
Latin
Pronunciation
 IPA^{(key)}: /ˈratioː/
Etymology
From rat (“"thought", from perfect participle of reor”) + iō
Noun
ratiō f (genitive ratiōnis); third declension
Inflection
Third declension.
Case  Singular  Plural 

nominative  ratiō  ratiōnēs 
genitive  ratiōnis  ratiōnum 
dative  ratiōnī  ratiōnibus 
accusative  ratiōnem  ratiōnēs 
ablative  ratiōne  ratiōnibus 
vocative  ratiō  ratiōnēs 
Descendants
See also
References
 ratio in Charlton T. Lewis and Charles Short (1879) A Latin Dictionary, Oxford: Clarendon Press
 ratio in Charlton T. Lewis (1891) An Elementary Latin Dictionary, New York: Harper & Brothers
 RATIO in Charles du Fresne du Cange’s Glossarium Mediæ et Infimæ Latinitatis (augmented edition, 1883–1887)
 Félix Gaffiot (1934), “ratio”, in Dictionnaire Illustré LatinFrançais, Paris: Hachette.
 Meissner, Carl; Auden, Henry William (1894) Latin PhraseBook^{}, London: Macmillan and Co.
 the spirit of the times, the fashion: saeculi consuetudo or ratio atque inclinatio temporis (temporum)
 the case is exactly similar (entirely different): eadem (longe alia) est huius rei ratio
 to have regard for; take into consideration: rationem habere alicuius rei
 to look after, guard a person's interests, welfare: rationibus alicuius prospicere or consulere (opp. officere, obstare, adversari)
 my interests demanded it: meae rationes ita tulerunt
 to form a conception, notion of a thing: notionem or rationem alicuius rei in animo informare or animo concipere
 without reflection; inconsiderately; rashly: nullo consilio, nulla ratione, temere
 after mature deliberation: inita subductaque ratione
 to have a theoretical knowledge of a thing: ratione, doctrina (opp. usu) aliquid cognitum habere
 to reduce a thing to its theoretical principles; to apply theory to a thing: ad artem, ad rationem revocare aliquid (De Or. 2. 11. 44)
 to adopt a didactic tone: ad praecipiendi rationem delābi (Q. Fr. 1. 1. 6. 18)
 logic, dialectic: dialectica (ae or orum) (pure Latin disserendi ratio et scientia)
 to arrange on strictly logical principles: ratione, eleganter (opp. nulla ratione, ineleganter, confuse) disponere aliquid
 system: ratio; disciplina, ratio et disciplina; ars
 to systematise: ad rationem, ad artem et praecepta revocare aliquid (De Or. 1. 41)
 systematic, methodical knowledge: ratio et doctrina
 to treat with scientific exactness; to classify: ad rationis praecepta accommodare aliquid
 to upset the whole system: totam rationem evertere (pass. iacet tota ratio)
 to proceed, carry on a discussion logically: ratione et via, via et ratione progredi, disputare (Or. 33. 116)
 to enter on a new method: novam rationem ingredi
 to be based on a sound principle: a certa ratione proficisci
 to deal with a subject on scientific principles: ad philosophorum or philosophandi rationes revocare aliquid
 to bring forward an argument (based on commonsense): rationem afferre (Verr. 3. 85. 195)
 the conclusion proves that..: ratio or rationis conclusio efficit
 the syllogism; reasoning: ratiocinatio, ratio
 chronology: temporum ratio, descriptio, ordo
 to calculate the date of an event: ad temporum rationem aliquid revocare
 to draw a mathematical conclusion: mathematicorum ratione concludere aliquid
 the connection of thought: ratio sententiarum
 the connection of thought: ratio, qua sententiae inter se excipiunt.
 to be endowed with reason: rationis participem (opp. expertem) esse
 to be endowed with reason: ratione praeditum esse, uti
 to act reasonably, judiciously: prudenter, considerate, consilio agere (opp. temere, nullo consilio, nulla ratione)
 to be contrary to all reason: rationi repugnare
 on principle: ratione; animi quodam iudicio
 a sound and sensible system of conduct: vitae ratio bene ac sapienter instituta
 the principles which I have followed since I came to man's estate: meae vitae rationes ab ineunte aetate susceptae (Imp. Pomp. 1. 1.)
 to follow fixed principles of conduct: certas rationes in agendo sequi
 finance; moneymatters: ratio pecuniarum
 accountbook; ledger: codex or tabulae ratio accepti et expensi
 to go through accounts, make a valuation of a thing: rationem alicuius rei inire, subducere
 to do something after careful calculation: inita subductaque ratione aliquid facere
 to balance accounts with some one: rationes putare cum aliquo
 the accounts balance: ratio alicuius rei constat (convenit, par est)
 the account of receipts and expenditure: ratio acceptorum et datorum (accepti et expensi) (Amic. 16. 58)
 to keep the accounts (daybook) carefully: rationem diligenter conficere
 to render count of a matter; to pass it for audit: rationem alicuius rei reddere
 to demand an account, an audit of a matter: rationem alicuius rei reposcere aliquem or ab aliquo
 to demand an account, an audit of a matter: rationem ab aliquo reptere de aliqua re (Cluent. 37. 104)
 credit and financial position: fides et ratio pecuniarum
 the interests of the state: commoda publica or rei publicae rationes
 to further the public interests: rei publicae rationibus or simply rei publicae consulere
 to consider a thing from a political point of view: ad rei publicae rationes aliquid referre
 a democratic leader: homo florens in populari ratione
 judicial organisation: ratio iudiciorum
 to change one's tactics: rationem belli gerendi mutare (Liv. 32. 31)
 the spirit of the times, the fashion: saeculi consuetudo or ratio atque inclinatio temporis (temporum)