Webster 1913 Edition



(rā′shĭ-ō̍ or rā′shō̍)
[L., fr.
, to reckon, believe, think, judge. See
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
; or (less commonly) the second term is made the dividend; as,
a:b =
☞ 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
Hence, fixed relation of number, quantity, or degree; rate; proportion;
as, the
of representation in Congress
Compound ratio
Duplicate ratio
Inverse ratio
, etc.
See under
, etc.
Ratio of a geometrical progression
the constant quantity by which each term is multiplied to produce the succeeding one.

Webster 1828 Edition



ra'sho. [L. from ratus, reor, to think or suppose, to set, confirm or establish. Reor is contracted from redor or retor, and primarily signifies to throw, to thrust, hence to speak, to set in the mind, to think, like L. suppono; and setting gives the sense of a fixed rate or rule. See Reason.]
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



See also: ratio



Ratio f (genitive Ratio, no plural)

  1. (philosophy) reason




See also: Ratio



ratio (plural ratios)

  1. A number representing a comparison between two things.
  2. (arithmetic) The relative magnitudes of two quantities (usually expressed as a quotient).
  3. (law) Short for ratio decidendi.

Derived terms

Related terms




ratio m (plural ratios)

  1. ratio



  • IPA(key): /ˈratioː/


From rat- ("thought", from perfect participle of reor) + -iō


ratiō f (genitive ratiōnis); third declension

  1. reason, explanation
  2. calculation, account
  3. manner, method


Third declension.

Case Singular Plural
nominative ratiō ratiōnēs
genitive ratiōnis ratiōnum
dative ratiōnī ratiōnibus
accusative ratiōnem ratiōnēs
ablative ratiōne ratiōnibus
vocative ratiō ratiōnēs


  • Occitan: rason
  • Portuguese: razão, ração, rácio
  • Romanian: rațiune, rație
  • Romansch: raschun, raschung, radschun
  • Sardinian: rajone, arraxoni, erresone, rasoni, regione, rexone
  • Sicilian: ragiuni, raggiuni, raciuni
  • Spanish: razón, ración
  • Venetian: raxon, rajon
  • Walloon: råjhon

See also


  • 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 Latin-Français, Paris: Hachette.
  • Meissner, Carl; Auden, Henry William (1894) Latin Phrase-Book, 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 common-sense): 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; money-matters: ratio pecuniarum
    • account-book; 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 (day-book) 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)



ratio f (plural ratios)

  1. ratio