# ratio

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## ratio.

The ratio of two quantities expressed in terms of the same unit is the fraction that has the first quantity as numerator and the second as denominator. For example, if in a group of 100 people 5 die, the ratio of deaths to the total number in the group is 5/100=1/20=.05. Ratios are indicated also by writing the two values with a colon between them, e.g., the ratio of 4 to 8 can be expressed by 4:8 as well as by 4/8.

## Ratio

A relationship in magnitude, quantity, or degree between two or more similar things.

## Ratio

The ratio of two numbers is the quotient from the division of the first number, by the second. The ratio of two homogeneous magnitudes is the number obtained by measuring the first magnitude when the second is chosen as the unit of measurement. If two magnitudes are measured in the same unit of measurement, their ratio is equal to that of the numbers that measure them.

The ratio of the lengths of two segments may be expressed by a rational or irrational number. In the former case the segments are said to be commensurable, and in the latter incommensurable. Mathematicians of the ancient world had no knowledge of irrational numbers. For them the concept of the ratio of two segments did not reduce to the concept of number. In their conception the geometrical theory of the ratios of magnitudes was not connected with the concept of number and played an independent role. In a sense, it substituted for a theory of real numbers. Indeed, according to Euclid the four segments, a, b, a’, and b’ form the proportion a: b = a’:b’ if for any natural numbers m and n one of the relations ma = nb, ma > nb, ma < nb is satisfied simultaneously with the corresponding relation ma’ = nb’, ma’> nb’, or ma’ < nb’. It follows that when a and b are incommensurable the subdivision of the rational numbers (x = m/n) into two classes according to whether a > xb or a < xb coincides with the subdivision according to whether a’ > xb’ or a’ < xb’ —this is the idea behind the modern theory of Dedekind cuts.

## ratio

[′rā·shō]
(mathematics)
A ratio of two quantities or mathematical objects A and B is their quotient or fraction A / B.

## ratio

Maths a quotient of two numbers or quantities
References in periodicals archive ?
2 (242b): et totum genus humanum lapsum fuerat et vitiatum, non solum ratione animae, verum etiam carnis: hine est, quod necesse fuit, quod totum assumeretur, lit totum curaretur.
Sed essentia angeli non includit virtualiter essentiam divinam sub ratione aliqua distincta; ergo nec sic cognosci earn.
26) <<Adde, nullam fore fidem contractuum inter homines, si hac ratione se possent expedire, dicendo se ficte promisisse>> (ibidem, lib.
Probatur Minor: Vel est foelicitas secundum eos, qui in bonis externis et voluptate eam ponebant, quia haec bona a fortuna dicuntur, quia fortuitis casibus sunt exposita, vel prope foelicitatem, quod dicit propter se, quia foelicitatem in contemplatione ponebat, sed ad eam iuuare dicebat bona externa, et amicos, et eius instrumenta: sed foelicitas non est quaecunque operatio, sed ex electione procedens, et ratione, ut primo Ethicorum cap.
Ergo eadem ratione et voluntas necessario movetur a suo objecto.
Utique, ex sua processuali agendi ratione, ob quam vir absens a iudicio permansit in tribus iudicii gradibus, confirmari videntur quae declarata sunt a d.
156: "Inquit Severinus Boethius: quaecumque a primaeva rerum natura constructa sunt, numerorum videntur ratione formata"; see Boethius, 3.
2 quibusdam Sodalibus, cum opportunitas id suadeat, peculiaria munera tribuere, ut coetus aptiore ratione suis vacet laboribus;
Our best understanding of God consists of a multiplicity of rationes only because it is a deficient understanding.
Nituntur autem duobus praecipue fundamentis: ratione propria, et autoritate Platonica.
Pulchritudo autem dei radius, quatuor illis insitus circulis circa deum quodammodo revolutis, huiusmodi radius omnes rerum omnium species in quatuor illis effingit: species illis in mente ideas, in anima rationes, in natura semina, in materia formas appellare solemus.
Torquemada (1388-1468) constructed a tightly organized apologetic based upon evidentes rationes, a procedure foreign to both Nicholas and Ricoldo.

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