QUANTITY is a property that can exist as a multitude or magnitude .
Quantities can be compared in terms of "more", "less", or "equal", or
by assigning a numerical value in terms of a unit of measurement.
**Quantity** is among the basic classes of things along with quality ,
substance , change , and relation. Some quantities are such by their
inner nature (as number), while others are functioning as states
(properties, dimensions, attributes) of things such as heavy and
light, long and short, broad and narrow, small and great, or much and
little. A small quantity is sometimes referred to as a QUANTULUM.

Two basic divisions of quantity, magnitude and multitude, imply the
principal distinction between continuity (continuum ) and
discontinuity .

Under the name of multitude come what is discontinuous and discrete
and divisible into indivisibles, all cases of collective nouns: army,
fleet, flock, government, company, party, people, chorus, crowd, mess,
and number. Under the name of magnitude come what is continuous and
unified and divisible into divisibles, all cases of non-collective
nouns: matter, mass, energy, liquid, material.

Along with analyzing its nature and classification, the issues of
quantity involve such closely related topics as the relation of
magnitudes and multitudes, dimensionality, equality, proportion, the
measurements of quantities, the units of measurements, number and
numbering systems, the types of numbers and their relations to each
other as numerical ratios.

Thus quantity is a property that exists in a range of magnitudes or
multitudes.
**Mass**

Mass , time , distance , heat , and angular separation are
among the familiar examples of quantitative properties . Two
magnitudes of a continuous quantity stand in relation to one another
as a ratio which is a real number .

CONTENTS

* 1 Background
* 2 Quantitative structure
* 3
**Quantity** in mathematics
* 4
**Quantity** in physical science
* 5
**Quantity** in natural language
* 6 Further examples
* 7 See also
* 8 References
* 9 External links

BACKGROUND

In mathematics the concept of quantity is an ancient one extending
back to the time of
**Aristotle**

Aristotle and earlier.
**Aristotle**

Aristotle regarded quantity
as a fundamental ontological and scientific category. In Aristotle's
ontology , quantity or quantum was classified into two different
types, which he characterized as follows: 'Quantum' means that which
is divisible into two or more constituent parts, of which each is by
nature a 'one' and a 'this'. A quantum is a plurality if it is
numerable, a magnitude if it is measurable. 'Plurality' means that
which is divisible potentially into non-continuous parts, magnitude
that which is divisible into continuous parts; of magnitude, that
which is continuous in one dimension is length; in two breadth, in
three depth. Of these, limited plurality is number, limited length is
a line, breadth a surface, depth a solid. (Aristotle, book v, chapters
11-14, Metaphysics).

In his Elements ,
**Euclid**

Euclid developed the theory of ratios of magnitudes
without studying the nature of magnitudes, as Archimedes, but giving
the following significant definitions: A magnitude is a part of a
magnitude, the less of the greater, when it measures the greater; A
ratio is a sort of relation in respect of size between two magnitudes
of the same kind.

For
**Aristotle**

Aristotle and Euclid, relations were conceived as whole numbers
(Michell, 1993).
**John Wallis**

John Wallis later conceived of ratios of magnitudes
as real numbers as reflected in the following: When a comparison in
terms of ratio is made, the resultant ratio often leaves the genus of
quantities compared, and passes into the numerical genus, whatever the
genus of quantities compared may have been. (John Wallis, Mathesis
Universalis)

That is, the ratio of magnitudes of any quantity, whether volume,
mass, heat and so on, is a number. Following this, Newton then defined
number, and the relationship between quantity and number, in the
following terms: "By number we understand not so much a multitude of
unities, as the abstracted ratio of any quantity to another quantity
of the same kind, which we take for unity" (Newton, 1728).

QUANTITATIVE STRUCTURE

Continuous quantities possess a particular structure that was first
explicitly characterized by Hölder (1901) as a set of axioms that
define such features as identities and relations between magnitudes.
In science, quantitative structure is the subject of empirical
investigation and cannot be assumed to exist a priori for any given
property. The linear continuum represents the prototype of continuous
quantitative structure as characterized by Hölder (1901) (translated
in Michell 2. mass nouns