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are by their own nature attributes of what is quantitative; but
these names are transferred to other things also. Of things that are
quanta incidentally, some are so called in the sense in which it was
said that the musical and the white were quanta, viz. because that
to which musicalness and whiteness belong is a quantum, and some are
quanta in the way in which movement and time are so; for these also
are called quanta of a sort and continuous because the things of which
these are attributes are divisible. I mean not that which is moved,
but the space through which it is moved; for because that is a quantum
movement also is a quantum, and because this is a quantum time is one.

'Quality' means (1) the differentia of the essence, e.g. man is an
animal of a certain quality because he is two-footed, and the horse is
so because it is four-footed; and a circle is a figure of particular
quality because it is without angles,-which shows that the essential
differentia is a quality.-This, then, is one meaning of quality-the
differentia of the essence, but (2) there is another sense in which it
applies to the unmovable objects of mathematics, the sense in which
the numbers have a certain quality, e.g. the composite numbers which
are not in one dimension only, but of which the plane and the solid
are copies (these are those which have two or three factors); and in
general that which exists in the essence of numbers besides quantity
is quality; for the essence of each is what it is once, e.g. that of
is not what it is twice or thrice, but what it is once; for 6 is
once 6.
(3) All the modifications of substances that move (e.g. heat and
cold, whiteness and blackness, heaviness and lightness, and the others
of the sort) in virtue of which, when they change, bodies are said
to alter. (4) Quality in respect of virtue and vice, and in general,
of evil and good.
Quality, then, seems to have practically two meanings, and one
of these is the more proper. The primary quality is the differentia of
the essence, and of this the quality in numbers is a part; for it is a
differentia of essences, but either not of things that move or not
of them qua moving. Secondly, there are the modifications of things
that move, qua moving, and the differentiae of movements. Virtue and
vice fall among these modifications; for they indicate differentiae of
the movement or activity, according to which the things in motion
act or are acted on well or badly; for that which can be moved or
act in one way is good, and that which can do so in another--the
contrary--way is vicious. Good and evil indicate quality especially in
living things, and among these especially in those which have purpose.
Things are 'relative' (1) as double to half, and treble to a
third, and in general that which contains something else many times to
that which is contained many times in something else, and that which
exceeds to that which is exceeded; (2) as that which can heat to
that which can be heated, and that which can cut to that which can
be cut, and in general the active to the passive; (3) as the
measurable to the measure, and the knowable to knowledge, and the
perceptible to perception.
(1) Relative terms of the first kind are numerically related
either indefinitely or definitely, to numbers themselves or to 1. E.g.
the double is in a definite numerical relation to 1, and that which is
'many times as great' is in a numerical, but not a definite,
relation to 1, i.e. not in this or in that numerical relation to it;
the relation of that which is half as big again as something else to
that something is a definite numerical relation to a number; that
which is n+I/n times something else is in an indefinite relation to
that something, as that which is 'many times as great' is in an
indefinite relation to 1; the relation of that which exceeds to that
which is exceeded is numerically quite indefinite; for number is
always commensurate, and 'number' is not predicated of that which is

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