“Potency”¹ means: (a) the source of motion or change which is in something other than the thing changed, or in it qua other. E.g., the science of building is a potency which is not present in the thing built; but the science of medicine, which is a potency, may be present in the patient, although not qua patient. Thus “potency” means the source in general of change or motion in another thing, or in the same thing qua other; or the source of a thing’s being moved or changed by another thing, or by itself qua other (for in virtue of that principle by which the passive thing is affected in any way we call it capable of being affected; sometimes if it is affected at all, and sometimes not in respect of every affection, but only if it is changed for the better). (b) The power of performing this well or according to intention; because sometimes we say that those who can merely take a walk, or speak, without doing it as well as they intended, cannot speak or walk. And similarly in the case of passivity. (c) All states in virtue of which things are unaffected generally, or are unchangeable, or cannot readily deteriorate, are called “potencies.” For things are broken and worn out and bent and in general destroyed not through potency but through impotence and deficiency of some sort; and things are unaffected by such processes which are scarcely or slightly affected because they have a potency and are potent and are in a definite state. Since “potency” has all these meanings, “potent” (or “capable”) will mean (a) that which contains a source of motion or change (for even what is static is “potent” in a sense) which takes place in another thing, or in itself qua other. 1019b(b) That over which something else has a potency of this kind. (c) That which has the potency of changing things, either for the worse or for the better (for it seems that even that which perishes is “capable” of perishing; otherwise, if it had been incapable, it would not have perished. As it is, it has a kind of disposition or cause or principle which induces such an affection. Sometimes it seems to be such as it is because it has something, and sometimes because it is deprived of something; but if privation is in a sense a state or “habit,” everything will be “potent” through having something; and so a thing is “potent” in virtue of having a certain “habit” or principle, and also in virtue of having the privation of that “habit,” if it can have privation; and if privation is not in a sense “habit,” the term “potent” is equivocal). (d) A thing is “potent” if neither any other thing nor itself qua other contains a potency or principle destructive of it. (e) All these things are “potent” either because they merely might chance to happen or not to happen, or because they might do so well . Even in inanimate things this kind of potency is found; e.g. in instruments; for they say that one lyre “can” be played, and another not at all, if it has not a good tone. “Impotence” is a privation of potency—a kind of abolition of the principle which has been described—either in general or in something which would naturally possess that principle, or even at a time when it would naturally already possess it (for we should not use “impotence”—in respect of begetting—in the same sense of a boy, a man and a eunuch). Again, there is an “impotence” corresponding to each kind of potency; both to the kinetic and to the successfully kinetic. Some things are said to be “impotent” in accordance with this meaning of “impotence,” but others in a different sense, namely “possible” and “impossible.” “Impossible” means: (a) that whose contrary is necessarily true; e.g., it is impossible that the diagonal of a square should be commensurable with the sides, because such a thing is a lie, whose contrary is not only true but inevitable. Hence that it is commensurable is not only a lie but necessarily a lie. And the contrary of the impossible, i.e. the possible, is when the contrary is not necessarily a lie; e.g., it is possible that a man should be seated, for it is not necessarily a lie that he should not be seated. “Possible,” then, means in one sense, as we have said, that which is not necessarily a lie; in another, that which is true; and in another, that which may be true. (The “power” in geometry² is so called by an extension of meaning.) These are the senses of “potent” which do not correspond to “potency.” Those which do correspond to it all refer to the first meaning, 1020ai.e. “a source of change which exists in something other than that in which the change takes place, or in the same thing qua other.” Other things are said to be “potent”³ because something else has such a potency over them; others because it does not possess it; others because it possesses it in a particular way. The term “impotent” is similarly used. Thus the authoritative definition of “potency” in the primary sense will be “a principle producing change, which is in something other than that in which the change takes place, or in the same thing qua other.”

“Quantity” means that which is divisible into constituent parts, each⁴ or every one of which is by nature some one individual thing. Thus plurality, if it is numerically calculable, is a kind of quantity; and so is magnitude, if it is measurable. “Plurality” means that which is potentially divisible into non-continuous parts; and “magnitude” that which is potentially divisible into continuous parts. Of kinds of magnitude, that which is continuous in one direction is length; in two directions, breadth; in three, depth. And of these, plurality, when limited, is a number; length, a line; breadth, a plane; depth, a body. Again, some things are essentially quantitative, but others only accidentally; e.g. the line is essentially, but “cultured” accidentally quantitative. And of the former class some are quantitative in virtue of their substance, e.g. the fine (because the definition which describes it is quantitative in some form); and others are attributes and conditions of a substance of this kind— e.g., “much” and “little,” “long” and “short,” “broad” and “narrow,” “deep” and “shallow,” “heavy” and “light,” etc. Moreover, “great” and “small,” and “greater” and “smaller,” whether used absolutely or relatively to one another, are essential attributes of quantity; by an extension of meaning, however, these terms are also applied to other things. Of things called quantitative in an accidental sense, one kind is so called in the sense in which we said above that “cultured” or “white” is quantitative—because the subject to which they belong is quantitative; and others in the sense that motion and time are so called—for these too are said in a sense to be quantitative and continuous, since the subjects of which they are attributes are divisible. I mean, not the thing moved, but that through or along which the motion has taken place; for it is because the latter is quantitative that the motion is quantitative, and because the motion is quantitative that the time is also.

“Quality” means (a) in one sense, the differentia of essence; e.g., a man is an animal of a certain quality because he is two-footed; and so is a horse, because it is four-footed. Also a circle is a geometrical figure of a certain quality, because it has no angles; 1020bwhich shows that the essential differentia is quality. In this one sense, then, “quality” means differentia of essence; but (b) in another it is used as of immovable and mathematical objects, in the sense that numbers are in a way qualitative—e.g. such as are composite and are represented geometrically not by a line but by a plane or solid (these are products respectively of two and of three factors)—and in general means that which is present besides quantity in the essence. For the essence of each number is that which goes into it once; e.g. that of 6 is not what goes twice or three times, but what goes once; for 6 is once 6. (c) All affections of substance in motion in respect of which bodies become different when they (the affections) change—e.g. heat and cold, whiteness and blackness, heaviness and lightness, etc. (d) The term is used with reference to goodness and badness, and in general to good and bad. Thus there are, roughly speaking, two meanings which the term “quality” can bear, and of these one is more fundamental than the other. Quality in the primary sense is the differentia of the essence; and quality in numbers falls under this sense, because it is a kind of differentia of essences, but of things either not in motion or not qua in motion. Secondly, there are the affections of things in motion qua in motion, and the differentiae of motions. Goodness and badness fall under these affections, because they denote differentiae of the motion or functioning in respect of which things in motion act or are acted upon well or badly. For that which can function or be moved in such-and-such a way is good, and that which can function in such-and-such a way and in the contrary way is bad. Quality refers especially to “good” and “bad” in the case of living things, and of these especially in the case of such as possess choice.