‘One’ means (1) that which is one by accident, (2) that which is one by its own nature. (1) Instances of the accidentally one are ‘Coriscus and what is musical’, and ‘musical Coriscus’ (for it is the same thing to say ‘Coriscus and what is musical’, and ‘musical Coriscus’), and ‘what is musical and what is just’, and ‘musical Coriscus and just Coriscus’. For all of these are called one by virtue of an accident, ‘what is just and what is musical’ because they are accidents of one substance, ‘what is musical and Coriscus’ because the one is an accident of the other; and similarly in a sense ‘musical Coriscus’ is one with ‘Coriscus’ because one of the parts of the phrase is an accident of the other, i.e. ‘musical’ is an accident of Coriscus; and ‘musical Coriscus’ is one with ‘just Coriscus’ because one part of each is an accident of one and the same subject. The case is similar if the accident is predicated of a genus or of any universal name, e.g. if one says that man is the same as ‘musical man’; for this is either because ‘musical’ is an accident of man, which is one substance, or because both are accidents of some individual, e.g. Coriscus. Both, however, do not belong to him in the same way, but one presumably as genus and included in his substance, the other as a state or affection of the substance.

The things, then, that are called one in virtue of an accident, are called so in this way. (2) Of things that are called one in virtue of their own nature some (a) are so called because they are continuous, e.g. a bundle is made one by a band, and pieces of wood are made one by glue; and a line, even if it is bent, is called one if it is continuous, as each part of the body is, e.g. the leg or the arm. Of these themselves, the continuous by nature are more one than the continuous by art. A thing is called continuous which has by its own nature one movement and cannot have any other; and the movement is one when it is indivisible, and it is indivisible in respect of time. Those things are continuous by their own nature which are one not merely by contact; for if you put pieces of wood touching one another, you will not say these are one piece of wood or one body or one continuum of any other sort. Things, then, that are continuous in any way called one, even if they admit of being bent, and still more those which cannot be bent; e.g. the shin or the thigh is more one than the leg, because the movement of the leg need not be one. And the straight line is more one than the bent; but that which is bent and has an angle we call both one and not one, because its movement may be either simultaneous or not simultaneous; but that of the straight line is always simultaneous, and no part of it which has magnitude rests while another moves, as in the bent line.

(b)(i) Things are called one in another sense because their substratum does not differ in kind; it does not differ in the case of things whose kind is indivisible to sense. The substratum meant is either the nearest to, or the farthest from, the final state. For, one the one hand, wine is said to be one and water is said to be one, qua indivisible in kind; and, on the other hand, all juices, e.g. oil and wine, are said to be one, and so are all things that can be melted, because the ultimate substratum of all is the same; for all of these are water or air.

(ii) Those things also are called one whose genus is one though distinguished by opposite differentiae-these too are all called one because the genus which underlies the differentiae is one (e.g. horse, man, and dog form a unity, because all are animals), and indeed in a way similar to that in which the matter is one. These are sometimes called one in this way, but sometimes it is the higher genus that is said to be the same (if they are infimae species of their genus)-the ............