Book 5
9
And the straight line is more truly one than the bent. We call the line which is bent and contains an angle both one and not one, because it may or may not move all at once; but the straight line always moves all at once, and no part of it which has magnitude is at rest while another moves, as in the bent line.
9
(b) Another sense of one is that the substrate is uniform in kind.
10
Things are uniform whose form is indistinguishable to sensation; and the substrate is either that which is primary, or that which is final in relation to the end. For wine is said to be one, and water one, as being something formally indistinguishable. And all liquids are said to be one (e.g. oil and wine), and melted things; because the ultimate substrate of all of them is the same, for all these things are water or vapor.
11
(c) Things are said to be one whose genus is one and differs in its opposite differentiae. All these things too are said to be one because the genus, which is the substrate of the differentiae, is one (e.g., horse, man and dog are in a sense one, because they are all animals); and that in a way very similar to that in which the matter is one.
12
Sometimes these things are said to be one in this sense, and sometimes their higher genus is said to be one and the same (if they are final species of their genus)—the genus, that is, which is above the genera of which their proximate genus is one; e.g., the isosceles and equilateral triangles are one and the same figure (because they are both triangles), but not the same triangles.
13
(d) Again, things are said to be one when the definition stating the essence of one is indistinguishable from a definition explaining the other; for in itself every definition is distinguishable 〈into genus and differentiae〉. In this way that which increases and decreases is one, because its definition is one; just as in the case of planes the definition of the form is one.
