Book 5
19
Thus that which is quantitatively and qua quantitative wholly indivisible and has no position is called a unit; and that which is wholly indivisible and has position, a point; that which is divisible in one sense, a line; in two senses, a plane; and that which is quantitatively divisible in all three senses, a body.
20
And reversely that which is divisible in two senses is a plane, and in one sense a line; and that which is in no sense quantitatively divisible is a point or a unit; if it has no position, a unit, and if it has position, a point.
21
Again, some things are one numerically, others formally, others generically, and others analogically; numerically, those whose matter is one; formally, those whose definition is one; generically, those which belong to the same category; and analogically, those which have the same relation as something else to some third object.
22
In every case the latter types of unity are implied in the former: e.g., all things which are one numerically are also one formally, but not all which are one formally are one numerically; and all are one generically which are one formally, but such as are one generically are not all one formally, although they are one analogically; and such as are one analogically are not all one generically.
23
It is obvious also that many will have the opposite meanings to one. Some things are called many because they are not continuous; others because their matter (either primary or ultimate) is formally divisible; others because the definitions of their essence are more than one.
1
Being means (1.) accidental being, (2.) absolute being. (1.) E.g., we say that the upright person is cultured, and that the man is cultured, and that the cultured person is a man; very much as we say that the cultured person builds, because the builder happens to be cultured, or the cultured person a builder; for in this sense X is Y means that Y is an accident of X.
