Aristotle, Metaphysics

[1016b] [1] And in general those things whose concept, which conceives the essence, is indistinguishable and cannot be separated either in time or in place or in definition, are in the truest sense one; and of these such as are substances are most truly one. For universally such things as do not admit of distinction are called "one" in so far as they do not admit of it; e.g., if "man" qua "man" does not admit of distinction, he is one man; and similarly if qua animal, he is one animal; and if qua magnitude, he is one magnitude.

Most things, then, are said to be "one" because they produce, or possess, or are affected by, or are related to, some other one thing; but some are called "one" in a primary sense, and one of these is substance. It is one either in continuity or in form or in definition; for we reckon as more than one things which are not continuous, or whose form is not one, or whose definition is not one.Again, in one sense we call anything whatever "one" if it is quantitative and continuous; and in another sense we say that it is not "one" unless it is a whole of some kind, i.e. unless it is one in form (e.g., if we saw the parts of a shoe put together anyhow, we should not say that they were one — except in virtue of their continuity; but only if they were so put together as to be a shoe, and to possess already some one form).Hence the circumference of a circle is of all lines the most truly one, because it is whole and complete.

The essence of "one" is to be a kind of starting point of number; for the first measure is a starting point, because that by which first we gain knowledge of a thing is the first measure of each class of objects. [20] "The one," then, is the starting-point of what is knowable in respect of each particular thing. But the unit is not the same in all classes,for in one it is the quarter-tone, and in another the vowel or consonant; gravity has another unit, and motion another. But in all cases the unit is indivisible, either quantitatively or formally.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.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.

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.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;