Book 5
16
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).
17
Hence the circumference of a circle is of all lines the most truly one, because it is whole and complete.
17
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. 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,
18
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.
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.
