Book 10
10
Thus unity is the starting point of number qua number. Hence in other cases too measure means that by which each thing is primarily known, and the measure of each thing is a unit—in length, breadth, depth, weight and speed.
11
(The terms weight and speed are common to both contraries, for each of them has a double meaning; e.g., weight applies to that which has the least amount of gravity and also to that which has excess of it, and speed to that which has the least amount of motion and also to that which has excess of it; for even the slow has some speed, and the light some weight.)
12
In all these cases, then, the measure and starting-point is some indivisible unit (since even in the case of lines we treat the one-foot line as indivisible). For everywhere we require as our measure an indivisible unit; i.e., that which is simple either in quality or in quantity.
13
Now where it seems impossible to take away or add, there the measure is exact. Hence the measure of number is most exact, for we posit the unit as in every way indivisible; and in all other cases we follow this example, for with the furlong or talent or in general with the greater measure an addition or subtraction would be less obvious than with a smaller one.
14
Therefore the first thing from which, according to our perception, nothing can be subtracted is used by all men as their measure of wet and dry, weight and magnitude; and they think that they know the quantity only when they know it in terms of this measure. And they know motion too by simple motion and the most rapid, for this takes least time.
