Kitap 10
15
Hence in astronomy a unit of this kind is the starting point and measure; for they assume that the motion of the heavens is uniform and the most rapid, and by it they judge the others. In music the measure is the quarter tone, because it is the smallest interval; and in language the letter. All these are examples of units in this sense—not in the sense that unity is something common to them all, but in the sense which we have described.
16
The measure is not always numerically one, but sometimes more than one; e.g., there are two quarter tones, distinguished not by our hearing but by their theoretical ratiosi.e., the enharmonic (or quarter-tone proper) and the chromatic, which was 1/3 of a tone (Aristoxenus 1.21, 2.51). There was also the δίεσις ἡμιολία, which was 3/8 of a tone.; and the articulate sounds by which we measure speech are more than one; and the diagonal of a square is measured by two quantities,The meaning seems to be that the diameter consists of two parts, one equal to the side, and the other representing its excess over the side; the two parts being incommensurate are measured by different units (Ross). καὶ ἡ πλευρά must, I think, be a gloss. and so are all magnitudes of this kind. Thus unity is the measure of all things, because we learn of what the substance is composed by dividing it, in respect of either quantity or form.
17
Hence unity is indivisible, because that which is primary in each class of things is indivisible. But not every unit is indivisible in the same sense—e.g. the foot and the arithmetical unit; but the latter is absolutely indivisible, and the former must be classed as indivisible with respect to our power of perception, as we have already stated; since presumably everything which is continuous is divisible.
