[1084b] [1] e.g. the first or indivisible line, then the 2, and so on; these too extending up to 10.1

Again, if number is separable, the question might be raised whether Unity is prior, or 3 or 2.Now if we regard number as composite, Unity is prior; but if we regard the universal or form as prior, number is prior, because each unit is a material part of number, while number is the form of the units. And there is a sense in which the right angle is prior to the acute angle—since it is definite and is involved in the definition of the acute angle—and another sense in which the acute angle is prior, because it is a part of the other, i.e., the right angle is divided into acute angles.Thus regarded as matter the acute angle and element and unit are prior; but with respect to form and substance in the sense of formula, the right angle, and the whole composed of matter and form, is prior. For the concrete whole is nearer to the form or subject of the definition, although in generation it is posterior.2

In what sense, then, is the One a first principle? Because, they say, it is indivisible.But the universal and the part or element are also indivisible. Yes, but they are prior in a different sense; the one in formula and the other in time. In which sense, then, is the One a first principle? for, as we have just said, both the right angle seems to be prior to the acute angle, and the latter prior to the former; and each of them is one.Accordingly the Platonists make the One a first principle in both senses. But this is impossible; for in one sense it is the One qua form or essence, [20] and in the other the One qua part or matter, that is primary. There is a sense in which both number and unit are one; they are so in truth potentially—that is, if a number is not an aggregate but a unity consisting of units distinct from those of other numbers, as the Platonists hold— but each of the two3 units is not one in complete reality. The cause of the error which befell the Platonists was that they were pursuing their inquiry from two points of view—that of mathematics and that of general definition—at the same time. Hence as a result of the former they conceived of the One or first principle as a point, for the unit is a point without position. (Thus they too, just like certain others,represented existing things as composed of that which is smallest.)4 We get, then, that the unit is the material element of numbers, and at the same time is prior to the number 2; and again we get that it is posterior to 2 regarded as a whole or unity or form. On the other hand, through looking for the universal, they were led to speak of the unity predicated of a given number as a part in the formal sense also. But these two characteristics cannot belong simultaneously to the same thing.

And if Unity itself must only be without position5(for it differs only in that it is a principle) and 2 is divisible whereas the unit is not, the unit will be more nearly akin to Unity itself; and if this is so, Unity itself will also be more nearly akin to the unit than to 2. Hence each of the units in 2 will be prior to 2. But this they deny; at least they make out that 2 is generated first.6

1 The "indivisible line" or point was connected with 1, the line with 2, the plane with 3 and the solid with 4 (Aristot. Met. 14.3.9); and 1+2+3+4=10.

3 Aristotle takes the number two as an example, but the principle is of course universal. In a sense both number and unit are one; but if the number exists as an actual unity, the unit can only exist potentially.

4 Perhaps the Atomists; but cf. Aristot. Met. 1.8.3, 4.

5 If the text is sound (and no convincing emendation has been suggested), it seems best to understand ἄθετον in a rather wider sense than the semi-technical one put forward by Ross. "Without position"=not localized, i.e. abstract. Unity as a principle has no concrete instance.