The Theology of Arithmetic

...for this is not of the nature of a principle, but [arises] from each other. Finally, their generation also occurs through mixture original: krasis; refers here to multiplication as a blending of factors. Therefore, "three times three" is more than "three and three" i.e., 3 × 3 = 9, which is greater than 3 + 3 = 6.

However, since both [addition and multiplication] are in opposition, the Dyad, being as if in the middle, will receive the properties of both at once, taking on the mean of each; for we have said that the Equal is the mean between the Greater and the Lesser. Therefore, Equality is found in this [number] alone; because of this, the result of mixture will be equal to the result of juxtaposition original: parathesis; addition. For "two and two" is equal to "twice two" 2 + 2 = 4 and 2 × 2 = 4.

12 For this reason, they used to call the Dyad "Equal."

That it gives form to such a principle and to all things belonging to it is clear, not only because the first manifestation of the activity of Equality appeared in it both in terms of planes and solids—specifically in the "two" of length and breadth, and in the "eight" 2 to the power of 3 which adds depth and height—but also in its division into two units which do not exist through each other. Furthermore, this is seen in the so-called "chosen one" derived from it, that is, the number sixteen original: ist'; the Greek numeral for 16. This is "twice two, twice" 2 × 2 × 2 × 2 = 16, and it exists through the so-called "color" original: chroia; a Pythagorean term for the surface or area of a shape of the plane derived from it, for it is "four times four."

In this way, a kind of mean is observed between the Greater and the Lesser, just as with the Dyad. For the squares before it have perimeters original: perimetros greater than their areas original: embadon, while those after it have the opposite, where the perimeters are smaller. Thus, [sixteen] alone is Equal A square with side 4 has an area of 16 and a perimeter of 16. A square with side 3 has area 9 and perimeter 12 (P > A). A square with side 5 has area 25 and perimeter 20 (P < A)..

For this reason, Plato also appears in the Theaetetus to have proceeded up to this point and then stopped at the "seventeen-footer" original: heptakaidekapodi; referring to the passage in Plato's dialogue where the mathematician Theodorus proves the irrationality of square roots up to 17, in order to manifest the property of the number seventeen and a certain participation in Equality.

Why, then, did the ancients, seeing this, call the Dyad "Unequal" and "Deficiency" and "Excess"? It was according to the concept of Matter original: hyle. In Matter, the first departure original: apostasis; distance from the Oneness of the Monad and the concept of the "side" original: pleura; the dimension of a shape were seen. This is already the beginning of difference and inequality.

And in another sense, because up to the Dyad, the comparison [of the sum of preceding numbers] is greater than the number itself, but up to the Tetrad (four), the comparison is less than the numbers preceding it. With the Triad (three) being in the middle of both, the principle of Equality will happen again in a different way...