The Theology of Arithmetic

THE TRIAD

The Triad the number three, following its various names, is "beyond-equal" original: perisos; a Pythagorean term for an odd number, here specifically the first odd number after the Monad and possesses something more than the equal in another part. Specifically, it is distinct because it is continuous with the two principles the Monad and the Dyad and is a system composed of both of them. It is "perfect" in a more particular way than other numbers, because the numbers following in order from the Monad the unit, 1 are found to be equal to the sum of their preceding parts only up to the Tetrad the number four.

By this I mean:

• The Monad, as a base, is equal to the Monad.
• The Triad is equal to the Monad and the Dyad 1 + 2 = 3.
• The Decad the number ten is equal to the Monad, Dyad, Triad, and Tetrad 1 + 2 + 3 + 4 = 10.

Therefore, the Triad appears to have something extra by being continuous with those very numbers to which it is also equal.

15

And indeed, because of this quality, they called it Mean and Proportion original: mesotēta and analogian. This is not merely because it was the very first of the numbers to obtain a "middle" term, nor because it alone is equal to its preceding extremes, but because it exists as an image of generic "Equality." Since equality stands as a middle point between the two forms of inequality—the Greater and the Lesser—the Triad itself is observed in the middle of the "more" and the "less," possessing a symmetrical nature.

For the number before it—the Two—is greater than the first number preceding it 2 is greater than 1 and is the root of the "Greater" relationship; for it is Double the ratio 2:1. But the number after it—the Four—is less than the sum of the numbers preceding it the sum of 1, 2, and 3 is 6; 4 is less than 6. Indeed, the Four is the first example of the "Lesser" relationship; for it is Sub-sesquialter original: hyphēmiolios; the ratio 4:6, which simplifies to 2:3. Yet the Triad stands between both of these, being exactly equal to the sum of the numbers preceding it 1 + 2 = 3.

Thus, the Triad is the "form-giving Mean" for all others. From this, and because of it, there are three means called "right":
1. Arithmetic
2. Geometric
3. Harmonic

There are also three means contrary to these, and three terms within each mean, and three "intervals"—that is, the differences in each term of the small to the middle, and the middle to the great. There are also an equal number of ratios, as discussed in the introduction, and another three "reversals" to be examined:

• Great to small
• Great to middle
• Middle to small.

The Monad holds within itself the unformed and unarticulated principle original: logos of every number, as if contained in a seed; while the Dyad is a certain small extension...