The Theology of Arithmetic

...circles defining the breadth, the summer and winter [tropics], and the one between these called the ecliptic the path the sun follows through the sky; original: ekleiptikos. And there are three kinds of living creatures: land-dwelling, winged, and aquatic. Three are also the Fates original: Moirai in theological discourse, because the entire conduct of divine and mortal affairs is governed by three things: sending forth original: proesis, receiving original: hypodochē, and thirdly, 18 giving back original: antapodosis. The celestial regions "sow," in a certain manner, while the earthly regions receive as it were, and the giving back is accomplished through the intermediary things, like an offspring between male and female. And the words of Homer original: Homēros might be adapted to these: "for all things were divided into three." A reference to Iliad 15.189, where the world is divided between Zeus, Poseidon, and Hades.

We also find that the virtues original: aretē are midpoints between two vices original: kakia, which are opposed both to each other and to virtue; and the reasoning agrees: in accordance with the Monad the number one; original: monas, the virtues are something defined, known, and wise—for the midpoint is one; but in accordance with the Dyad the number two; original: dyas, the vices are indefinite, unknown, and foolish. Furthermore, they call [the Triad] Friendship original: philia, Peace original: eirēnē, and additionally Harmony original: harmonia and Concord original: homonoia; for these bring together and unite things that are opposite and unlike. For this reason, they also call it Marriage original: gamos. There are also three ages [of man].

4. Concerning the Tetrad the number four.

In the natural progression up to the Tetrad original: tetras, all things in the cosmos appear to be brought to completion, both as a whole and in part, as well as things in number and in all simple natures. It is exceptional and contributes most to the realization of the result that the Decad the number ten; original: dekas is brought to its peak by the Tetrad along with the numbers preceding it the Pythagorean Tetraktys: 1 + 2 + 3 + 4 = 10, being a standard original: gnōmōn and a unifying bond. But also, the embodiment and the three-way extension reach their limit at the number four; for the smallest and most fundamental solid, the pyramid original: pyramis, specifically the tetrahedron, is seen in the Tetrad, whether by its angles or its faces; just as the perceptible object made of matter original: hylē and form original: eidos, which is a result in three [dimensions]...