The Theology of Arithmetic

In addition to these points, they say that at the center of the four elements The classic elements: Earth, Air, Fire, and Water. there lies a certain monadic original: henadikon; pertaining to the unit or the "One" fiery cube. They claim that even Homer was aware of this central position when he said:

As far beneath Hades as heaven
is from earth.
original: "Tósson énerth’ aïdos, hóson ouranós est’ apò gaíēs"; a quote from the Iliad (8.16) regarding Tartarus, here interpreted as the distance to the central fire.

It appears that in these matters, the followers of Empedocles and Parmenides, as well as most of the ancient sages, followed the Pythagoreans by asserting that the nature of the Monad is established in the center after the manner of Hestia The goddess of the hearth; in Pythagoreanism, "Hestia" refers to the central fire of the universe around which the planets revolve., and that it maintains this same seat because of its equilibrium. Indeed, Euripides, being a student of Anaxagoras, mentions the Earth in this way: "the wise among mortals call you Hestia."

Furthermore, the Pythagoreans say that the right-angled triangle also derived its composition through the Monad, since Pythagoras observed the numbers within it.

They also link Matter original: hyle to the Dyad The principle of "twoness" or duality.; for while Matter is the source of otherness in the natural world, the Dyad is its source in the realm of number. Just as Matter is indefinite original: aoristos and shapeless in itself, so too the Dyad—alone among all numbers—is not capable of receiving a geometric shape. For this reason, the Dyad can be called "indefinite." This is because a shape is contained, in actuality energeia; the state of being fully realized, by a minimum of three first angles or lines, whereas the Monad contains shape only in potentiality dynamis; the latent power to become something.

Not without reason did they also call the Dyad Proteus The sea-god from Egyptian myth capable of changing into any shape., after the many-formed hero in Egypt, because it contains the distinct properties of all things—just as Proteus did—serving as the "joint-work" of every number.

2. Anatolius on the Dyad

Anatolius (c. 230–282 CE) was the Bishop of Laodicea and a mathematician; his work on the "Decad" is a primary source for Pythagorean number symbolism.

Note that the Dyad, when added to itself, is equal to its own square; for its addition (2 + 2) and its multiplication (2 × 2) produce the same result, namely four original: d; the Greek numeral for 4. In all other numbers, however, multiplication produces a result greater than addition.

In terms of the virtues, they likened the Dyad to Courage original: andreia; for it has already advanced toward action original: praxin. For this reason, they also cal-