Nicomachus’s Theologoumena original: Theologoumena Arithmeticae, or The Theology of Arithmetic

The Triad the number three is the beginning of number in actualization, being defined as a system of monads units. For while the Dyad the number two is, in a certain sense, a Monad the number one due to its primordial nature, the Triad is the first true system consisting of a monad and a dyad. Moreover, it is the very first to admit a beginning, a middle, and an end, 17 through which all perfection is brought to completion. The Triad is the form of the completion of all things and is truly "number" in the proper sense; it provides a certain equality and a removal of "the more and the less" to the whole of things, having defined matter and given it shape through the powers of all qualities. Indeed, the number three possesses a unique and exceptional property compared to other numbers: it is equal to the sum of the numbers preceding it 1 + 2 = 3.

Furthermore, those who ask God for their prayers to be fulfilled pour libations three times and sacrifice three times. We also speak of the "thrice-blessed," the "thrice-happy," and the "thrice-fortunate"—as well as the opposites of these—whenever each of these states is present in a state of perfection. They also say that this number was named the Triad original: trias because it is "unwearying" original: ateirēs and untiring; it is called this because it cannot be divided into two equal parts referring to its nature as the first odd number.

The Triad is also the first plurality; for we speak of "singular" and "dual" things, but thereafter we no longer use a "triple" form, but specifically use the "plural" referring to Greek grammar, which has singular, dual, and plural forms. The Triad also extends into the very nature of number itself. There are three species of the odd original: perittos: the first is prime and incomposite, the second is secondary and composite, and the third is a mixture—which is secondary in relation to itself, but prime in relation to another. Again, there is the super-perfect original: hypertheles, often meaning abundant, the imperfect original: ateles, or deficient, and the equal original: ison, or perfect.

The Triad is most naturally suited to geometry; for the most fundamental element in plane surfaces is the triangle, and of this there are three types: the acute-angled, the obtuse-angled, and the scalene.

There are also three configurations of the Moon: waxing, the full moon, and waning. There are also three modes of the "anomaly" the irregular or retrograde motion of planets: progression, regression, and the station original: stērigmos that occurs between them. And three are those [which/who] the zodiac... The text breaks off here; it likely refers to the triplicities or the decans of the zodiac signs.