c) Finally, the mythological meaning of the binary is also unlikely to require any commentary. She is also a well-known muse - Erato (13, 6), and Rhea (14, 7), and Isis (13, 12).

§3. Numbers 3-9

1. Trinity (trias)

What the author of the treatise lacked in his analysis of unity and duality is given in the clearest form in the analysis of the category of trinity. Of course, the modern reader will complain about the author of the treatise because of his predilection for external arithmetic operations. These latter often only obscure the main idea of this chapter. And this idea is very important.

(a) In fact, the unit, in spite of all its numerous and even infinite secondary functions, nevertheless gravitates towards absolute singularity, that is, towards absolute identity, towards the absolute self-identity of all reality. To break away from this all-consuming unity and to take the path of the free functioning of each individual thing is to make a leap from an all-consuming unity to an all-pervading multiplicity. But the latter also does not provide stable freedom for individual existence. A new dialectical leap is still needed here, namely, such a leap as would at once create for a thing both its individuality and its becoming. Naively, but at the same time very wisely, the Pythagorean author of the treatise calls this synthesis of closed individuality and the free openness of its becoming by means of the term "trinity." Arithmetical argumentation here, however, is too naïve. It is said that if an arithmetical triple contains one and two, then this means that the trinity also combines both the functions of one and the functions of two. The author of the treatise does not know how to formulate a dialectical synthesis of the trinity on the basis of one and two, and replaces this dialectical leap with an indication of the property of the arithmetical triple, which is determined simultaneously by the presence of one and two in it.

Surprisingly, the author of the treatise passes by a long line of philosophers who knew how to merge the limit and the infinite in what they called number. And such is Plato in the Philebus (16c-20e). In a surprising way, the logical construction is replaced here by a purely intuitive picture. However, for intuition in life, in nature, and in the whole world, there is an infinite number of such things and events "in which it is precisely this unity of stable being and the unstable becoming of this being that comes to the fore. And almost the entire chapter devoted to the trinity consists of pointing out examples of a deep synthesis of certain mutually contradictory moments.

When we say "peace" in the sense of tranquility, we certainly mean a certain kind of unity of opposites (19, 17). The same is meant in the use of such words as "good counsel" (16:18), "piety" (17:1), "like-mindedness" (19:18). Of course, it is impossible to imagine what "knowledge" is (16, 22) if one does not find in it the ability to distinguish and identify. The same must be said of "reasonableness" or "prudence" (16:19). In "friendship" (19, 17) and in "marriage" (19, 20), according to the author of the treatise, the trinity is also realized (although marriage finds its full expression here only in the five, as we shall see presently), not to mention "proportion" in general (15, 5) or "harmony" in general (19, 18). This trinity ensures for each thing its independent existence, "everyness" (16, 10 to hecaston), as well as everything in general to be everything, that is, to be "allness" for it (16, 11 to pan).

(b) A more precise definition of the trinity is the principle by virtue of which a beginning, a middle, and an end arise in all things and in the whole world, and this is the principle of "perfection" (17:17-18). In another way, it is said that the trinity is not just the middle, but the "middle" (15, 5) for everything that exists, that is, it is its semantic center, which comprehends it all. It is also clear in what sense "proportionality" is spoken of (15, 5), which the Greek term can also be translated as "proportionality".

c) Finally, from the point of view of the history of ancient aesthetics, it is very important to note that the author of the treatise himself connects the trinity with "beauty" and "splendor" (14, 14-15). If it is still possible to argue with regard to "beauty" whether it is an indication of the synthesis of the inner and the outer, then the term "splendor" used here, by virtue of this very Greek word-formation, testifies precisely to the fixation here of the identity of the inner and the outer. The impersonal Greek verb prepei means "fits," "fits," "fits," "fits," "fits," "fulfills its purpose." Another word included in this term, namely eu, also means in Greek "good", "important", "valuable". Therefore, this whole term "splendor" (eyprepeia) very accurately expresses the basic essence of all beauty, which requires, first of all, conformity to its purpose. This moment did not exist in either one or two, if we take them as two independent categories. And although the analysis of these two categories already leads to the need for an internal-external synthesis, in a special sense this synthesis is achieved only in the trinity. It can be said that the first three numbers, in the opinion of the author of the treatise, are a characteristic of beauty as a single whole. But in this aesthetic principle, unity is determined by unity, separateness is determined by two, and wholeness is determined by trinity.

It seems to us that if we stand from the point of view of Pythagorean Platonism, then it is difficult to imagine a better and in any case a more fundamental formula of beauty.

2. Quaternary (tetras)