(b) The sixfold (hexas), as the author deduces from the presence in it of unity, two, and trinity, and from the multiplication of the double by the trinity, is also the masculine-feminine principle and also a marriage (43:5, 7), but only in a more special sense. It is marriage in the sense of the reproduction of offspring, that is, the generation of one's own kind. And that which is like itself is the whole and the parts (43:8). And since the whole governs the parts, the six are also the soul, that is, the soul that governs the body (45:8-13). But in this case, the six is also what has often been called the cosmos, since in the cosmos we find the unity of opposites, which arises "according to harmony" (48:18-20). Therefore the sixfold is also "the division of the whole" (45:11), and moreover not only in space but also in time (49:11, 17-18), and in this sense it is the "eidos of eidos" (45:7), and "far-reaching" (the epithet of Apollo) (49:11), "wholly caring" (holomeleia 48:6), "all-healing" (50:2), "perfect" (42:19), "health" (48:21), "love" (philosis 48:14). In short, all such definitions of the Six come down to the fact that it is a living and animate cosmos, soul and body, which are in eternal harmony. In other words, the Six is simply the entire cosmos, but as yet only at the level of the universal organism. If the five pointed to "vitality," that is, to the principle of the living organism, then the six no longer indicates the principle of the organism, but the organism itself. At the same time, a strict sequence of thought is observed here. Being not the principle of life, but life itself, the organism itself, the sixfold points to this organism in a global form. This is the cosmos, that is, as yet only a cosmic organism in general. The details necessary here follow immediately, in the next few days of the decade.

c) The week (heptas), after the amazingly eccentric numerical combinations, appears before our historical and philosophical gaze as an attempt to express not simply the unidivisibility of the cosmos, as we find in the six, but to express the rhythmic recurrence of the individual periods of the cosmos. Here again the point is not at all that a child can be born after seven months of pregnancy, and not that four sevens are equal to 28, and 28 is a perfect number equal to the sum of its factors. And the fact is that seven is the ubiquitous uniformity of periods of life development. If we do not draw this conclusion from this chapter of the treatise, then the individual epithets of the week have too general a meaning and say little. She is Athena (71:2), and "fate" (tyche 59:3; 70:24), and "leading away prey" (56:10), and "moment" (59:4; 70:24), and "purposeful" (55:6). Generally speaking, the septenary is also a cosmic organism, but already conceivable in all the mobile details of its organic structure.

d) The octal (octas), being the cube of the two, embraces the entire cosmos as a mother. Therefore she is not merely a mother (74:5), but is also a mother everywhere, which is why she is "all-harmonious" (panarmonios 73:5). She is Rhea, that is, the mother of all gods (74:7). After all, a cube in the geometric sense is a three-dimensional body. This means that motherhood here is also three-dimensional, that is, pancosmic, panharmonious. The treatise borrows from Philolaus (44A12) the definition of the eightfold as the culprit of "love, friendship, wisdom (metis) and ingenuity" (74, 14-15). However, this is a more general definition, as are "seat" and "security" (Q[75], A[2]), although all these general definitions still point to a solid ubiquity of harmony. For us, it is especially important to say that the eightfold "everywhere beautifully (pagcalos) and intercorrespondingly (parallelos) brought all harmonies into harmony" (76, 6-7). In other words, the eightfold is not just the principle of life (the five), nor the organic living cosmos (the six), nor the repetition of the universal organism in its individual organs or parts (the septenary). But this repetition is everywhere in agreement with itself and with the living cosmos as a universal wholeness, that is, cosmic organization is the omnipresent harmony of life. This is the essence of the eightfold.

In comparison, the other features of the eightfold indicated in the treatise have a tertiary meaning and are accidental. Thus, for example, it is indicated that there are eight stellar spheres, eight astronomical circles (zodiac, horizon, equinox circle, etc.), and that the octal is Euterpe or Cadmea. She is Euterpe because she is eytreptos ("agile"), which reminds one of the famous muse Euterpe. Cadmea is because Harmony is the wife of Cadmus. The most important thing in the eightfold, presumably, is cosmic all-harmony, while the septenary is simply the presence of harmony in the cosmos in general. The Eightfold is "all-harmonious" because of the "extraordinary harmonization" it produces (dia ten hyperphye catharmosin 73, 6).

e) The nine (enneas) is characterized in the treatise in such a contradictory and even contradictory way that it is not an easy task to find some main idea here and distinguish it from secondary thoughts. As far as can be judged, a novelty in comparison with the preceding numbers is the characterization of the ninefold as Hera, the sister and consort of Zeus (78, 3), which, according to the fantastic but constant etymology of the ancient Greeks, is air (aer), and this air is thought of in this case as the upper air, that is, as ether. Ether, on the other hand, is the finest substance, which permeates the entire cosmos, embraces it, and therefore makes it round (78:2). From here it is the Ocean (77, 4) and the horizon (77, 4). The fact that she is also Hephaestus (77:23) also indicates the fiery nature of ether. She is also Hyperion (78:9), because she stands above everything and embraces everything. The purposeful roundness of movement is indicated by the understanding of her as Terpsichore, the muse of dance (78, 11). She is also Prometheus (77:6), but instead of fire, thinking is indicated here.

If we understand the idea of the ninefold correctly, then of all the disparate features given in this characterization, the most important is probably the cosmic activity of the principle of harmony established above. In essence, this is still the same cosmic all-harmoniousness, but given in the aspect of its activity and general curvature of figures. It is an all-harmonious organism in the aspect of its active functioning.

The rest of the definitions and epithets of the ninefold seem to us too general, so that in a certain sense they can be applied to any number. Such, for example, are the epithets "blameless" (77, 14), "likeness" (77, 16), "like-mindedness" (77, 12), "perfect" (78, 16), "goal-setting" (78, 15), "far-sighted" (78, 4).

§4. Decas

1. The Paradigm of Harmonious Eternity

A very interesting picture is presented in the treatise by the analysis of the decimal, however, if we abstract to a large extent from the abundant formal-arithmetic operations here. The author himself defines the decimal in a very clear form as that prototype or "model" (paradeigma) which is the "seed" or "seed logos" for the entire structure of the cosmos from heaven to earth, including not only cosmic statics but also the dynamics of the world's periodic returns to itself as a result of its self-development (79:5-24; 83:4-5). The decimal is "an artistic [or artistic] eidos as a foundation for cosmic achievements" (cosmicois apotelesmasi 83:3-4). Simply put, it is the focus of the "logos of the spheres" (82, 8), that is, the comprehensive power of all cosmic harmony. If we compare the decimal with the nine, which is also a symbol of actively arising cosmic harmony, then the decimal contains the unprecedented news that it is the prototype of this all-cosmic harmony. The active all-cosmic harmony at the ninefold stage was only a fact, but not yet the idea of this fact. If every thing is understood as itself only because it is itself and not something else, that is, because it contains a definite idea, then the whole cosmos, both static and dynamic, exists only because of its idea, because of its prototype, because of its paradigm. The decimal testifies to the active transition of the ideal prototype into the real and material picture of the living cosmos both in its statics and in its dynamics. If this is so, then the dialectic of the decimal becomes the clearest and most intelligible construction. This, it seems to us, is the main thing. But this main thing is illustrated in the treatise by many images, which, of course, already have a conventional meaning, and, moreover, are not always understandable. These images are presented in the treatise, as always, separately and rather chaotic. But if we pursue logical order, then we can say the following.

2. Appropriate Terminology