/lit/ - Literature

>>20451078
This is all from pseudo-iamblichus, theology of arithmetic by the way:

>The triad has a special beauty and fairness beyond all numbers, primarily because it is the very first to make actual the potentiali ties of the monad—oddness, perfection, proportionality, unifica tion, limit. For 3 is the first number to be actually odd, since in conformity with its descriptions it is 'more than equal' and has something more than the equal in another part; [1.] and it is special in respect of being successive to the two sources and a system of them both. At any rate, it is perfect in a more particular way than the other numbers to which consecutive numbers from the monad to the tetrad are found to be equal—I mean, that is, the monad, triad, hexad and decad. The monad, as the basic number of this series, is equal to the monad; the triad is equal to monad and dyad; the hexad is equal to monad, dyad and triad; the decad is equal to monad, dyad, triad and tetrad. So the triad seems to have something extra in being successive to those to which it is also equal. Moreover, they called it 'mean' and 'proportion/ not so much because it is the very first of the numbers to have a middle term, which it in particular maintains in a relation of equality to the extremes, [2.] but because in the manner of equality among things of the same genus, where there is a mean between greater and less inequality of species, it too is seen as midway between more and less and has a symmetrical nature. For the number which comes before it, 2, is more than the one before it, and this, being double, is the root of the basic relation of being more than; and the number which comes after it, 4, is less than the numbers which precede it, and this, being sesquialter, is the very first to have the specific identity of the basic relation of being less than,- but the triad, between both of these, is equal to what precedes it, so it gains the specific identity of a mean between the others.

Notes:
>[1.] Peziisos (more than equal) is a word made up for the similarity withperissos (odd); similarly for the phrase 'more than the equal'—'the equal' being the dyad, presumably. There could also be a reference to the point made in the next paragraph: the triad is 'more than just equal/ because it is also successive to the monad and the dyad.
>[2.] I suppose this means either that 3 is 1+1+1, where the middle term is naturally equal to either of the extremes; or that in the series 1, 2, 3, the middle term is equidistant from (the arithmetic mean of) the extremes.