On the cave in the VIIth book of the Republic
The Divided Line, 287.20 – 290.30
Between these two (accounts) he somewhere posits in this comparison, following that which has been determined before, that there are four sections of the all. Let us take these things up then in a few words, by which we should see how the whole image is in agreement.
Since he wants to show that the procession of being from the one is continuous and unified, he compares this continuous series of things to a single line, with the second order always proceeding in likeness and coherence from the first order, with no part being separated by a void. For this was not lawful, as the good brings forth everything and reverts them back to itself.
There needs to be a resemblance of the creation to the creator. This (creator) being one, it is therefore necessary for creation to be continuous, for the continuous is similar to the one and the cause of this continuity is the similarity of the following sections to the first and everyone agrees that this (similarity) comes from the One. For what similar is derived from the nature of the One. He therefore takes a single line, and he cuts it in two, not in equal parts of the section, but in unequal, yet in two nevertheless. For in the Philebus, for those who contemplate true being, it is advised to contemplate after the One, the Two, if it is at all, and if not, the number closest to the Dyad. And so the unequal cut of the All shows the value of the division to him, setting the inequality according to the continuous as an image of the inequality of the substance. And of this analogy of the two unequal sections that he cuts from the original line, he distinctly signifies again an analogy of identity with the second, subservient to the first.
For the analogy is an identity of reason, “the most beautiful of bonds”, as we have understood in the Timaeus (31 c2), and a “judgment of God” as we have heard in the Laws (VI 751 b6).
Moreover, as the cosmos was created according to analogy, all things are then held together by a permanent friendship, and in this way the All proceeded, joining all things together and harmonizing them and as the four sections of the single line are introduced by him, he assumes that the first two make up the greater part, being the genus of the intelligible world (noumenon), and the lesser being the genus of the visible world.
 The One being the Neoplatonic absolute transcending ultimate principle. It is actually the demiurge that is considered to be responsible for the creation of the material universe, but the One is considered the creator because ultimately all planes of reality are emanated from it.
 This passage deals with Pythagorean metaphysics, see my introduction and the related fn. 11.
 To translate certain Neoplatonic ontological concepts, which in the Greek have the form of single nouns in the genitive case or participles, I variously add the term “world” or “order” to convey the meaning.