Plato's number

Below is a typical text from a relatively recent translation of Republic 546b–c: Now for divine begettings there is a period comprehended by a perfect number, and for mortal by the first in which augmentations dominating and dominated when they have attained to three distances and four limits of the assimilating and the dissimilating, the waxing and the waning, render all things conversable and commensurable [546c] with one another, whereof a basal four-thirds wedded to the pempad yields two harmonies at the third augmentation, the one the product of equal factors taken one hundred times, the other of equal length one way but oblong,-one dimension of a hundred numbers determined by the rational diameters of the pempad lacking one in each case, or of the irrational lacking two; the other dimension of a hundred cubes of the triad.

[1] Shortly after Plato's time his meaning apparently did not cause puzzlement as Aristotle's casual remark attests.

[6] Half a millennium later, however, it was an enigma for the Neoplatonists, who had a somewhat mystic penchant and wrote frequently about it, proposing geometrical and numerical interpretations.

Next, for nearly a thousand years, Plato's texts disappeared from Western Europe and it is only in the Renaissance that the enigma briefly resurfaced.

Schleiermacher interrupted his edition of Plato for a decade while attempting to make sense of the paragraph [citation needed].