ὧν ἐπίτριτος πυθμὴν κτλ. In ἀνθρωπείῳ δὲ—ἀπέφηναν the Pythagorean triangle
was employed to construct the period of gestation for the microcosm or man: here it is
used to construct two periods in the lifetime of the macrocosm or Universe, for that is
what Plato means by the two ‘harmonies.’ The translation is:
‘of which, 4, 3 married with 5, yields two harmonies when thrice increased,
the one equal an equal number of times, so many times 100, the other of equal length one
way, but oblong:—on the one side, of 100 squares of rational diameters of five
diminished by one each, or if of irrational diameters, by two: on the other of one
hundred cubes of three.’ The antecedent of ὧν is ὁμοιούντων τε καὶ ἀνομοιούντων καὶ
αὐξόντων καὶ φθινόντων, which I have already interpreted as the numbers
3, 4, 5. Of these numbers (ὧν) the ἐπίτριτος πυθμήν i.e. 3, 4 (cf. Theo Smyrn. p. 80 ed.
Hiller, Proclus l. c. II p. 37 ὁ ἐπίτριτος πυθμὴν γ́ καὶ
δ́), is ‘married’ or ‘coupled’ with 5.
That is to say, 3, 4, and 5 are multiplied together: whence we get 3 x 4 x 5=60.
‘Thrice increased’ is ‘three times multiplied by
itself’; and 60 thrice increased is therefore 60 x 60 x 60 x 60. This sum,
which is 12,960,000, yields two harmonies. One of the two harmonies is ‘equal
an equal number of times, viz. so many times 100,’ in
other words, it is a square (cf. Theaet. 147
E) each of whose sides is a certain number of times 100 (for τοσαυτάκις cf. τοσοῦτον in

Alc. I 108 E), viz. of course 36 times 100, for 60 x 60 x 60 x
60=3600^{2}. See Fig. 4.