Dialogue

 1 Intro|    composition of the elements: (4) in the fourth section I
 2 Intro|        in the ratios of 1, 2, 3, 4, 9, 8, 27, and proceeded
 3 Intro|        intervals thus—~— over 1, 4/3, 3/2, — over 2, 8/3, 3, —
 4 Intro|           over 2, 8/3, 3, — over 4, 16/3, 6, — over 8: — over
 5 Intro|         of the extremes, e.g. 1, 4/3, 2; the other kind of
 6 Intro| equidistant from the extremes—2, 4, 6. In this manner there
 7 Intro|         thirds, 3:2, of fourths, 4:3, and of ninths, 9:8. And
 8 Intro|         or in proportions of 1:2:4:8 and 1:3:9:27, or compounds
 9 Intro|         on the properties of 1:2:4:8, or 1:3:9:27, or of 3,
10 Intro|         8, or 1:3:9:27, or of 3, 4, 5, they discovered in them
11 Intro|       that was to be.’ He means (4) to draw an absolute distinction
12 Intro|       series of numbers 1, 2, 3, 4, 9, 8, 27, composed of the
13 Intro|   Pythagorean progressions 1, 2, 4, 8 and 1, 3, 9, 27, of which
14 Intro|          a point, 2 and 3 lines, 4 and 8, 9 and 27 the squares
15 Intro|      e.g. 2 squared, 3 squared = 4, 9), have always a single
16 Intro|          mean proportional (e.g. 4 and 9 have the single mean
17 Intro|    regular pyramid (20 = 8 x 2 + 4); and therefore, according
18 Intro|       sides of two pyramids (8 = 4 x 2), a particle of air
19 Intro|          similarly transformed: (4) different sizes of the
20 Intro|        and not infinite.~Section 4.~The astronomy of Plato
21 Intro|          Sun 2, Venus 3, Mercury 4, Mars 8, Jupiter 9, Saturn
22 Intro|      meant rotation on an axis. (4) The immobility of the earth
23 Intro|          sun or a central fire; (4) that the beginnings of
24 Timae|     twice as much as the second (4), and a fifth part which
25 Timae|    intervals (i.e. between 1, 2, 4, 8) and the triple (i.e.
26 Timae|      extremes (as for example 1, 4/3, 2, in which the mean
27 Timae|          3, 2, in which the mean 4/3 is one-third of 1 more
28 Timae|     equal number (e.g.~— over 1, 4/3, 3/2, — over 2, 8/3, 3, —
29 Timae|           over 2, 8/3, 3, — over 4, 16/3, 6, — over 8: and —
30 Timae|          intervals of 3/2 and of 4/3 and of 9/8, made by the
31 Timae|          up all the intervals of 4/3 with the interval of 9/
32 Timae|         243 (e.g.~243:256::81/64:4/3::243/128:2::81/32:8/3::
33 Timae|         128:2::81/32:8/3::243/64:4::81/16:16/3::242/32:8.).~
34 Timae|    intervals (i.e. between 1, 2, 4, 8), and the three triple
35 Timae|        by the ratios of 3:2, and 4:3, and of 9:8—these, although