Dialogue

 1 Intro|           the conception of them: (3) the theology and physics
 2 Intro|     another 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|     intervals thus—~— over 1, 4/3, 3/2, — over 2, 8/3, 3, — over
 5 Intro|           1, 4/3, 3/2, — over 2, 8/3, 3, — over 4, 16/3, 6, —
 6 Intro|           4/3, 3/2, — over 2, 8/3, 3, — over 4, 16/3, 6, — over
 7 Intro|            2, 8/3, 3, — over 4, 16/3, 6, — over 8: — over 1,
 8 Intro|             6, — over 8: — over 1, 3/2, 2, — over 3, 9/2, 6, —
 9 Intro|             over 1, 3/2, 2, — over 3, 9/2, 6, — over 9, 27/2,
10 Intro|            the extremes, e.g. 1, 4/3, 2; the other kind of mean
11 Intro|        formed intervals of thirds, 3:2, of fourths, 4:3, and
12 Intro|         thirds, 3:2, of fourths, 4:3, and of ninths, 9:8. And
13 Intro|             light that burns not, (3) the red heat of the embers
14 Intro|       proportions of 1:2:4:8 and 1:3:9:27, or compounds of them,
15 Intro|        properties of 1:2:4:8, or 1:3:9:27, or of 3, 4, 5, they
16 Intro|            4:8, or 1:3:9:27, or of 3, 4, 5, they discovered in
17 Intro|   requirements of thought.~Section 3.~Plato’s account of the
18 Intro|            of the other. He means (3) to say that the creation
19 Intro|            series of numbers 1, 2, 3, 4, 9, 8, 27, composed of
20 Intro|     progressions 1, 2, 4, 8 and 1, 3, 9, 27, of which the number
21 Intro|          represents a point, 2 and 3 lines, 4 and 8, 9 and 27
22 Intro|        cubes respectively of 2 and 3. This series, of which the
23 Intro|          the heavenly bodies; and (3) may possibly contain an
24 Intro|           numbers (e.g. 2 squared, 3 squared = 4, 9), have always
25 Intro|          the cubes of primes (e.g. 3 cubed and 5 cubed) have
26 Intro|           found in his words; nor (3) is there any evidence to
27 Intro|           original triangles; and (3) a reunion of them in new
28 Intro|            regular solid figures: (3) three of them, fire, air,
29 Intro| progression:— Moon 1, Sun 2, Venus 3, Mercury 4, Mars 8, Jupiter
30 Intro|            factors, as 6 = 1 + 2 + 3. This, although not literally
31 Intro|           We must admit, further, (3) that Aristotle attributed
32 Intro|             Quaest; Plac. Phil.); (3) that even by Philolaus
33 Timae|        times as much as the first (3), and then he took a fourth
34 Timae|            triple (i.e. between 1, 3, 9, 27) cutting off yet
35 Timae|      extremes (as for example 1, 4/3, 2, in which the mean 4/
36 Timae|             2, in which the mean 4/3 is one-third of 1 more than
37 Timae|           number (e.g.~— over 1, 4/3, 3/2, — over 2, 8/3, 3, —
38 Timae|        number (e.g.~— over 1, 4/3, 3/2, — over 2, 8/3, 3, — over
39 Timae|           1, 4/3, 3/2, — over 2, 8/3, 3, — over 4, 16/3, 6, —
40 Timae|           4/3, 3/2, — over 2, 8/3, 3, — over 4, 16/3, 6, — over
41 Timae|            2, 8/3, 3, — over 4, 16/3, 6, — over 8: and — over
42 Timae|              over 8: and — over 1, 3/2, 2, — over 3, 9/2, 6, —
43 Timae|             over 1, 3/2, 2, — over 3, 9/2, 6, — over 9, 27/2,
44 Timae|            there were intervals of 3/2 and of 4/3 and of 9/8,
45 Timae|          intervals of 3/2 and of 4/3 and of 9/8, made by the
46 Timae|          up all the intervals of 4/3 with the interval of 9/8,
47 Timae|         243 (e.g.~243:256::81/64:4/3::243/128:2::81/32:8/3::243/
48 Timae|            4/3::243/128:2::81/32:8/3::243/64:4::81/16:16/3::242/
49 Timae|            8/3::243/64:4::81/16:16/3::242/32:8.).~And thus the
50 Timae|         intervals (i.e. between 1, 3, 9, 27), together with the
51 Timae|         expressed by the ratios of 3:2, and 4:3, and of 9:8—these,
52 Timae|           the ratios of 3:2, and 4:3, and of 9:8—these, although