Dialogue

 1 Intro|         outline of the dialogue: (2) I shall consider the aspects
 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, — over
 4 Intro|          over 1, 4/3, 3/2, — over 2, 8/3, 3, — over 4, 16/3,
 5 Intro|          6, — over 8: — over 1, 3/2, 2, — over 3, 9/2, 6, —
 6 Intro|            over 8: — over 1, 3/2, 2, — over 3, 9/2, 6, — over
 7 Intro|       over 1, 3/2, 2, — over 3, 9/2, 6, — over 9, 27/2, 18, —
 8 Intro|           3, 9/2, 6, — over 9, 27/2, 18, — over 27;~in which
 9 Intro|        the extremes, e.g. 1, 4/3, 2; the other kind of mean
10 Intro|     equidistant from the extremes—2, 4, 6. In this manner there
11 Intro|     formed intervals of thirds, 3:2, of fourths, 4:3, and of
12 Intro|        kinds of fire— (1) flame, (2) light that burns not, (
13 Intro|     only-begotten heaven.~Section 2.~Nature in the aspect which
14 Intro|  triangles or in proportions of 1:2:4:8 and 1:3:9:27, or compounds
15 Intro|  meditated on the properties of 1:2:4:8, or 1:3:9:27, or of
16 Intro|           not yet distinguished; (2) that he supposes the process
17 Intro|         to a series of numbers 1, 2, 3, 4, 9, 8, 27, composed
18 Intro|       Pythagorean progressions 1, 2, 4, 8 and 1, 3, 9, 27, of
19 Intro|      number 1 represents a point, 2 and 3 lines, 4 and 8, 9
20 Intro|         and cubes respectively of 2 and 3. This series, of which
21 Intro|          Pythagoreans and Plato; (2) the order and distances
22 Intro|        any two such numbers (e.g. 2 squared, 3 squared = 4,
23 Intro|        limited to prime numbers; (2) that the limitation of
24 Intro|         regular pyramid (20 = 8 x 2 + 4); and therefore, according
25 Intro|          of two pyramids (8 = 4 x 2), a particle of air is resolved
26 Intro|        which they are collected; (2) a resolution of them into
27 Intro|         to one another, but also (2) of smaller bodies to larger
28 Intro|          places at the creation: (2) they are four in number,
29 Intro|         progression:— Moon 1, Sun 2, Venus 3, Mercury 4, Mars
30 Intro|           its factors, as 6 = 1 + 2 + 3. This, although not
31 Intro|       both explanations. A doubt (2) may also be raised as to
32 Intro|         of the early physicists; (2) that the development of
33 Intro|   secondary qualities of matter. (2) Another popular notion
34 Intro| recognized principle of geology.~(2) Plato is perfectly aware—
35 Intro|           of authority and value.~2. It is an interesting and
36 Timae|       which was double the first (2), and then he took away
37 Timae|        intervals (i.e. between 1, 2, 4, 8) and the triple (i.e.
38 Timae|            as for example 1, 4/3, 2, in which the mean 4/3 is
39 Timae|          than 1, and one-third of 2 less than 2), the other
40 Timae|          one-third of 2 less than 2), the other being that kind
41 Timae|     number (e.g.~— over 1, 4/3, 3/2, — over 2, 8/3, 3, — over
42 Timae|          over 1, 4/3, 3/2, — over 2, 8/3, 3, — over 4, 16/3,
43 Timae|           over 8: and — over 1, 3/2, 2, — over 3, 9/2, 6, —
44 Timae|        over 8: and — over 1, 3/2, 2, — over 3, 9/2, 6, — over
45 Timae|       over 1, 3/2, 2, — over 3, 9/2, 6, — over 9, 27/2, 18, —
46 Timae|           3, 9/2, 6, — over 9, 27/2, 18, — over 27.).~Where
47 Timae|         there were intervals of 3/2 and of 4/3 and of 9/8, made
48 Timae|           256::81/64:4/3::243/128:2::81/32:8/3::243/64:4::81/
49 Timae|        intervals (i.e. between 1, 2, 4, 8), and the three triple
50 Timae|      expressed by the ratios of 3:2, and 4:3, and of 9:8—these,