The entire compound was divided by the Creator in certain
proportions and reunited; it was then cut into two strips, which
were bent into an inner circle and an outer, both moving with an
uniform motion around a centre, the outer circle containing the
fixed, the inner the wandering stars. The soul of the world was
diffused everywhere from the centre to the circumference. To this
God gave a body, consisting at first of fire and earth, and
afterwards receiving an addition of air and water; because solid
bodies, like the world, are always connected by two middle terms
and not by one. The world was made in the form of a globe, and
all the material elements were exhausted in the work of creation.
The proportions in which the soul of the world as well as the
human soul is divided answer to a series of numbers 1, 2, 3, 4,
9, 8, 27, composed of the two Pythagorean progressions 1, 2, 4, 8
and 1, 3, 9, 27, of which the number 1 represents a point, 2 and
3 lines, 4 and 8, 9 and 27 the squares and cubes respectively of
2 and 3. This series, of which the intervals are afterwards
filled up, probably represents (1) the diatonic scale according
to the Pythagoreans and Plato; (2) the order and distances of the
heavenly bodies; and (3) may possibly contain an allusion to the
music of the spheres, which is referred to in the myth at the end
of the Republic. The meaning of the words that ‘solid bodies are
always connected by two middle terms’ or mean proportionals has
been much disputed. The most received explanation is that of
Martin, who supposes that Plato is only speaking of surfaces and
solids compounded of prime numbers (i.e. of numbers not made up
of two factors, or, in other words, only measurable by unity).
The square of any such number represents a surface, the cube a
solid. The squares of any two such numbers (e.g. 2 squared, 3
squared = 4, 9), have always a single mean proportional (e.g. 4
and 9 have the single mean 6), whereas the cubes of primes (e.g.
3 cubed and 5 cubed) have always two mean proportionals (e.g.
27:45:75:125). But to this explanation of Martin’s it may be
objected, (1) that Plato nowhere says that his proportion is to
be limited to prime numbers; (2) that the limitation of surfaces
to squares is also not to be found in his words; nor (3) is there
any evidence to show that the distinction of prime from other
numbers was known to him. What Plato chiefly intends to express
is that a solid requires a stronger bond than a surface; and that
the double bond which is given by two means is stronger than the
single bond given by one. Having reflected on the singular
numerical phenomena of the existence of one mean proportional
between two square numbers are rather perhaps only between the