Chapter XI.—Theory
of the Size of the Heavenly Bodies in Accordance with Numerical
Harmonies.
These (numerical) relations, therefore, the greater than
ninefold, and less than half, and greater than double, and less than
two-fifths, and greater than half, and less than double, are beyond all
symphonies, from which not any proportionate or harmonic system could
be produced. But the whole world, and the parts of it, are in all
respects similarly framed in conformity with proportion and
harmony. The proportionate and harmonic relations, however, are
preserved—as we have previously stated—by double and triple
intervals. If, therefore, we consider Archimedes reliable in the
case of only the first distance, that from the Moon to the Earth, it is
easy also to find the rest (of the intervals), by multiplying (them) by
double and treble. Let then
the distance, according to Archimedes, from Earth to Moon be 5,544,130
stadii; there will therefore be the double number of this of stadii
which the Sun is distant from the Moon, viz. 11,088,260. But the
Sun is distant from the Earth 16,632,390 stadii; and Venus is likewise
distant from the Sun 16,632,390 stadii, but from the Earth 33,264,780
stadii; and Mercury is distant from Venus 22,176,520 stadii, but from
Earth 55,441,300 stadii; and Mars is distant from Mercury 49,897,170
stadii, and from Earth 105,338,470 stadii; and Jupiter is distant from
Mars 44,353,040 stadii, but from Earth 149,691,510 stadii; Saturn is
distant from Jupiter 149,691,510 stadii, but from Earth 299,383,020
stadii.