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 30treble. 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.