are not based on principles of concord, it is easy to understand—that is, for those who attend to the matter—how the numbers are mutually related, and on what principles they depend. That, however, they should not be in harmony and symphony—I mean those that are parts of the world which consists according to harmony—this is impossible. Since, therefore, the first number which the Moon is distant from the earth is 5,544,130, the second number which the Sun is distant from the Moon being 50,272,065, subsists by a greater computation than ninefold. But the higher number in reference to this, being 20,272,065, is [comprised] in a greater computation than half. The number, however, superior to this, which is 50,817,165, is contained in a greater computation than half. But the number superior to this, which is 40,541,108, is contained in a less computation than two-fifths. But the number superior to this, which is 20,275,065, is contained in a greater computation than half. The final number, however, which is 40,372,065, is comprised in a less computation than double.
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;
