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Chapter X.—Theory of Stellar Motion and Distance in Accordance with Harmony.

Concerning the Moon, however, a statement has been
previously made. The distances and profundities of the spheres
Archimedes thus renders; but a different declaration regarding them has
been made by Hipparchus; and a different one still by Apollonius the
mathematician. It is sufficient, however, for us, following the
Platonic opinion, to suppose twofold and threefold distances from one
another of the erratic stars; for the doctrine is thus preserved of the
composition of the universe out of harmony, on concordant
principles^{190}^{190} The
Abbe Cruice thinks that the word should be “tones,”
supporting his emendation on the authority of Pliny, who states that
Pythagoras called the distance of the Moon from the Earth a tone,
deriving the term from musical science (see Pliny’s *Hist.
Nat*., ii. 20). in keeping with these
distances. The numbers, however, advanced by Archimedes,^{191}^{191}
These numerical speculations are treated of by Archimedes in his
work *On the Number of the Sand*, in which he maintains the
possibility of counting the sands, even on the supposition of the
world’s being much larger than it is (see Archimedes,
τὰ
μεχρὶ νῦν
σωζόμενα
ἅπαντα, Treatise ψαμμίτης,
p. 120, ed. Eustoc. Ascalon., Basil, 1544). and the accounts rendered by the rest
concerning the distances, if they be not on principles of
symphony,—that is, the double and triple (distances) spoken of by
Plato,—but are discovered independent of harmonies, would not
preserve the doctrine of the formation of the universe according to
harmony. For it is neither credible nor possible that the
distances of these should be both contrary to some reasonable plan, and
independent of harmonious and proportional principles, except perhaps
only the Moon, on account of wanings and the shadow of the Earth, in
regard also of the distance of which alone—that is, the lunar
(planet) from earth—one may trust Archimedes. It will,
however, be easy for those who, according to the Platonic dogma itself,
adopt this distance to comprehend by numerical calculation (intervals)
according to what is double and triple, as Plato requires, and the rest
of the distances. If, then, according to Archimedes, the Moon is
distant from the surface of the Earth 5,544,130 stadii, by
increasing these numbers double and triple, (it will be) easy to find
also the distances of the rest, as if subtracting one part of the
number of stadii which the Moon is distant from the Earth.

But because the rest of the numbers—those alleged by Archimedes concerning the distance of the erratic stars—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.

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