Philosophumena; or, The refutation of all heresies, Volume I
David Hume · en
But since the rest of the numbers stated by Archimedes about the
distance of the Wanderers are not in accordant ratios, it is easy to
know how they stand in regard to one [Sidenote: p. 73.] another and in
what ratios they have been observed to be. But that the same are not in
harmony and accord[63] when they are parts of the cosmos established
by harmony is impossible. So then, as the first number (of stadia)
by which the Moon is distant from the Earth is 5,544,130, the second
number by which the Sun is distant from the Moon being 50,262,065, it
is in ratio more than ninefold; and the number of the interval above
this being 20,272,065 is in ratio less than one-half. And the number of
the interval above this being 50,815,108 is in ratio more than twofold.
And the number of the interval above this being 40,541,108 is in ratio
more than one and a quarter.[64] And the number of the interval above
this being 20,275,065 is in ratio more than half. And the number of
the highest interval above this being 40,372,065 is in ratio less than
twofold.[65]
11. These same ratios indeed--the more than ninefold, [Sidenote: p.
74.] less than half, more than twofold, less than one and a quarter,
more than half, less than half and less than twofold are outside all
harmonies and from them no enharmonic nor accordant system can come to
pass. But the whole cosmos and its parts throughout are put together in
an enharmonic and accordant manner. But the enharmonic and accordant
ratios are kept alive as we have said before by the twofold and
threefold intervals. If then we deem Archimedes worthy of faith on the
distance given above, _i. e._, that from the Moon to the Earth, it is
easy to find the rest by increasing it in the ratios of 2 and 3. Let
the distance from the Earth to the Moon be, according to Archimedes,
5,544,130 stadia. The double of this will be the number of stadia by
which the Sun is distant from the Moon, viz., 11,088,260. But from
the Earth the Sun is distant 16,632,390 stadia and Aphrodite indeed
from the Sun--16,632,390 stadia, but from the Earth 33,264,780. Ares
indeed is distant from Aphrodite 22,176,520 stadia but from the Earth
105,338,470. But Zeus is distant from Ares 44,353,040 stadia, but from
[Sidenote: p. 75] the Earth 149,691,510. Kronos is distant from Zeus
40,691,510 stadia, but from the Earth 293,383,020.[66]