Note 66 — BOOK IV DIVINERS AND MAGICIANS
Francis Legge translation
The object of all these figures is apparently to prove that those of Archimedes are wrong and that the Platonic theory—said, one does not know with what truth, to have been inherited from Pythagoras, viz., that the intervals between the orbits of the different bodies of the cosmos are arranged like the notes on a musical scale—is to be preferred. This was perhaps to be expected from a Churchman as favouring the doctrine of creation by design. It is difficult at first sight to see how the figures in the text bear out Hippolytus’ contention, inasmuch as the distances here given of the seven planets (including therein the Sun and Moon) from the Earth proceed in an irregular kind of arithmetical progression ranging from one to fifty-four, the distance from the Earth to the Moon which Hippolytus accepts from Archimedes as correct being taken as unity. Thus, let us call this unit of distance x, and we have the table which follows:—
Table I (of distances)
Distance of Earth (♁) from ☽ = 5,544,130 stadia or x
” ” ” ☉ = 16,632,390 ” 3x
” ” ” ♀ = 33,264,780 ” 6x
” ” ” ☿ = 55,441,300 ” 10x
” ” ” ♂ = 105,338,470 ” 19x
” ” ” ♃ = 149,691,510 ” 27x
” ” ” ♄ = 299,383,020 ” 54x
But let us take the figures given in the text for the intervals between the Earth and the seven “planets” arranged in the same order, and again taking the Earth to Moon distance as unity, we have:—
Table II (of intervals)
Interval between ♁ and ☽ = 5,554,130 stadia or x
” ” ☽ ” ☉ = 11,088,260 ” 2x
” ” ☉ ” ♀ = 16,632,390 ” 3x
” ” ♀ ” ☿ = 22,176,520 ” 4x(22)
” ” ☿ ” ♂ = 49,897,170 ” 9x(32)
” ” ♂ ” ♃ = 44,353,040 ” 8x(23)
” ” ♃ ” ♄ = 149,691,510 ” 27x(33)
This agrees almost entirely with the theory which M. Bigourdan in the work mentioned in the last note has worked out as the Platonic theory of the distances of the different planets from the Earth, “the supposed centre of their movements” (p. 228). Thus:—
Planets ☽ ☉ ♀ ☿ ♂ ♃ ♄
Distances 1 2 3 4 8 9 27
which distances are, in his own words, “les termes enchevêtrés de deux progressions géométriques ayant respectivement pour raison 2 et 3, savoir 1, 2, 4, 8—1, 3, 9, 27; on voit que l’unité est, comme chez Pythagore, la distance de la Terre à la Lune.” This conclusion is amply borne out by Hippolytus’ figures, which, as given in Table II above, show a regular progression from 2 and 3 to 22 and 32, then to 23 and 33, which explains what our author means by increasing the Earth to the Moon distance, κατὰ τὰ διπλάσιον καὶ τριπλάσιον. The only discrepancy between this and M. Bigourdan’s table is that he has transposed the distances between ☿—♂ and ♂—♄ respectively; but as I do not know the details of the calculation on which he bases his figures, I am unable to say whether the mistake is his or Hippolytus’.