[61] See last note.

[62] See note on p. [81] infra as to what this doubling and tripling means.

[63] συμφωνίᾳ.

[64] ἐπιτετάρτῳ, superquarta, Cr., 1 + ¼; see Liddell and Scott, quoting Nicomachus Gerasenus Arithmeticus.

[65] It is not easy to see from this confused statement whether it is the system of Plato or Archimedes at which Hippolytus is aiming. The one, however, that it most resembles is that of the neo-Pythagoreans, of which the following table is given in M. Bigourdan’s excellent work on L’Astronomie: Evolution des Idées et des Méthodes, Paris 1911, p. 49:—

Planets♁☽☿♀☉♂♃♄Fixed stars
Interval{in tones1½½1½1½½½
in thousands of stadia1266363189126636363
Absolute distances in thousands of stadia0126189252441567630693756

[66] 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)

DistanceofEarth(♁)from☽=5,544,130stadia orx
”””☉=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:—