[Footnote 60: ἐν λόγοις συμφώνοις. Cruice would read τόνοις for λόγοις on the strength of what Pliny, _Hist. Nat._, II, 20, says about Pythagoras having taught that the intervals between the planets’ orbits were musical tones. He seems to mean the gamut or chromatic scale as contrasted with the enharmonic.] [Footnote 61: See last note.] [Footnote 62: See note on p. 81 _infra_ as to what this doubling and tripling means.] [Footnote 63: συμφωνίᾳ.] [Footnote 64: ἐπιτετάρτῳ, _superquarta_, Cr., 1 + ¼; see Liddell and Scott, quoting Nicomachus Gerasenus Arithmeticus.] [Footnote 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 tones 1 ½ ½ 1½ 1 ½ ½ ½ { in thousands of } 126 63 63 189 126 63 63 63 { stadia } Absolute distances } in thousands } 0 126 189 252 441 567 630 693 756 of stadia } ] [Footnote 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_) Distance of Earth (♁) from ☽ = 5,544,130 stadia or _x_ “ ” “ ☉ = 16,632,390 ” 3_x_ “ ” “ ♀ = 33,264,780 ” 6_x_ “ ” “ ☿ = 55,441,300 ” 10_x_ “ ” “ ♂ = 105,338,470 ” 19_x_ “ ” “ ♃ = 149,691,510 ” 27_x_ “ ” “ ♄ = 299,383,020 ” 54_x_