[Footnote 53: Lit., “if one section be severed.”]
[Footnote 54: Cf. Plato, _Timæus_, c. 12.]
[Footnote 55: A palpable mistake. As Cruice points out, if the Earth’s diameter is as said in the text, its perimeter must be 251,768 stadia, which is not far from the 252,000 stadia assigned to it by Eratosthenes.]
[Footnote 56: Lacunæ in both these sentences.]
[Footnote 57: The common Greek name for the planet Ares or Mars (♂).]
[Footnote 58: All these numbers are hopelessly corrupt in the text and the scribe varies the notation repeatedly. I have given the figures as finally settled by Cruice and his predecessors. The Shining One is the planet Hermes or Mercury (☿).]
[Footnote 59: βάθη, “depths”; rather height if we consider the orbits of the planets as concentric and fitting into one another like jugglers’ caps or the skins of an onion.]
[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 62: See note on p. 81 _infra_ as to what this doubling and tripling means.]
[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:--