[Footnote 69: Hippolytus seems to have been entirely ignorant that the calculations he derides were anything but mere guesswork. They were not only singularly accurate considering the imperfection of the observations at the disposal of their author, but have also been of the greatest use to science as laying the foundation of all future astronomy.]
[Footnote 70: ἀμέτρους. Another pun on their _measurements_.]
[Footnote 71: Nothing definite is known of this Colarbasus or his supposed astrological heresy. The accounts given of him by Irenæus and Epiphanius describe him as holding tenets identical with those of Marcus. Hort, following Baur, believes that he never existed, and that his name is simply a Greek corruption of _Qol arba_, “the Voice of the Four.” See _D.C.B._, s.h.v.]
[Footnote 72: περὶ μαθηματικῶν. The article is omitted; but he must mean the students and not the study. This is curious, because Mathematicus in the Rome of Hippolytus must have meant astrologer and nothing else, and what follows has nothing to do with astrology. Rather is it what was called in the Renaissance Arithmomancy. Cruice refers us to Athanasius Kircher’s _Arithmologia_ on the subject. Cornelius Agrippa, _De vanitate et incertitudine Scientiarum_, writes of it as “The Pythagorean lot,” and it is described in Gaspar Peucer’s _De præcipuis Divinationum generibus_, 1604.]
[Footnote 73: ψῆφοι, lit., pebbles, _i. e._ counters.]
[Footnote 74: στοιχεῖα: letters as the component parts or elements of words.]
[Footnote 75: Reading with the text τινὰς for Cruice’s τινὰ.]
[Footnote 76: In the text the Kappa and Tau are written at full length, the other numbers in the usual Greek notation, a proof that the scribe was here writing from dictation and not copying MS.]
[Footnote 78: The name is spelt Πάτροκλος.]
[Footnote 79: So that the “root” may be either 7 or 6 according as you use the “rule of 9” or of 7. A _reductio ad absurdum_.]
[Footnote 80: ἐὰν ἀπαρτίσῃ, “is even or complete.”]
[Footnote 81: I omit the Rho, which in the Codex precedes the Alpha. Cruice suggests it is put for Π.]
[Footnote 82: They do not, but make 26. Cruice adds an Alpha between the 8 and the 3: but in any case the rule just enunciated is broken by the reckoning in of two 2’s.]