¹ Dillon, J., lsquo;A date for the death of Nicomachus of Gerasa?’, CRn.s. 19 (1969), 274–5, reprinted in J. Dillon, The Golden Chain,XV (Variorum, 1990).Google Scholar

² ‘He (Proclus) was convinced that he belonged to the Hermetic tradition and he believed according to a dream he once had that he possessed the soul of the Pythagorean philosopher j Nicomachus.’ ‘Life of Proclus’ by Marinus ch. 28 (translated by L. J. Rosan in his The Philosophy of Proclus,1949). In ch. 35 a horoscope for Proclus is given which dates his birth as February 18, 412. kGoogle Scholar

³ Text, V de Falco (Leipzig, 1922), translation by R. Waterfield, The Theology of Arithmetic f(Grand Rapids, MI, 1988).Google Scholar

⁴ Taran, L., ‘Nicomachus of Gerasa.’, Dictionary of Scientific Biography(1974), p. 113, n. 1.Google Scholar

⁵ Levin, F. R., Harmonics of Nicomachus and the Pythagorean Tradition(Pennsylvania, 1975)Google Scholar; McDermott, W. C., ‘Plotina Augusta and Nicomachus of Gerasa’, Historia26 (1977), 192–203.Google Scholar

⁶ Nicomachus of Gerasa, Introduction to Arithmetic,translated with introduction by M. L. D'Ooge et al.(New York, 1926).Google Scholar

⁷ Theologumena Arithmeticae,pp. 52–3, translation by R. Waterfield, The Theology of Arithmetic(Grand Rapids, MI, 1988).Google Scholar

⁸ See the Hippocratic or pseudo-Hippocratic works, Peri hebdomadon, Peri eptamenou,and Peri oktamenou.

⁹ Excerpta ex Nicomacho,p. 6, ‘For indeed the sounds of each sphere of the seven each sphere naturally producing one certain kind of sound are called vowels. They are ineffable in and of themselves but are recalled by the wise with respect to everything made up of them. Wherefore also here this sound has power which in arithmetic is a monad in geometry a point in grammar a letter. And combined with the material letters which are the consonants as the soul to the body and the musical scale to the strings—the one producing living beings the other pitch and melody—they accomplish active and mystic powers of divine beings. [Wherefore when especially the theurgists are worshipping such they invoke it symbolically with hissing sounds and clucking with inarticulate and foreign sounds]’ (extract translated by B. A. Pearson, passage in square brackets may be a gloss by the excerptor), and less explicitly in the Nicomachean section of the Theologumena Arithmeticaerespecting the number Seven. I

¹⁰ Robinson, J. M. (ed.), The Nag Hammadi Library in English(Leiden, 3rd edn, 1988).Google Scholar

¹¹ PGMIV, 675–834.Google Scholar

¹² Irenaeus, Adversus Haereses,ok. 1, ch. 14.

¹³ ‘But they themselves most of all impair the inviolate purity of the higher powers in another Iway too. For when they write magic chants intending to address them to those powers, not only to L the soul but to those above it as well, what are they doing except making the powers obey the word and follow the lead of people who say spells and charms and conjurations, any one of us i who is well skilled in the art of saying precisely the right things in the right way, songs and cries and aspirated and hissing sounds and everything else which their writings say has magic power in the higher world? But even if they do not want to say this how are the incorporeal beings affected by sounds?’ Plotinus, Enneads, 11.9.14, translated by A. H. Armstrong.;

¹⁴ See Bonner, C., Studies in Magical Amulets chiefly Graeco-Egyptian(Ann Arbor, 1950), ipp. 186–7. PGoogle Scholar

¹⁵ Dornseiff, F., Das Alphabet in Mystik und Magie(Leipzig, 2nd edn, 1925).Google Scholar