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Emendations of [Iamblichus], Theologoumena Arithmeticae (De Falco)

Published online by Cambridge University Press:  11 February 2009

R. A. H. Waterfield
R. A. H. Waterfield
Affiliation:
Teddington, Middlesex
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Extract

The reputation Theologoumena Arithmeticae has acquired is largely that of being an odd, and frequently opaque, compilation of arithmological lore. As a sourcebook for this aspect of the Pythagorean tradition it is, of course, invaluable. However, its poor reputation is increased, and its historical value lessened, by the depredations time has wrought on the text. ThA was never great prose: it is a compilation, largely from the lost Theologoumena Arithmeticae of Nicomachus of Gerasa and from Anatolius' Peri Dekados; and the text which cannot be safely or conjecturally assigned to these two sources often reads like little more than the written-up notes of some student. However, the treatise contains passages of considerable lucidity, within the context of its peculiar framework.

Type
Research Article
Information
The Classical Quarterly , Volume 38 , Issue 1 , January 1988 , pp. 215 - 227
Copyright
Copyright © The Classical Association 1988

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References

1 I am grateful to the anonymous referee, to Professor John Dillon, and to the Editors for help both general and particular.

2 By F. Ast (Leipzig, 1817) and V. de Falco (Leipzig, 1922; Teubner series). De Falco's edition gained extra notes by U. Klein in 1975. The only edition prior to Ast's was Wechel's, C.editio princeps (Paris, 1543)Google Scholar, which de Falco dismisses as ‘nullius pretii’. Ast's edition was based on theeditio princeps, but has the saving grace of a number of judicious emendations. De Falco, however, was the first to undertake a thorough collation of the manuscripts.

3 The bibliography is not extensive: the only substantial item to add to Klein's bibliography on pp. xviii–xxiii of the Teubner is Tarán, L., Speusippus of Athens (Leiden, 1981), 140–2, 257–98CrossRefGoogle Scholar.

4 Of course, the opacity of the subject matter means that in emending the text one has to beware of emendations which are suggested merely by one's own incomprehension.

5 Dodds, E. R., Classical Review 37 (1923), 138CrossRefGoogle Scholar; Oppermann, H., Gnomon 5 (1929), 545–58Google Scholar.

6 Oppermann (see previous note) contains the best analysis of the structure of ThA, as consisting of excerpts from various sources. Note, however, that Oppermann overlooks the excerptor's ὅτι at 71.13.

7 See also [Hippocrates, ], On the Nature of the Child 18Google Scholar.

8 On this image, see Heath, T. L., A History of Greek Mathematics (Oxford, 1921), i. 114Google Scholar; and D'Ooge, M. L., Robbins, F. E. and Karpinski, L. C., Nicomachus of Gerasa: Introduction to Arithmetic (Macmillan, 1926), p. 247Google Scholar.

9 Heteromecic numbers are oblong numbers whose sides differ by a factor of 1. These were the type of oblong numbers with which the Pythagoreans were most impressed, because any heteromecic number is the sum of two equal triangular numbers, and is also the sum of successive even numbers.

10 Loc. cit.

11 See e.g. Proclus, , Elements of Theology, Proposition 46Google Scholar: πἄν τφθειρομενον ποστν τς αυτο αἰτας φθερεται.

12 On the failure of this, as of all similar ancient and modern explanations of Theaetetus 147d, see Burnyeat, M. F., ‘The Philosophical Sense of Theaetetus' Mathematics’, Isis 69 (1978), 489–513CrossRefGoogle Scholar.

13 See e.g. Aphorisms 3.24: ‘In the progress of a disease, the fourth day in every seven-day period is significant.’

14 In our treatise, see 54.13–55.1 and 68.11–70.22. Otherwise see e.g. Theon of Smyrna 34.16ff. (Hiller), and Nicomachus, of Gerasa, Introduction to Arithmetic 2.20.5Google Scholar.

15 See e.g. Heath, T. L., Aristarchus of Samos (Oxford, 1913)Google Scholar, Lloyd, G. E. R., Greek Science After Aristotle (London, 1973)Google Scholar.

16 I have changed το at line 54.3 to τς, as de Falco himself suggested in his apparatus criticus.

17 I suspect that we should add κβων δ μνων δ' in 68.19.