Herodotus and Aristotle on Egyptian Geometry Author(s): J.

Gwyn Griffiths Reviewed work(s): Source: The Classical Review, New Series, Vol. 2, No. 1 (Mar., 1952), pp. 10-11 Published by: Cambridge University Press on behalf of The Classical Association Stable URL: http://www.jstor.org/stable/705264 . Accessed: 05/03/2012 11:59
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instances that go to show the viciousness of the in Graecorum gymnasiisnata It is true that there are passagesin which namappears to do little more than mark a transition, but always to offer such non-committal translations as 'Now .. .' or 'As for .. .' in instancesof the kind quoted above is to obscure the significance of the word.
University Cardif College,
s Cf. also Quint. x. I. 81-84 (the list of eloquent philosophers in which Theophrastus provides a further instance, 83 'namin Theophrasto .. .'), Petron. 38. 4 'nam mulam quidem nullam habet quae non ex onagro nata sit', in which namintroduces yet another example of Trimalchio's practice of importing in order to obtain the best. He imports rams from Tarentum in order to have the best sheep, bees from Athens in order to have the best honey, etc., and similarlyhe brings
. consuetudo)

G. H. POYSER
in wild asses, instead of breeding from domesticated ones, in order to have the best mules. E. V. Marmorale's comment, 'nam ha assai spesso in Petronio un significato assai tenue, che oscilla fra "inoltre" e "e"', appears to do this nam less than justice: so also that of Perrochat; 'nam sert souvent B introduire une autre idee, un autre fait, "quant a"; frequent avec cette valeur dans la Cena': Friedlander assumes an ellipse.

HERODOTUS AND ARISTOTLE ON GEOMETRY EGYPTIAN (C.R. lxiv. I2)

IN C.R. lxiv. 12 Mr. C. Macdonald has tried to reconcile two different Greek views about the rise of geometry in Egypt. Aristotle states that it was the leisure of the priestly class which enabled the science to develop, while Herodotus ascribes its origin to the practical needs of land mensuration. Mr. Macdonald rightly champions Herodotus as giving the true explanation, but he states, by way of reconciling the two accounts, that Herodotus found in the priests 'one of his main sources of information', and that 'the priests would have played no small part in land mensuration'. It is not likely that Herodotus had access to the important ranks of the priesthood. He claims to have conversed with priests in the temples of Memphis, Heliopolis, and Thebes (ii. 3). But as Wiedemann' points out, Herodotus does not distinguish between the various classes of priests, although several other Greek writers do. Spiegelberg2 has aptly drawn attention to the mention made by H. in ch. 28 of a ypaiLLaTrt7?)' Trovlpaov 7-r)S XP-rq7aaTwv q4AOvat7s7 ?di rdvAt-'a title', ,V in Egyptian will says Spiegelberg, 'which have been something like "scribe of the Herodots ZweitesBuch (Leipzig, 189o), 28. 2 The Credibilityof Herodotus'Account of Egypt (tr. Blackman: Oxford, 1927), 17.

treasury of the goddess Neith in Sais"'. Spiegelberg adds: 'Herodotus apparently mistook this person for a distinguished and learned gentleman, though in reality he was a humble accountant of the temple . . More important as sources of information were the Greek settlers in Egypt and the However, some of the lower-grade priests may well have been engaged in land mensuration, as Mr. Macdonald suggests. They would be concerned with the land belonging to the temples. That this land was considerable in extent in the Ramesside era has been shown by Sir Alan Gardiner in his monumental work on the Wilbour Papyrus, which reveals that the great temple of Karnak possessed land as far north as the vicinity of Heracleopolis in the reign of Ramesses III. The 'chief assessment-master' is several times referred to in the papyrus. Other land was dealt with by secular scribes. Aristotle's reference to the leisure of the priests may be compared with the statement 56 Kal yaO&G of Herodotus (ii. 37), radaXovUe OUKdAlya, KTrA.,where, as Waddell points out, the advantages enumerated arise from the possession of land. Many of the priests were scribes, of varying station, and a point often made in the Egyptian literature of the New Kingdom is that the office of scribe freed one from manual work. An ostracon now in Florence3 extols the scribe's office
3 See Erman (tr. Blackman), The Literature of the AncientEgyptians (London, 1927), 193-

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thus: 'Put writing in thy heart, that thou mayest protect thyself from hard labour of any kind ... .' Cf. P. Anastasi ii. 6. 7 ff.(= Gardiner, Late-Egyptian Miscellanies, x6): 'Become a scribe. He is saved from labour and protected from all toil.' It is clear, at the same time, that the royal scribes were mainly in charge of the less menial work of measuring the land and assessing its taxable value, and that practical needs called for the aid of geometry. Nor were these needs confined to land mensuration. The Rhind Papyrus' shows that geometry was used also in techniques like pyramid-building, where angles had to be calculated.

CICERO,

DE FINIBUS

iii. 76

THE third book of Cicero's de Finibus ends

with an eloquent panegyric on the Stoic wise man. The last sentence of the panegyric and of the book is this: 'quod si ita est ut neque quisquam nisi bonus uir et omnes boni beati sint, quid philosophia magis colendum aut quid est uirtute diuinius ?' This is no model of elegance: the conditional clause is awkwardly phrased, and the first half of the conclusion only follows if we reflect that no one is good who is not also wise. In a carefully written passage such as this Cicero would surely have attained J. GWYN GRIFFITHS clarity and concinnity. This may be achieved by inserting one word, that will make the College,Swansea University sentence a proper conclusion to the praises of the wise man: 'quod si ita est ut neque quisquam nisi <sapiens) bonus uir et omnes boni beati iii. 962 LUCRETIUS sint, quid philosophia magis colendum aut quid est uirtute diuinius?' IN C.R. lxii. 62 Dr. W. R. Inge writes conof this kind can be paralleled. Expressions cerning the famous crux aequo animoque Acad. Prior. ii. I44 'scire negatis quemquam agedummagnis concede:necessest.He inquires rem ullam nisi sapientem'; ibid. '(scientiae) whether anyone has suggested humanis.This compotem nisi sapientem esse neminem'; De it with the was Munro's first love; he printed Diu. ii. 129 'negant quemquam nisi sapienmeagre comment 'scripsi' in the edition of tem diuinum esse posse'; De Am. 18 'negant Lucretius which he prepared in i 86o for the enim quemquam uirum bonum esse nisi Latin and Texts series. Greek Cambridge Later he abandoned it in favour of Bernays's sapientem'; Seneca, Ep. mor.8i. 1o 'negamus quemquam scire gratiam referre nisi gnatis, and it has been allowed to slide into oblivion. sapientem'. F. H. SANDBACH We should be grateful to Dr. Inge for Trinity College,Cambridge The excellent emendation. this recalling obvious parallel is at iv. I 191 praetermittere et humanisconcedere rebus,which conveys the same idea of acceptance of human limitaPETRONIUS 44. 5 tions. This parallel (and Dr. Inge's likewise) sicilia et larvas sic istos interiorest t'similia leaves us to face the rarity of the neuter ut illis Iuppiter iratus esset.' adjective employed alone where its form is percolopabant at times the equivalent indistinguishable. But we recall Lucretius' THE adjective interior, fondness for slight variations and his unof sinister(in the left-hand turn at the end of the race-course: e.g. Ovid, Am. iii. 2. 12 grammatical trick of confusing the neuter nuncstringammetasinteriore adjective with the use of res (see especially rota, and A.A. ii. Bailey's note on i. 19o). And, of course, 426 interiorcurrumeta tirendameo est), is also humanis concedewould not be entirely unapplicable to the contestant who rounds the exampled: is it fanciful to regard tu ne cede meta as closely as possible, thereby 'cuttingmalis as, in some sense, the Stoic rejoinder? out' his rivals by taking the inside position on the extreme left. Such was Cloanthus' A. D. FrrrONBROWN manoeuvre in the boat-race as described by Virgil: 'ille inter navemque Gyae scopuUniversity Collegeof North Wales, Bangor losque sonantes I radit iter laevum interior, subitoque priorem I praeterit et metis tenet 1 Science in Cf. Farrington, Antiquity2 aequora tuta relictis' (Aen. v. 169-71: cf. (Oxford, 1947), 19. For other practical 202-3).2 The adaptation of this to a problems discussed by Egyptian mathe2 In his note on 162 Henry compares maticians see R. W. Sloley in The Legacyof Manil. v. 82, and says 'encountering the Egypt (Oxford, 1942), 173 ff.