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Published online by Cambridge University Press: 11 February 2009
In an interesting passage in the Philebus (51c, cf. 56b–c, an enlarged and slightly modified list), Plato associates pure beauty with geometrical forms created by certain measuring tools used both by mathematicians and carpenters. The ‘beauty of figures’ is analysed as' something straight [εὐθ⋯ τι]… and round [περιφερ⋯ς] and the two- and three-dimensional figures (sc. σχ⋯7mu;ατα) generated from these by [τ⋯ρνοι] and ruler [καν⋯σ7iota;] and set-squares [γων⋯αι]' He continues: ‘For I maintain that these things are not beautiful in relation to something, as other things are, but they are always beautiful by nature, by themselves…’
1 (51b-d) ΣΩ. π⋯νε μ⋯ν οὖν οὐθĐς δ⋯λ⋯ ⋯στιν ἃ λ⋯λω πειρατ⋯ον μ⋯ν δηλο⋯ν. σχημ⋯των τε γ⋯ κ⋯λλος οὐχ ⋯περ ἄν ὑπολ⋯βοιεν οἱ πολλο⋯ πειρ⋯μαι ν⋯ν λ⋯γειν, ἣ ζῴων ἥ τινων ζωγραφημ⋯των, ⋯λλ εὐθ⋯ τι λ⋯γω, φησ⋯ν ⋯ λ⋯γος καἰ περιφε⋯ς κα⋯ ⋯π⋯ το⋯των δ⋯ τ⋯ τε τοῖς τ⋯ρνοις γιγν⋯μενα ⋯π⋯πεδ⋯ τε κα⋯ στερε⋯ κα⋯ τ⋯ τοῖς καν⋯σι καἰ γων⋯7alpha;ις, εἵ μοε μανθ⋯νεις. τα⋯7tau;α γ⋯ρ οὐ7kappa; εἷναι πρ⋯ς τι καλ⋯ λ⋯γω, κα7theta;⋯περ ἅλλα, ⋯λλ' καλ⋯ καθ αὑτ⋯ πεφε7kappa;⋯ναι κα⋯ τινας ⋯δον⋯ς οἰ7kappa;ε⋯7alpha;ς ἓχε7iota;ν, οὐδ⋯ν ταῖς των κν⋯σεων προσφερεῖς καἰ χρώματα δ⋯ το⋯τον
(56b-c) ΣΩ. Tεκτονικ⋯ν δ⋯ γε οἷμαι πλἰστοις μ⋯τρις τε κα⋯ ⋯γ⋯νοις ρρωμ⋯νην τ⋯ πολλ⋯ν ⋯7kappa;ρ⋯βειαν αὐ7tau;⋯ πορ⋯ζοντα τεχνικωτ⋯ρακ τ⋯ν πολλ⋯ν ⋯πιστη;μ⋯ν παρ⋯χεται.
πPΩ. Пῇ:
ΣΩ. Kατ⋯ τε ναεπηγ⋯αν κα⋯ κατ οἰκοδομ⋯7alpha;ν κα⋯ ⋯ν πολλοις τ⋯ς ξελοεργικ⋯ς. καν⋯νι γ⋯ρ οἷμαι κα⋯ τ⋯ρνῳ χρ⋯τα7iota κα⋯ διαβ⋯τῇ κα⋯ στ⋯θμῃ κα⋯ τινι προσαγωγε⋯ῳ κεκομψεεμ⋯νῳ.
1 This follows Hesychius who defines τ⋯ρνος as ⋯ργαλεῖ ον τεκνονικ⋯ν, ᾧ τ⋯ στρογγ⋯λα σχ⋯ματα περιγρ⋯φεται.
3 A related word, νορνε⋯ω is found five times in Plato, and it has some of the same ambiguity of meaning. It translates comfortably as ‘make round’, ‘round off’ (see Critias 113d8), though it can specifically refer to lathe-working, e.g.Theages 1246.2.Epist. VII, 342c,2, probably refers to rounding by compasses.
4 A partial list: Jowett, B., The Dialogues of Plato (Oxford, 1871)Google Scholar; Burges, G., The Works of Plato (London, 1848–1854)Google Scholar; Fowler, H., Plato, Philebus (London, 1925)Google Scholar; Hackforth, R., Plato's Examination of Pleasure: A Translation of the Philebus (Cambridge, 1945)Google Scholar, though, inconsistently, in 56b–c, he translates τ⋯ρνος as ‘peg and cord’ Taylor, A. E., Philebus and Epinomis (Folkestone/London, 1956)Google Scholar; Gosling, J., Philebus, translation with notes and commentary (Oxford, 1975)Google Scholar -like Hackforth, he changes the lathe to compasses in 56b-c; Waterfield, R., Philebus (London, 1982)Google Scholar. All ad loc. Dodds, E. R. also accepts this translation, in Euripides, Bacchae 2 (Oxford, 1960), p. 210Google Scholar.
5 Bury, R., The Philebus of Plato (New York, 1897)Google Scholar; Yates, J. and Flather, J., ‘Circinus’, in Smith, W., A Dictionary of Greek and Roman Antiquities 3 (London, 1890), i. 429–30Google Scholar; Badham, C., The Philebus of Plato, with introduction and notes (Oxford, 1860), 90Google Scholar(in a note confused by a mistranslation of γων⋯αι7sigmav; Stallbaum, G., Platonis Philebus rec, proleg. et commun. illustr. (Leipzig, 1820), p. 295Google Scholar. These usually quote Hesychius and give little more by way of argument.
6 Perhaps it should be noted that English usage does not distinguish between the singular and plural of this word. The διαβ⋯της could also be used to measure uniform lengths, widths (like dividers and callipers), and angles.
7 Though this rare word (modified by κεκομψε7upsiv;μ⋯νῳ ‘ingenious’; or ‘sophisticated’, which suggests its unusual or ad hoc nature) has been subjected to varied interpretation in the scholiastic and lexicographic traditions, Waterfield (ad loc.,ne,) correctly notes that a second century Boeotian inscription (/G 7.3073.118, 139) shows clearly that προσαγωγεῖον there denotes a try-square. The tradition in late antiquity is somewhat bizarre, describing this tool as a kind of vice to straighten bent wood - see scholia, in Hermann, C. F., Platonis Dialogi (Leipzig, 1870–1880), vi. 255Google Scholarad loc.: τε7kappa;τονικ⋯ν ⋯στιν ὃργανον, ὃ πρ^ogr;σ⋯γοντες εὐνοεσι τ⋯ στρεβλ⋯ ξ⋯λα, borrowing, or borrowed by, Suidas, followed by Ast, D. F., Lexicon Platonicum (Leipzig, 1836), iii. 190Google Scholar. Why or how successfully one might straighten out bent wood is not at all adumbrated. Even without the inscription as evidence, Badham, op. cit.,ad loc., followed by Bury, rejects this, and suggests that the πνοσαγωγεῖον is ‘an instrument for taking the angles of curves’, i.e. the calliper. The inscription, though, suggests that this instrument was used to bring stones together at right angles: εὐγων⋯οες πρ⋯ προσαγωεῖον, 118: ‘with angles regular according to the square’, cf.IG 2(2).1666 A64. In line 139 we have, καθ ἓκαστον τ⋯ν λ⋯θων ⋯ν ⋯ρθῷ πρ⋯ς τ⋯ προσα[γωγεῖον], ‘by each of the stones in uprightness according to the square’
F. Paley's interpretation is puzzling: a ‘contrivance for applying the plummet’ (quoted in Bury ad loc). Neither Plato nor the inscription suggest the plumb line, though the plumb bob can be combined with the square.
English translations reflect the confusion in late antiquity: ‘square’: Hackforth, Gosling, Waterfield; ‘calliper’: Taylor (but with ‘screw’ as an alternative possibility!), cf. Gosling n. ad loc; ‘vice’: Fowler, Jowett (‘machine for straightening wood’); ‘rule with plumb bob’: Burges.
My anonymous referee writes, plausibly, that τινι προσαγω7gama;ε⋯ῳ ‘suggests prima facie that there are various kinds of προσαγωεια (presumably devices “applied” for checking accuracy, alignment, etc.)...One thinks of “formers” devised for a particular purpose, e.g. for the profile of a moulding.’
8 Literally, ‘straighter’, but here in a metaphorical, ethical sense: ‘more exactly true’, ‘more perfect’, ‘more honest’. If this were not meant metaphorically, ‘straighter than a peg and line’ would be nonsense. Whether τ⋯ρνος is compasses or lathe, it is always involved with circles -see the standard etymological dictionaries, Chantraine, P., Diclionnaire Étymologique de la langue Grecque 4 (Heidelberg, 1950), s.v.Google Scholar; Frisk, H., Griechisches Etymologisches Wörterbuch (Heidelberg, 1961), s.vGoogle Scholar.
9 Cf. Yates, and Flather, , op. cit., p. 430Google Scholar.
10 Willink, C. W., ‘Some Problems of Text and Interpretation in Bacchae. II’, CQ 60 (1966), 220–42, pp. 237–40CrossRefGoogle Scholar.
11 Willink, , art. cit., p. 237Google Scholar.
12 Roux, Jeanne, Euripide, Us Bacchantes (Paris, 1970–1972), ii. 573Google Scholar.
13 Willink, , art. cit., p. 237Google Scholar.
14 Cf. the figurative sense of words related to the carpenter's instruments that draw a straight line, i.e. rule, canon. ‘Normal’ of course derives from norma, the Roman carpenter's square.
15 This is the definition given by the perspicacious Powell, J. E. in A Lexicon to Herodotus (Hildesheim, 1977), p. 359Google Scholar.
16 Cf. Tyrrell, , op. cit., p. 128Google Scholar. Herodotus ‘is thinking of a plane surface accurately measured out by an instrument.’ Once again, we have a measuring instrument.
17 For Euripides, , cf. also τορνε7upsiv; in H.F. 978Google Scholar.
18 κεκλο⋯το δ, ὣστε τ⋯ξον ἥ κερτ⋯ς τροχ⋯ς
τ⋯ρνωι γραφ⋯ορ⋯ν
1066 κεκλο⋯7tau;αι P 1067 περιφορ⋯ν P
19 Dodds, , op. cit., pp. 210–11Google Scholar, argues for the received text, against Willink and a number of other scholars, e.g. Robertson, E. S., ‘Notes on the Bacchae of Euripides’, Hermathena 3 (1879), 387–93Google Scholar; Tyrrell, R. Y., The Bacchae of Euripides (London, 1928), pp. 129–31Google Scholar (though cf. a convincing argument for the compass, p. 128); Palmer, L. R., ‘Mortar and Lathe’, Eranos 44 (1946), 54–61Google Scholar; Campbell, A. Y., ‘Notes on Euripides' Bacchae’, CQ 49 (1956), 56–67, pp. 64–6CrossRefGoogle Scholar; Willink, C. W., art. cit. pp. 237–40Google Scholar; Roux, , op. cit., i. 189Google Scholar; ii. 569–74.
20 Not surprisingly, γραφ⋯μενος) has been a favoured target for emendation - e.g. Palmer (γλαφ⋯μενος) Campbell (στρφ⋯μενον); Roux ταν⋯μενος).
21 Roux, op. cit., writes that the ‘lathe’ interpreters ‘ont contribué à éclairer le sens genéral de la comparaison, mais sans parvenir à résoudre les difficultés que soulèvent dans le dètail l'établissement du texte, sa construction et sa traduction’, 569. One of the Bacchae's recent editors states flatly, of this passage, ‘hos versiculos non intelligo, atque minime mihi placet iste tornus’ Kopff, E. C., ed., Euripides, Bacchae (Leipzig, 1982), p. 41Google Scholar.
22 Plato, of course, was much more interested in geometry than technology. Cf. Mittelstrass, J., ‘Die geometrischen Wurzeln der Platonischen Ideenlehre’, Gymnasium 92 (1985), 399–418Google Scholar. For the ideal beauty of the circle and sphere in Plato's thought, see Tim. 33b; Leg. 897d-e;Symp. 190-1 (the original male-female unity is circular);Rep. 616b-c; cf. Ballew, L., Straight and Circular (Assen, 1979), pp. 45, 86–7, 114Google Scholar; Jameson, C. J., ‘Well-rounded Truth and Circular Thought in Parmenides’, Phron. 4 (1958), 15–30CrossRefGoogle Scholar.