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MEASURING UP: THE GREEK ANALOGIES BEHIND VITRUVIUS' GEOMETRY OF THE BODY

Published online by Cambridge University Press:  27 May 2024

Daniel Anderson*
Affiliation:
Coventry University ac8883@coventry.ac.uk
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Extract

Vitruvius’ book is chock full of bodies. It is by means of his oiled body that Dinocrates gains an audience with Alexander (2.praef.1), and by means of his naked one, and the equivalent body of water that it displaces, that Archimedes solves his well-known quandary (9.praef.9f.). The body is a living, vital thing (7.praef.2f.), even as it is a book, a body of work (7.praef.10), arising from a body of education (1.1.12). Most important of all, Vitruvius outlines a ‘body of architecture’ (corpus architecturae, 6.praef.7) to propagate and extend the reach of the deified Augustus, commander-in-chief (1.praef.1), and this idea arguably gives rise to that of the ‘body politic’ (corpus imperii). Vitruvius’ text has been interpreted in terms of these bodies in important studies by Indra Kagis McEwen and John Oksanish; both authors treat the body as replete with meaning, the site of contact between architecture and the political, between text and author. This chapter adds to our understanding of the repertoire of bodies in Vitruvius by looking at those earlier incarnations of circular and square bodies which Vitruvius inherits, and in terms of which he construes the human body as a site of ideal proportions.

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Research Article
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Copyright © The Author(s), 2024. Published by Cambridge University Press

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References

1. See Tom Geue in this special issue.

2. Cf. McEwen (2003), 10f.

3. McEwen (2003) and John Oksanish (2019).

4. This distinction between Foucault and his predecessors loosely follows Koopman (2013), ch. 2, although Koopman's dissociation of Foucault's genealogies from normative positioning may ultimately be problematic (May [2014], 423–6). Some critics have similarly attempted to save Nietzschean genealogy from the birdlime of the genetic fallacy (Guess [1994], 285–8; Kail [2011]). Foucault linked his own genealogical approach to that of Nietzsche (Foucault [1971], cf. Bernasconi [2017], 157–60, 173f.), and while the ‘genealogy of genealogy’ can and has been traced through various other figures, from Boulainvilliers (Levy [1998]) to Overbeck (Sommer [2003], 100f.), or at a more fundamental level, d'Alembert and Diderot in the Encyclopédie (Hellström [2019], 228–36), Rousseau is arguably the next most important predecessor for the specific Nietzschean manoeuvre (Neuhouser [2012], comparing also Fichte, Feuerbach, Hegel, Marx, and Heidegger at p.372). Bernard Williams (2002), ch. 2, differs in his use of genealogy to affirm a position.

5. As per LSJ s.v. fenestro II.

6. On this image, see especially Rigoni (1974) and Laterza (2018).

7. haec non ita sed uti natura rerum uoluit sunt constituta (‘things are not constituted in this way, but rather how nature intends’, 3.praef.1).

8. Rigoni (1974), 452f., drawing on a note in the edition of Ferri (1960), 160f., has suggested that Vitruvius is in fact misremembering Alcibiades’ comparison of Socrates to a type of carved wooden receptacle like a matryoshka doll, commonly found in the herm-makers’ shops, depicting the ugly Silenus on the outside, opened in two to reveal the image of a god within (Pl. Symp. 215b). Rigoni's main argument is that Vitruvius’ interpretation of the image of the window onto the heart matches Alcibiades’ of the wooden Silenus figurine, namely that wisdom is not perceptible in the exterior form or appearance of a person.

9. Eustathius (ad Od. 7.125) relates the image to the Aesopan version. Laterza (2018), 194, notes the presence of the image of an open breast in an Attic scolion: εἶθ’ ἐξῆν ὁποῖος τις ἦν ἕκαστος | τὸ στῆθος διελόντ’, ἔπειτα τὸν νοῦν | ἐσιδόντα, κελείσαντα πάλιν, | ἄνδρα φίλον νομίζειν ἀδόλῳ φρενί (‘If only it were possible [to learn] what each person is like by opening his breast, then peering at his mind, and closing it back up again, so as to to recognize a man as a friend by means of his authentic heart’, Athen. 15.694e). While this suggests the specific image of the open chest is earlier than Babrius, the image lacks the specifically architectural reference to a window found in Vitruvius.

10. τοῦ δέ γ’ ἀνθρώπου, | μὴ σχεῖν θυρωτὰ μηδ’ ἀνοικτὰ τὰ στήθη (Babrius 59.10–12 Perry).

11. Plut. Quaest. conv. 3.1, 645a–c; Luc. Herm. 20, cf. Rigoni (1974), 448–52.

12. Also noted by Laterza (2018), 195, ‘nella rivisitazione di Vitruvio si configura come uno spazio costruito tecnicamente e architettonicamente’.

13. Cf. Vesely (2002), 36.

14. Riggsby (2016), 296, ‘In one sense, a Doric temple could really be the product of dimensionless proportionality. A souvenir model of the Parthenon could follow the proportions of the real one exactly. But that would be a toy, not a temple. The difference is that while columns, capitals, and triglyphs can all scale together, there is a mostly unspoken element that fixes the rest fairly narrowly: the human users of the structure. Most of them are around the same size and interact with it in broadly similar ways.’ See also Oksanish (2019), 96f.

15. This notion of assemblage, or better agencement, is taken from Deleuze and Guattari's Mille Plateaux; see Nail (2017).

16. The sculptural basis of the whole passage is standard fare in the scholarship, e.g. Steuben (1973), 68–71; Berger (1990), 162f.

17. … καθάπερ ἐν τῷ Πολυκλείτου Κανόνι γέγραπται. πάσας γὰρ ἐκδιδάξας ἡμᾶς ἐν ἐκείνῳ τῷ συγγράμματι τὰς συμμετρίας τοῦ σώματος ὁ Πολύκλειτος ἔργῳ τὸν λόγον ἐβεβαίωσε δημιουργήσας ἀνδριάντα κατὰ τὰ τοῦ λόγου προστάγματα καὶ καλέσας δὴ καὶ αὐτὸν τὸν ἀνδριάντα καθάπερ καὶ τὸ σύγγραμμα Κανόνα (‘… just as in the Canon written by Polykleitos. For having elaborated all the proportions of the body for us in this book, Polykleitos confirmed his account in a work, by fashioning a sculpture according to the prescriptions of his theory, and calling the sculpture itself Canon just like his book’, Galen, De placitis Hippocratis et Platonis 5.3.16 de Lacy = 5.448 Kühn). The equivalence of this sculpture with the Doryphoros is suggested by Pliny's description of it, once Jahn's supplement is adopted: Polyclitus … et doryphorum uiriliter puerum fecit [et] quem canona artifices uocant liniamenta artis ex eo petentes ueluti a lege quadam (‘Polykleitos … also made the Doryphoros, a virile-looking boy, which artists [also] called the “Canon”, since they draw the outlines of their art from it as if from a rule’, HN 34.55). Recent work using 3D laser modelling of extant copies of the Doryphoros and related sculptures by Polykleitos and others suggests that the Doryphoros was in fact used as a model for other sculptures (Sengoku-Haga et al. [2017] with further references). Our limited ancient references of the content of Polykleitos’ treatise are usefully collected and translated by Stewart (1978), 124f.

18. Modularity of the Vitruvian proportional body is similarly reflected in Vitruvius’ definition of ‘proportion’ as ‘the correspondence of a measured share of the parts in the whole work, and of the whole’ (proportio est ratae partis membrorum in omni opere totiusque commodulatio, 3.1.1), cf. Neumeister (1990), 433.

19. Tobin (1975).

20. This idea is already reflected in Plin. HN 34.55 (immediately following the quotation in n.17): solusque hominum artem ipsam fecisse artis opere iudicatur (‘He [Polykleitos] was the only man to have formally critiqued an artwork he himself had made, using a work of art’). The position of Borbein (2019), 32, reaffirmed by Papadopoulos (2019), 61 in the same volume, namely that the Canon referred only to the treatise and not to the sculpture, fails to convince; the word ‘measuring-rule’ was certainly already part of the semantic field of sculpture in the fifth century (or it would not have been used of the treatise), and the view that Galen's unambiguous testimony is too late to matter is excessively sceptical; more generally, it is circular to suggest that innovations do not occur because they are not regular occurrences.

21. καὶ πού τις ἀνδριὰς ἐπαινεῖται Πολυκλείτου Κανών ὀνομαζόμενος, ἐκ τοῦ πάντων τῶν μορίων ἀκριβῆ τὴν πρὸς ἄλληλα συμμετρίαν ἔχειν ὀνόματος τοιούτου τυχών (‘There is a highly regarded statue by Polykleitos called the Canon, which has this name because of the precision with which all of its parts are in proportion to the others’, Galen, De temperamentis 1.566 Kühn).

22. Another important (and related) connection is to the conceit of the city of Rome as ‘squared’ but also ‘perfected’ and ‘sanctified’ (quadrata), on which see McEwen (2003), 162–7, with earlier references. The ‘squaring’ in question here may be that of a circle divided into four quadrants via two intersecting lines, rather than enclosure in a square (Szabó [1938] and [1956]).

23. quadrata tamen esse ea ait Varro et paene ad exemplum (‘However Varro called them [sc. Polykleitos’ sculptures] square and almost copied from a blueprint’, Plin. HN 34.55f). See discussion in Steuben (1973), 35f., 55f.; Pollitt (1974), 267; Hurwit (1995), 12; Steiner (2003), 42f.; McEwen (2003), 268f.

24. Scholarship on the fragments to this poem is extensive; key bibliography is found in Budelmann (2018), 216f.

25. e.g., Archil. fr. 114, cf. Steiner (2003), 42. That τετράγωνον has a strong positive moral connotation is clear from its appearance in the Pythagorean table of opposites alongside other positively connotative terms (Arist. Met. Α.5.986a22–6). The elements listed together on each side of this table were regularly associated in early Greek thought, for which see Lloyd (1966), 48–65.

26. Prt. 311c–d, 328c–d, cf. Onians (1999), 41.

27. ἡ τετράγωνος ἐργασία (‘they [sc. herms] are square in construction’, Thuc. 6.27.1).

28. This dichotomy is by no means absolute, and indeed the more convincing examples of the latter approach suggest that a primary metaphor drawn from sculpture refers to the embodiment of Pythagorean ideas, for example Fraenkel (1973) [orig. 1962], 307–11; Svenbro (1976), 144–61; Steiner (2003), 43. Among these authors, Svenbro (1976), 156, notably understands τετράγωνος in reference to Archaic kouroi.

29. Johnston and Mulroy (2004).

30. See n.27 above.

31. Ps.-Pl. Hipp. 228–9b, cf., e.g., Quinn (2007), 93–5.

32. For the use of unadorned stelae in cult worship, see Gaifman (2012), 181–241; for the use of stelae as grave-markers, see Sourvinou-Inwood (1995), 108–40.

33. For individual characteristics in early herms (hair and facial expressions), which suggest they may be representative of specific individuals, see Quinn (2007), 96.

34. I thank Megan Goldman-Petri for bringing these sculptures to my attention.

35. This section has been strongly influenced by David Sedley's valedictory lecture ‘Godlikeness’, delivered on 30 May 2014 at the Faculty of Classics in Cambridge, cf. Sedley (1997) and Sedley (1999). The roundness of perfected bodies among the pre-Socratics is also surveyed in Guthrie (1975), 47, cf. Ballew (1974), 189.

36. σφαιροειδὴς γὰρ ὁ κόσμος (‘the cosmos is spherical’, SVF 2.1009); solisque orbem lunaeque rotundum (‘the disk of both sun and moon is circular’, Manil. 1.208); cf. McEwen (2003), 160–2.

37. On Manilius’ rounded cosmos, see Henderson (2011).

38. ξυνὸν γὰρ ἀρχὴ καὶ πέρας ἐπὶ κύκλου περιφερείας (‘beginning and end are the same at the perimeter of a circle’, Heracl. DK 22B103 = D54 Laks-Most). This is also the basis for the association of circularity with the eternal (Manil. 1.211); since change always has a beginning, locomotion in a circle escapes generation itself (Arist. Cael. 1.3 and 4).

39. φησὶ δέ … οὐσίαν θεοῦ σφαιροειδῆ, μηδὲν ὅμοιον ἔχουσαν ἀνθρώπῳ (‘He [sc. Xenophanes] said that the nature of divinity was spherical, and not like that of a human being’, Diog. 9.19 = Xenoph. DK 21A1).

40. Guthrie (1975), 383, notes the Empedoclean origin in the description of androgynous beings at an early stage of development under the influence of Love (Emped. DK 31B61). These beings have ‘double faces’ (ἀμφιπρόσωπα, Emped. DK 31B61.1 ~ πρόσωπα δύ[ο], Pl. Symp. 189e).

41. Note how reference to humans as κόσμιοι (‘orderly’) in this passage (e.g., Symp. 193a) may also recall their descent from heavenly bodies, where κόσμος means ‘universe’.

42. Gros (1990), 66; Howe in Rowland, Howe, and Dewar (1999), 189; Gros (2001).

43. For a description of the concept of a body without organs, see Smith (2018).

44. Faraone (2018), 132–6, esp. 134 with references in the notes at 351.