¹ Published by Harvard University Press, 1914; reprint by Dover, New York, 1960.

De architectura vii. praef. 11: namque primum Agatharchus Athenis Aeschylo docente tragoediam scaenam fecit et de ea commentarium reliquit. ex eo moniti Democritus et Anaxagoras de eadem re scripserunt, quemadmodum oporteat, ad aciem oculorum radiorumque extentionem certo loco centra constituto, ad lineas ratione naturali respondere, uti de incerta re certae imagines aedificiorum in scaenarum picturis redderent speciem et, quae in directis planisque frontibus sint figurata, alia abscedentia, alia prominentia esse uideantur.

For variant manuscript traditions, see Pollitt, J.J., The Ancient View of Greek Art (London 1974) 240–42.Google Scholar

² ‘Agatharchos’, JHS 40 (1920) 180–89.CrossRefGoogle Scholar

³ See (n.1) 242. Vitruvius could be referring to the premiere of Aeschylus' Oresteia trilogy in Athens, 458 BC, but the phrasing is equivocal and could mean simply ‘when plays by Aeschylus were staged’.

⁴ Posch, W., Antike Kunst 37 (1994) 21–30Google Scholar, rejects the notion of systematic perspective in the fifth century BC and reads the above text to mean that Agatharchus built a stage, not that he decorated one. Posch's distinction between scaena and scaenographia seems factitious in the context of Vitruvius' seventh book. Wright, L., Perspective on Perspective (London 1983) 35Google ScholarPubMed, questions any knowledge of methodical geometric construction for this period. C. Hobey-Hansher's article on Agatharchus in the Macmillan/Grove Dictionary of Art (1996) assumes that the artist's decorations used numerous unrelated points of view for individual objects and parts of objects.

⁵ The title of a lost treatise, Aktinographia, ‘The drawing of rays’, seems relevant to our subject.

⁶ Mainly by virtue of White's, John scrutiny in Perspective in Ancient Drawing and Painting (London 1956)Google Scholar, and The Birth and Rebirth of Pictorial Space² (Boston 1967)Google Scholar.

Pollitt, J.J., The Art of Ancient Greece (New Haven 1965)Google Scholar, called the passage on Agatharchus ‘probably the most obscure and problematical of all the ancient texts on art’, but later, in The Ancient View (n.1), he accepted White's arguments regarding Vitruvius' use of responsus (respondere) for ‘convergence’ and White's reading of circinique centrum (Vitruvius i 2.2) as the vanishing point: ‘Hence, when Vitruvius says that “the lines correspond by a natural law” to “the sight of the eyes and the extension of the rays”, he means that drawn lines converging on a central vanishing point in a painting are analogous to the rays of vision which converge at the apex of the Euclidian visual cone’ (241).

⁷ See Birth and Rebirth (n.6) 257-58.

⁸ See Birth and Rebirth (n.6) 261; (n.l) 244.

⁹ According to Euclid's Optics, items that are perpendicular to the viewer seem to slant toward the left if they are on the viewer's right-hand side, and vice versa (theorem 12). Correspondingly, perpendiculars above eye-height seem to slant downwards and those above appear to slant upwards (theorem 13). These theorems do not describe the perpendiculars as parallel, but the fact that they are treated separately, right from left, horizontal from vertical, seems to imply that Euclid had four sets of non-converging lines in mind.

¹⁰ To paraphrase John White (on the murals of the House of the Labyrinth). See Birth and Rebirth (n.6) 261.

¹¹ It seems significant that an early Apulian vase, dated to the first decade of the fourth century, shows a temple in which the orthogonal ceiling boards clash disruptively with the lintels at both sides of the building. Apparently, techniques for mediating this disagreement were as yet undeveloped. Trendall, A.D. and Cambitoglou, A., The Red-figured Vases of Apulia (Oxford 1978) pl. 12.Google Scholar

¹² See (n.1) 242 f.

¹³ Trendall, A.D., Red Figure Vases of South Italy and Sicily (London 1989) 27Google Scholar.

¹⁴ First identified by Panofsky, E., Perspective as Symbolic Form, translated by Wood, C.S. (New York 1991) pl. 2Google Scholar. For another example see Trendall, A.D. and Cambitoglou, A., First Supplement to the Redfigured Vases of Apulia (London 1983) pl. 37.Google Scholar

¹⁵ See (n. 13) pl. 355.

¹⁶ Probably that of king Pelias. Though the play may be lost, the extant fragments suggest a scene in which the daughters of Pelias are eavesdropping on his conversation with Jason. See Pickard-Cambridge, A.W., The Theatre of Dionysus in Athens (Oxford 1973 ²) 170Google Scholar; Simon, E., The Ancient Theatre (London, 1982) 24.Google Scholar

¹⁷ This solution was sound, but the mathematical proof eluded Renaissance theorists. Cf. (n.6) 122; Elkins, J., The Poetics of Perspective (Ithaca 1994)Google Scholar. Beyen, H.G., Die pompejanische Wanddekoration (The Hague 1938) i 159CrossRefGoogle Scholar, recognized in the Würzburg fragment an early use of diagonals predating examples at Pompeii.

¹⁸ Richter, G.M.A., Perspective in Greek and Roman Art (London 1970) 3Google Scholar, presumed that even the murals of the Room of the masks ‘could have been produced by a careful observer’ without a geometric model. This ‘careful observer’ is, of course, purely fictitious.

¹⁹ We may still trace this disposition in Roman-Campanian murals (e.g. the stage designs of the Room of the masks) where the top and middle registers of paintings are in perfect agreement with a single vanishing point, while the bases invariably are off. Krause, C., ‘Skenographie, Architektur und perspektivisches Sehen’, La prospettiva pittorica, Krause, C., ed. (Rome 1985) 45–77.Google Scholar

²⁰ J.Six (n.2) 186; Walton, J.M., The Greek Sense of Theatre (London 1984) 50Google Scholar; A.W. Pickard-Cambridge (n.16) 122; Allen, J.T., The Greek Theater of the Fifth Century (New York 1966) 67Google Scholar. Most scenes in Greek tragedies are set in front of a palace or a temple.

²¹ See (n.14) 38. Panofsky presents a scheme for spherical projection that matches the ‘fishbone’ perspective (what I call ‘parallel obliques’), but he admits that it remains conjectural.

²² Knorr, W.R., ‘On the principle of linear perspective in Euclid's Optics’, Centaurus 34, 3 (1991) 193–210CrossRefGoogle Scholar, refutes efforts to find applied projection in Euclid (sc. his tenth theorem), but recognizes evidence of an alternative tradition in the writings of Pappus of Alexandria. Knorr concludes: ‘to whatever extent such techniques (sc. projective distension, vanishing point, etc.) arose among the ancients, they were only partial and dispersed among different fields (e.g. optics proper, scenography, etc.) and never integrated into a comprehensive system’.

²³ To judge from comparable scenes, the plinth is circular. However, my line of argument remains the same if a square base is presumed.

²⁴ Vitruvius i 2.2. D. Gioseffi, ‘Continuità della prospettiva da Democrito a Brunelleschi’, in C. Krause (n. 19) 25-41, speculates that Brunelleschi's famous demonstration of exact perspective was fuelled by familiarity with Vitruvius.

²⁵ See Trendall (n.13) figs. 140 (by the Iliupersis Painter), 203, 204, 209 (a detail of which is my PLATE 12a), 229. Also, White, Birth and rebirth (n. 6) pi. 60 a and b.

Curious self-contradictions mark these early works, e.g., one by the Iliupersis Painter (Trendall fig. 138, the reverse of my PLATE 14a), in which a character in the upper register sits on a stool that is shown from below—evidently not because he was meant to be above the characters in the lower (‘frontal’) register, but because the artist no longer accepted the registral convention at face value.