This chapter combines a focus on the scenic trajectories of Antigone and Creon with analyses of the tragedy’s choral songs. It traces the ways in which the characters’ actions, speech and deliberations are conditioned by the extent to which they understand (or misunderstand) the play’s complex reality. It argues that beyond the ethical conflict between them and questions of law and justice, both characters are presented in their own way as paradigms of human vulnerability and the limits of reason. Although Antigone’s action is eventually vindicated, it is not explicitly acknowledged by the gods, at least in her lifetime; instead, by the end of the play, her sacrifice appears to have been mere collateral damage in the gods’ plan to seek compensation for the exposure of Polynices’ corpse. Creon, because of his error of judgement in forbidding Polynices’ burial, undergoes a violent reversal of fortune from powerful and authoritative ruler to a ghost of a man. In the background, a pattern of divine control is interwoven with human agency in ways that are difficult to disentangle, both for the characters and Chorus and for the audience.

This chapter demonstrates that Sophocles’ Electra is pervaded by a strong sense of the fragility of human language and perception, drawing the spectators’ attention to the characters’ partial and often superficial understanding of events and conceptual categories such as familial strife, ancestral suffering, revenge and justice. The chapter focuses in turn on Orestes, Electra and the Paedagogus, analysing their experience of the tragedy’s reality and attempting to trace the larger networks of agency at work in their lives. Like Deianeira, Antigone or Creon, these characters operate in a world that is characterised by obscurity and constant upheaval; yet in Electra, the gods and the broad causal patterns governing the cosmos are more remote and elliptical than ever. Thus, the play can be located within the same intellectual, religious and philosophical traditions as other Sophoclean tragedies – but it engages with, and builds on, these traditions in a different way and to different effects, particularly in its radical questioning of humans’ ability to communicate successfully with the divine, and thus to access any kind of reality.

This chapter introduces the main argument and themes of the book, and positions it within earlier and existing scholarship on archaic and classical Greek literature, religion and philosophy. Particular points of focus include the relationship between Greek tragedy, ritual and theology, and influential mid-twentieth-century research on Sophocles (the ’classics’ of Sophoclean scholarship). The chapter also discusses ancient biographical traditions surrounding Sophocles’ religiosity and piety.

Book 3 of the CPAE. The risings of the southern constellations. The settings of the southern constellations. The risings of the zodiacal constellations. The settings of the zodiacal constellations. The 24 hourly circles.

Within the context of Greek mathematics, as developed by figures such as Euclid, Aristarchus, Archimedes, Eratosthenes and Apollonius, the contribution of Hipparchus is not nearly so well established. Circumstantial evidence suggests that he was the principal developer of trigonometry, in both its plane and spherical forms, but no ancient source credits him with this directly. It is likely that he was driven to devise trigonometric techniques in order to solve certain specific astronomical problems involving oblique ascensions that had already been discussed in general geometrical terms by Autolycus and Euclid. In pursuit of this, he devised a chord table which related the lengths of lines to subtended angles. Using this, he was able to provide exact solutions to specific astronomical problems concerning the risings and settings of stars, as well solar and lunar theory. As suggested by slender evidence in Plutarch, Hipparchus may also have worked on algebra and combinatorics. From evidence in other writers also, it appears that he took an interest in some aspects of what today is called physics.

Hipparchus is often mentioned by ancient writers, but these reports vary greatly in quality and quantity. The two principal sources are Ptolemy and Strabo, who contribute most of what is known about the general scope of his astronomical and geographical work, respectively. By comparison, other writers tend to be less expert in their reporting or are very brief. These include Cicero, Geminus, Cleomedes, Pliny the Elder, Theon of Smyrna, Vettius Valens, Galen, Sextus Empiricus, Pappus, Firmicus, Theon of Alexandria, as well as several anonymous texts. However, they are still valuable in building up an overall picture of Hipparchus and his contribution to astronomy and mathematics. Many of these ancient sources are discussed here.