, the third head of the Alexandrian Library, sent a letter to King Ptolemy outlining his solution for the geometric problem, the doubling of the cube. Although traditionally the preserve of historians of mathematics, the text quotes from tragedy, recounts mathematical research at Plato's Academy, and concludes with an epigram. Here, I address each generic gesture and its particular audience and aim. This article reads the letter not only as a dynamic unified whole which innovatively integrates mathematics and literature, but as a text which lays out the mechanics of the Ptolemaic empire for its readership.

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In 1773, the celebrated enlightenment thinker G.E. Lessing discovered in Wolfenbüttel's Herzog August Library a manuscript which contained a previously unknown Ancient Greek poem. The manuscript identified the author as Archimedes (c.287-212 BCE), and the work became known as the Cattle Problem (henceforth CP). On the surface, its twenty-two couplets capitalise on Homer's depiction of the ‘Cattle of the Sun’ in Book 12 of the Odyssey and its numerical aspect. A description of the related proportions of black, white, brown and dappled herds of cattle, which are then configured geometrically on Sicily, creates a strikingly colourful image. The author's decision to encode a number into the figure of the Cattle of the Sun styles the poem as a response to, and expansion of, Homer's scene. Reading through the work, though, it becomes clear that the mathematics is more complex than that of Homer's Odyssey.

would at least complicate the basic monitory function of the myth as 'a mythological exemplum of the consequences for young men who would ignore the narrator's exhortation to avert their eyes from the statue [sc. during the ritual]' (p. 234), but it is left to readers to ponder their consequences. A similar issue arises in the treatment of the Demeter, where S. puts particular emphasis on the comic antecedents of the Erysichthon story (p. 264), which she interprets as 'a humorous inversion of the serious cult frame' that produces 'a potent criticism of aristocratic excess'. This is plausible and certainly helps to make sense of the poet's focus on the social consequences of Erysichthon's plight (72-86), but numerous features, such as the consequences of his behaviour for his mother, sisters and slave women (94-5), Triopas' lament to Poseidon (98-110) and the final picture of Erysichthon at the crossroads begging for scraps from strangers (114-15), complicate the poem's emotional tone. S. is too attentive a reader to treat these nuances reductively: in her note on 96-110, she comments that 'the tragic tone of the speech is undercut by the bathos of the conclusion', while also detecting 'elements of comedy' in 94-5. But we might wonder whether the passage creates less a relation between separate registers (bathos, tragedy) in which one predominates, than an indeterminate commingling that leaves readers unsure how they are meant to react. At stake here is a distinction between an ironically distanced mode of reading which mirrors that of a knowing narrator, and a mode of reading more open to reflection on the relationship between the poem's subject and the adequacy of the critical resources brought to bear on it. Nor of course is this distinction absolute: individual readers might well find themselves responding to the hymn in both ways. Yet while such passages might be felt to demand more elaborated interpretations than S. provides, this criticism is offset by the limitations imposed by the book's form, and the usefulness of the commentary as a starting point for further engagement. The Hymns will doubtless continue to provide fruitful ground for critical debate, and S.'s keen observations and lucid arguments will be a valuable tool for the participants.

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