The Philonian Method of Cube Duplication

Abstract

Extant in multiple versions, the cube duplication of Philo of Byzantium, like the Hero-Apollonius method surveyed in the preceding chapters, provides opportunities for revealing the sources and aims of the commentators. From Philo’s own works a version survives in the Belopoeica (PB), although another version that appeared in the first book of his mechanical writings (PB*) is now lost. Eutocius presents a version (PE) among his series of solutions. Furthermore, two of the three methods in Philoponus’ commentary on Aristotle’s Posterior Analytics follow the Philonian method in very similar texts, although one (PJ) is unattributed, while the other (PK) is assigned to “Apollonius of Perga, as Parmenion says.”¹ This last immediately raises difficulties, for we have seen that Philoponus makes the identical attribution for his version of the Heronian method (AJ). Moreover, strong resemblances both in technique and text linking PK and a version well known in Arabic sources, particularly in the form due to Abû Bakr al-Harawî,² may indicate an ancient alternative to the Philonian method no longer extant in Greek.