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The Commentary on Plato's Parmenides by Proclus (AD 412-85) is the most important extant document on the interpretation of this enigmatic dialogue, and has had a crucial influence on all subsequent readings. In Proclus' Commentary, the Parmenides provides the argumentative and conceptual framework for a scientific theology wherein all mythological discourse about the gods can be integrated. Its exposition was therefore the culmination of the curriculum of the Platonic school. This theological reading of the Parmenides persisted, through the medium of Ficino, until the nineteenth century. Previously this important text was only accessible in the edition of V. Cousin (Paris, 1864). This new critical edition is based on an exhaustive study of both the Greek tradition and the medieval Latin translation. This volume contains Books IV and V.