In Books III and IV of the Hypotyposis, Proclus deals with the perfection of Socratic theory about Ideas by Parmenides within the Platonic dialogue. More specifically, the two books deal with the four forest questions concerning Ideas: "Do Ideas exist?" "Which things have Ideas and which do not?" "How do sensible things participate in Ideas?" "Where are Ideas located?" The first two of the four questions are examined in Book III, while the other two are examined in Book IV. In fact, the first question is not examined within the Platonic Parmenides, but Proclus examines it on his own initiative. [...]

(from the introduction of the book)