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οἱ περὶ κτλ. In CE, as will afterwards appear, are included five sciences, which form the προοίμιον (VII 531 D) or προπαιδεία (ib. 536 D) to Dialectic, represented by EB. They are the Science of Number, Plane Geometry, Stereometry, Astronomy, and Harmonics: VII 522 C—531 C. In each of these the method, according to Plato, is the same. Certain ὑποθέσεις are taken for granted, and inferences drawn from them by purely deductive reasoning, aided by the use of sensible likenesses or illustrations. See also App. I to Book VII.

ὡς εἰδότες. They have no knowledge of their ὑποθέσεις, otherwise they would be able to give an account of them: see VII 533 C and 531 E μὴ δυνατοί τινες ὄντες δοῦναί τε καὶ ἀποδέξασθαι λόγον εἴσεσθαί ποτέ τι ὧν φαμὲν δεῖν εἰδέναι; Οὐδ̓ αὖ, ἔφη, τοῦτό γε.

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