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τῷ ὀξύτατα καθορῶντι κτλ. “Induction conceived as inference from particulars to particulars, its test being prediction (not explanation), and its method being association of images or unanalysed likenesses, by contiguity in co-existence or succession” Bosanquet. Plato is thinking chiefly of the empirical politician and political adviser, who foretells the future from the present and the past (cf. Thuc. I 22), but limits his intellectual horizon by his own experience, and knows nothing of the real determining causes of events. The vast majority of Athenian statesmen belonged in Plato's opinion to this category: see on V 473 C and VI 488 B. αὐτῶν does not of course depend on πρότερα (as D. and V. translate), but is a partitive genitive after ὅσα.
The Republic of Plato. James Adam. 1902. Cambridge. Cambridge University Press.
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