The Republic · ¶260

Our hope of understanding the passage depends principally on an accurate study of the words themselves; on which a faint light is thrown by the parallel passage in the ninth book. Another help is the allusion in Aristotle, who makes the important remark that the latter part of the passage (from ὧν ἐπίτριτος πυθμὴν, κ.τ.λ.) describes a solid figure. Some further clue may be gathered from the appearance of the Pythagorean triangle, which is denoted by the numbers 3, 4, 5, and in which, as in every right-angled triangle, the squares of the two lesser sides equal the square of the hypotenuse (3² + 4² = 5², or 9 + 16 = 25).

Plato · translated by Benjamin Jowett · composite transcription based on the 1888 third edition
Benjamin Jowett, revised third edition (1888), with Stephanus numbering from the 1908 edition; composite transcription, Project Gutenberg #55201
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