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ἐάν τις κτλ. αὐτὸ τὸ ἕν means ‘the unit itself’ i.e. the mathematical number ‘one’ which is ex hypothesi and by definition ἀμέριστον καὶ ἀδιαίρετον (Theo Smyrn. 18). If any one maintains that the mathematical unit is divisible, the mathematicians καταγελῶσί τε καὶ οὐκ ἀποδέχονται. Quâ mathematicians, they never condescend to justify either this or any other mathematical definition (οὐδένα λόγον οὔτε αὑτοῖς οὔτε ἄλλοις ἔτι ἀξιοῦσι—διδόναι VI 510 C), and think it ridiculous that any one should question the foundations of their science. The moment they begin to render an account of their ὑποθέσεις they cease to be mathematicians and become διαλεκτικοί. See also on VI 510 C and App. III. ἐὰν σὺ κερματίζῃς κτλ.: ‘if you mince it, they multiply it.’ If you insist on dividing their unit, they insist on multiplying it (viz. by your divisor), and so defeat your purpose and keep the unit one and indivisible as before. ‘I cut that unit up!’ you exclaim. ‘I multiply it!’ is their reply; and you are checkmated. They have just as much right to multiply it as you to divide it; for the mathematical unit is only a ὑπόθεσις when all is said and done. Plato is humorously describing a passage-atarms between mathematicians and some obstinate fellow who will not admit the indivisibility of their unit. The words ‘back again’ in D. and V.'s translation “they multiply it back again” correspond to nothing in the Greek and suggest an erroneous idea; nor can the Greek mean “that division is regarded by them as a process of multiplication, for the fractions of one continue to be units” (as Jowett suggests). Each of these explanations misses the humour of the original. The word μόρια is doubtless genuine, though its rejection (proposed by Herwerden) would improve the antithesis. Cf. μόριόν τε ἔχον ἐν ἑαυτῷ οὐδέν (526 A), for which μόρια here prepares the way.
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