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6The mathematicians, on the other hand, contend for the perfection of the number six, because, according to their reasoning, its divisors equal its number: for a sixth part is one, a third two, a half three, two-thirds four, which they call δίμοιρος; the fifth in order, which they call πεντάμοιρος, five, and then the perfect number six. When it advances beyond that, a sixth being added, which is called ἔφεκτος, we have the number seven. Eight are formed by adding a third, called triens, and by the Greeks, ἐπίτριτος. Nine are formed by the addition of a half, and thence called sesquialteral; by the Greeks ἡμιόλιος; if we add the two aliquot parts of it, which form ten, it is called bes alterus, or in Greek ἐπιδίμοιρος. The number eleven, being compounded of the original number, and the fifth in order is called ἐπιπεντάμοιρος. The number twelve, being the sum of the two simple numbers, is called διπλασίων.
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