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6. The mathematicians, however, maintaining a different view, have said that the perfect number is six, because this number is composed of integral parts which are suited numerically to their method of reckoning: thus, one is one sixth; two is one third; three is one half; four is two thirds, or δίμοιρος as they call it; five is five sixths, called πεντάμοιρος; and six is the perfect number. As the number goes on growing larger, the addition of a unit above six is the ἔφεκτος; eight, formed by the addition of a third part of six, is the integer and a third, called ἐπίτριτος; the addition of one half makes nine, the integer and a half, termed the addition of two thirds, making the number ten, is the integer and two thirds, which they call ἐπιδίμοιρος; in the number eleven, where five are added, we have the five sixths, called ἐπίπεμπτος; finally, twelve, being composed of the two simple integers, is called διπλάσιος.
Vitruvius: The Ten Books on Architecture. Vitruvius. Morris Hicky Morgan. Cambridge: Harvard University Press. London: Humphrey Milford. Oxford University Press. 1914.
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