‹‹‹ Vitr. 3.1.5 | Table of Contents | Vitr. 3.1.7 ›››
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.
6The 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 δἱμοιρος as they call it; five is five sixths, called πεντἁμοιρος; and six is the perfect number. As the number goes on growing larger, the addition of a unit above six is the ἑφεκτος; eight, formed by the addition of a third part of six, is the integer and a third, called ἑπἱτριτος; the addition of one half makes nine, the integer and a half, termed ἡμιὁλιος; the addition of two thirds, making the number ten, is the integer and two thirds, which they call ἑπιδἱμοιρος; in the number eleven, where five are added, we have the five sixths, called ἑπἱπεμπτος; finally, twelve, being composed of the two simple integers, is called διπλἁσιος.