On Architecture

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 di/moiros as they call it; five is five sixths, called penta/moiros; and six is the perfect number. As the number goes on growing larger, the addition of a unit above six is the e)/fektos; eight, formed by the addition of a third part of six, is the integer and a third, called e)pi/tritos; 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 e)pidi/moiros; in the number eleven, where five are added, we have the five sixths, called e)pi/pemptos; finally, twelve, being composed of the two simple integers, is called dipla/sios.