Cum ad supplicationem crescat, supra sex adiecto asse ephectum; cum facta sunt octo, quod est tertia adiecta, tertiarium alterum, qui epitritos dicitur; dimidia adiecta cum facta sunt novem, sesquialterum, qui hemiolius appellatur; duabus partibus additis et decusis facto bes alterum, quem epidimoerum vocitant; in undecim numero quod adiecti sunt quinque, quintarium, quem epipempton dicunt; duodecim autem, quod ex duobus numeris simplicibus est effectus, diplasiona.
When it grows to the double, a twelfth added above six makes ephectos; when eight is reached, because a third is added, there is a second third, which is called epitritos; when half is added and there are nine, there is half as much again, and it is called hemiolios; when two parts are added and a decad is made, we have the second two-thirds, which they call epidimoeros: in the number eleven, because five are added, we have five-sixths, which they call epipemptos; twelve, because it is produced from two simple numbers, they call diplasios.
final_alignments\Vitruvius_Architecture_Book_3.json