Admit a right-angled parallelogram, A B C D, the lesser side of which A B consists of five, the longer side A C contains seven squares. Let the lesser division be unequally divided into two and three squares, marked by E; and the larger division in two unequal divisions more of three and four squares, marked by F. Thus A E F G comprehends six, E B G I nine, F G C H eight, and G I H D twelve. By this means the whole parallelogram, containing thirty-five little square areas, comprehends all the proportions of the first concords of music in the number of these little squares. For six is exceeded by eight in a sesquiterce proportion (3: 4), wherein the diatessaron is comprehended. And six is exceeded by nine in a sesquialter proportion (2: 3), wherein also is included the fifth. Six is exceeded by twelve in duple proportion (1: 2), containing the octave; and then lastly, there is the sesquioctave proportion of a tone in eight to nine. And therefore they call that number which comprehends all these proportions harmony. This number is 35, which being multiplied by 6, the product is 210, which is the number of days, they say, which brings those infants to perfection that are born at the seventh month’s end. 13. To proceed by way of multiplication,—twice 3 make 6, and 4 times 9 thirty-six, and 8 times 27 produce 216. Thus six appears to be a perfect number, as being equal in its parts; and it is called matrimony, by reason of the mixture of the first even and odd. Moreover it is composed of the original number, which is one, of the first even number, which is two, and the first odd number, which is three. Then for 36, it is the first number which is as well quadrangular as triangular, being quadrangular from 6, and triangular from 8.[191] The same number arises from the multiplication of the first two square numbers, 4 and 9; as also from the addition of the three cubical numbers, 1, 8, and 27, which being put together make up 36. Lastly, you have a parallelogram with unequal sides, by the multiplication of 12 by 3, or 9 by 4. Take then the numbers of the sides of all these figures, the 6 of the square, the 8 of the triangle, the 9 for the one parallelogram, and the 12 for the other; and there you will find the proportions of all the concords. For 12 to 9 will be a fourth, as nete to paramese. To eight it will prove a fifth, as nete to mese. To six it will be an octave, as nete to hypate. And the two hundred and sixteen is the cubical number proceeding from six which is its root, and so equal to its own perimeter.