XV. (47) This is the cause why the earth bore fruit and herbs before God proceeded to adorn the heaven. And next the heaven was embellished in the perfect number four, and if any one were to pronounce this number the origin and source of the all-perfect decade he would not err. For what the decade is in actuality, that the number four, as it seems, is in potentiality, at all events if the numerals from the unit to Four{3}{by addition, that is 1+2+3+4= 10.} are placed together in order, they will make ten, which is the limit of the number of immensity, around which the numbers wheel and turn as around a goal. (48) Moreover the number four also comprehends the principles of the harmonious concords in music, that in fours, and in fifths, and the diapason, and besides this the double diapason from which sounds the most perfect system of harmony is produced. For the ratio of the sounds in fourths is as four to three; and in fifths as three to two; and in the diapason that ratio is doubled: and in the double diapason it is increased fourfold, all which ratios the number four comprehends. At all events the first, or the epistritus, is the ratio of four to three; the second, or the hemiolius, is that of three to two: the twofold ratio is that of two to one, or four to two: and the fourfold ratio is that of four to one.