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.
XVI. (49) There is also another power of the number four which is a most wonderful one to speak of and to contemplate. For it was this number that first displayed the nature of the solid cube, the numbers before four being assigned only to incorporeal things. For it is according to the unit that that thing is reckoned which is spoken of in geometry as a point: and a line is spoken of according to the number two, because it is arranged by nature from a point; and a line is length without breadth. But when breadth is added to it, it becomes a superficies, which is arranged according to the number three. And a superficies, when compared with the nature of a solid cube, wants one thing, namely depth, and when this one thing is added to the three, it becomes four. On which account it has happened that this number is a thing of great importance, inasmuch as from an incorporeal substance perceptible only by intellect, it has led us on to a comprehension of a body divisible in a threefold manner, and which by its own nature is first perceived by the external senses. (50) And he who does not comprehend what is here said may learn to understand it from a game which is very common. Those who play with nuts are accustomed when they have placed three nuts on the floor, to place one more on the top of them producing a figure like a pyramid. Accordingly the triangle stands on the floor, arranged up to the number three, and the nut which is placed upon it makes up four in number, and in figure it produces a pyramid, being now a solid body. (51) And in addition to this there is this point also of which we should not be ignorant, the number four is the first number which is a square, being equal on all sides, the measure of justice and equality. And that it is the only number the nature of which is such that it is produced by the same numbers whether in combination, or in power. In combination when two and two are added together; and again in power when we speak of twice two; {4}{thus 2+2= 4, or 2×2= 4.} and in this is displays an exceedingly beautiful kind of harmony, which is not the lot of any other number.
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