De Opificio Mundi

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.

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.

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

If we examine the number six which is composed of two threes, if these two numbers are multiplied it is not the number six that is produced, but a different one, the number nine.

And the number four has many other powers also, which we must subsequently show more accurately in a separate essay appropriated to it. At present it is sufficient to add this that it was the foundation of the creation of the whole heaven and the whole world. For the four elements, out of which this universe was made, flowed from the number four as from a fountain. And in addition to the four elements the seasons of the year are also four, which are the causes of the generation of animals and plants, the year being divided into the quadruple division of winter, and spring, and summer, and autumn.