Philonos Ioudaiou Syngrammata / Omnia Quae Extant Opera (1691 Greek)

A ...seems to be in potentiality. If, therefore, numbers are composed in order from unity up to the quaternary, they will complete the decad, which is the limit of the infinity of numbers, around which they turn and reflect themselves as if around a turning post. Moreover, the same quaternary contains the ratios of musical symphonies, namely the fourth, the fifth, the octave, and the double octave, from which a most absolute harmony is made. For the fourth has a supertertiary B proportion, the fifth a sesquialter, the octave a double. The quaternary contains all these proportions within itself. The supertertiary in four to three. The sesquialter in three to two, the double in two to one, or four to two. But the quadruple in four to one. And there is another power of the quaternary, wonderful to be told and thought. For this is the first to show the nature of the solid, since the preceding numbers are dedicated to incorporeal things. For in unity is considered the point, which geometers call so, in the binary the line. This is length without breadth, which, when it is added, becomes a surface, belonging to the C ternary. This, in order to become a body solid by nature, lacks one depth: which, added to the ternary, becomes the quaternary. Whence much estimation came to this number, which led us from the incorporeal and intelligible essence to the consideration of a body extended in three ways, which is perceived by sense first by its own nature. Whoever understands little of what is said, will know it from a certain common game. Those who play with nuts are accustomed, after placing three on a plane, to D place the fourth on top, in the form of a pyramid. That triangle, therefore, stands on the plane within the ternary: to which, placed on top, it makes a quaternary in number, but in figure a pyramid, a solid body by now. Furthermore, one must not be ignorant that the first of the four numbers, the square, is equally equal, a measure of equality and E justice: and also that it alone consists of the same things both by composition and by innate power. By composition from two and two. Again by power from twice two, showing forth a certain most beautiful species of consonance, which is in none of the other numbers. For soon the senary, composed of two ternaries, is no longer generated by these multiplied by themselves but another, namely the nonary. The quaternary is endowed with many other powers, which are to be indicated more accurately and copiously in its own treatise. Now it will be enough to have added this,

...in potentiality; for if the numbers from the monad up to the tetrad are added in order, they will generate the decad, which is the boundary of the infinity of numbers, around which they wheel and return as if around a turning point. And the tetrad contains the ratios of musical symphonies, that of the fourth, and of the fifth, and of the octave, and moreover of the double octave, from which the most perfect system is born. For the ratio of the fourth is supertertiary; that of the fifth, sesquialter; and that of the octave, double. All of which the tetrad contains, having encompassed them. The supertertiary in four to three; the sesquialter in three to two; the double in two to one, or four to two; and the quadruple in four to one. There is also another power of the tetrad, most wonderful to be told and thought; for this is the first to show the nature of the solid, since the numbers before it are dedicated to incorporeal things. For in the one is set that which is called a point in geometry; in the two, a line; and a line is length without breadth. And when breadth is added, it becomes a surface, which is set according to the triad. And surface, for the nature of the solid, needs one thing: depth; which, added to the triad, becomes the tetrad. Whence it has come about that this number is a great thing, which led us from the incorporeal and intelligible essence to the concept of a body extended in three ways, which is by nature first perceived by sense. And he who does not understand what is said will know it from a certain very common child's game. Those who play with nuts are accustomed, after setting three nuts on a plane, to place one on top, generating a pyramid-like shape. That triangle, then, stands on the plane up to the triad; but the one placed on top generates a tetrad in numbers, and in figure a pyramid, a solid body by now. And in addition to these, it must not be ignored that the number four is the first square, equally equal, a measure of justice and equality; because it alone is by nature generated from the same things both by composition and by power; by composition, from two and two; and by power again, from twice two, showing forth a certain most beautiful species of consonance, which has not happened to any of the other numbers. For soon the six, composed of two triads, is no longer generated by those being multiplied, but the other, the nine. The tetrad uses many other powers, which must be addressed more accurately in the specific treatise about it. It suffices to add this,