XXXIII. (99) And such great sanctity is there in the number seven, that it has a pre-eminent rank beyond all the other numbers in the first decade. For of the other numbers, some produce without being produced, others are produced but have no productive power themselves; others again both produce and are produced. But the number seven alone is contemplated in no part. And this proposition we must confirm by demonstration. Now the number one produces all the other numbers in order, being itself produced absolutely by no other; and the number eight is produced by twice four, but itself produces no other number in the decade. Again, four has the rank of both, that is, of parents and of offspring; for it produces eight when doubled, and it is produced by twice two. (100) But seven alone, as I said before, neither produces nor is produced, on which account other philosophers liken this number to Victory, who had no mother, and to the virgin goddess, whom the fable asserts to have sprung from the head of Jupiter: and the Pythagoreans compare it to the Ruler of all things. For that which neither produces, nor is produced, remains immovable. For generation consists in motion, since that which is generated, cannot be so without motion, both to cause production, and to be produced. And the only thing which neither moves nor is moved, is the Elder, Ruler, and Lord of the universe, of whom the number seven may reasonably be called a likeness. And Philolaus gives his testimony to this doctrine of mine in the following Words:ù”for God,” says he “is the ruler and Lord of all things, being one, eternal, lasting, immovable, himself like to himself, and different from all other beings.”

XXXIV. (101) Among the things then which are perceptible only by intellect, the number seven is proved to be the only thing free from motion and accident; but among things perceptible by the external senses, it displays a great and comprehensive power, contributing to the improvement of all terrestrial things, and affecting even the periodical changes of the moon. And in what manner it does this, we must consider. The number seven when compounded of numbers beginning with the unit, makes eight-and-twenty, a perfect number, and one equalised in its parts. And the number so produced, is calculated to reproduce the revolutions of the moon, bringing her back to the point from which she first began to increase in a manner perceptible by the external senses, and to which she returns by waning. For she increases from her first crescent-shaped figure, to that of a half circle in seven days; and in seven more, she becomes a full orb; and then again she turns back, retracing the same path, like a runner of the diaulos, {6}{this refers to the Greek games. “The straight race was called stadion or dromos. In the diaulos dromos the runners turned round the goal, and came back to the starting place.”ùSmith in v. Stadium.} receding from an orb full of light, to a half circle again in seven days, and lastly, in an equal number she diminishes from a half circle to the form of a crescent; and thus the number before mentioned is completed. (102) And the number seven by those persons who are in the habit of employing names with strict propriety is called the perfecting number; because by it, everything is perfected. And any one may receive a confirmation of this from the fact, that every organic body has three dimensions, length, depth, and breadth; and four boundaries, the point, the line, the superficies, and the solid; and by theses, when combined, the number seven is made up. But it would be impossible for bodies to be measured by the number seven, according to the combination of the three dimensions, and the four boundaries, if it did not happen that the ideas of the first numbers, one, two, three and four, in which the number ten is founded, comprised the nature of the number seven. For the aforesaid numbers have four boundaries, the first, the second, the third, the fourth, and three intervals. The first interval being that between one and two; the second, that between two and three; the third, that between three and four.

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