De Opificio Mundi

But after the whole world had been completed according to the perfect nature of the number six, the Father hallowed the day following, the seventh, praising it, and calling it holy. For that day is the festival, not of one city or one country, but of all the earth; a day which alone it is right to call the day of festival for all people, and the birthday of the world.

And I know not if any one would be able to celebrate the nature of the number seven in adequate terms, since it is superior to every form of expression. But it does not follow that because it is more admirable than anything that can be said of it, that on that account one ought to keep silence; but rather we ought to try, even if one cannot say everything which is proper, or even that which is most proper, at all events to utter such things as may be attainable by our capacities.

The number seven is spoken of in two ways; the one within the number ten which is measured by repeating the unit alone seven times, and which consists of seven units; the other is the number outside ten, the beginning of which is altogether the unit increasing according to a twofold or threefold, or any

For in every case the number which is combined from the unit in double or treble ratio, or any other ratio, whatsoever, is the seventh number, a cube and a square, embracing both species, both that of the incorporeal and that of the corporeal essence. That of the incorporeal essence according to the superficies which quadrangular figures present, and that of the corporeal essence according to the other figure which cubes make;

and the clearest proof of this is afforded by the numbers already spoken of. In the seventh number increasing immediately from the unit in a twofold ratio, namely, the number sixty-four, is a square formed by the multiplication of eight by eight, and it is also a cube by the multiplication of four and four, four times. And again, the seventh number from the unit being increased in a threefold ratio, that is to say, the number seven hundred and twenty-nine, is a square, the number seven and twenty being multiplied by itself; and it is also a cube, by nine being multiplied by itself nine times.

And in every case a man making his beginning from the unit, and proceeding on to the seventh number, and increasing in the same ratio till he comes to the number seven, will at all times find the number, when increased, both a cube and a square. At all events, he who begins with the number sixty-four, and combines them in a doubling ratio, will make the seventh number four thousand and ninety-six, which is both a square and a cube, having sixty-four as its square root, and sixteen as its cube root.

And we must also pass on to the other species of the number seven, which is contained in the number ten, and which displays an admirable nature, and one not inferior to the previously mentioned species. The number seven consists of one, and two and four, numbers which have two most harmonious ratios, the twofold and the fourfold ratio; the former of which affects the diapason harmony, while the fourfold ratio causes that of the double diapason. It also comprehends other divisions, existing in some kind of yoke-like combination. For it is divided first of all into the number one, and the number six; then into the two and the five; and last of all, into

And the proportion of these numbers is a most musical one; for the number six bears to the number one a six-fold ratio, and the six-fold ratio causes the greatest possible difference between existing tones; the distance namely, by which the sharpest tone is separated from the flattest, as we shall show when we pass on from numbers to the discussion of harmony. Again, the ratio of four to two displays the greatest power in harmony, almost equal to that of the diapason, as is most evidently shown in the rules of that art. And the ratio of four to three effects the first harmony, that in the thirds, which is the diatessaron.

The number seven displays also another beauty which it possesses, and one which is most sacred to think of. For as it consists of three and four, it displays in existing things a line which is free from all deviation and upright by nature. And in what way it does so I must show.

The rectangular triangle, which is the beginning of all qualities, consists of the numbers three[*](This discussion about numbers is not very intelligible; but here Philo is probably referring to the problem of Euclid on the subject of the square of the hypothenuse. Thus, if 3 and 4 represent the sides containing the angle, and 5 the side subtending it, we get 3 * 3 = 9; 4 * 4 = 16; 5 * 5 = 25.) and four, and five; and the three and the four, which are the essence of the seven, contain the right angle; for the obtuse angle and the acute angle show irregularity, and disorder, and inequality; for one may be more acute or more obtuse than another. But a right angle does not admit of comparison, nor is one right angle more a right angle than another: but one remains similar to another, never changing its peculiar nature. But if the right-angled triangle is the beginning of all figures and of all qualities, and if the essence of the number seven, that is to say, the numbers three and four together, supply the most necessary part of this, namely, the right angle, then seven may be rightly thought to be the fountain of every figure and of every quality.

And besides what has been already advanced, this also may be asserted that three is the number of a plane figure, since a point has been laid down to be, according to a unit, and a line according to the number two, and a plane superficies according to

And such great sanctity is there in the number seven, that it has a preeminent 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.

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:—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.