has fallen upon them has crushed them altogether, or snow has chilled them, or the violence of the winds has torn them up by the roots; for water and air cause many alterations, tending to destroy the productiveness of the crops. But if the immo

derate violence of the passions were appeased by temperance, and the inclination to do wrong and depraved ambition were corrected by justice, and in short if the vices and unhallowed actions done in accordance with them, were corrected by the virtues, and the energies in accordance with them, the war of the soul being terminated, which is in good truth the most grievous and heavy of all wars, and peace being established, and founding amid all our faculties, a due regard for law, with all tranquillity and mildness, then there would be hope that God, as being a friend to virtue, and a friend to honour, and above all a friend to man, would bestow upon the race of man, all kinds of spontaneous blessings from his ready store. For it is evident that it is easier to supply most abundantly the requisite supplies without having recourse to agricultural means, from treasures which already exist, than to bring forth what as yet has no existence. XXVII. I have now mentioned the second reason.

There is also a third, which is as follows:-God, intending to adapt the beginning and the end of all created things together, as being all necessary and dear to one another, made heaven the be ginning, and man the end: the one being the most perfect of incorruptible things, among those things which are perceptible by the external senses; and the other, the best of all earthborn and perishable productions a short-lived heaven if one were to speak the truth, bearing within himself many starlike natures, by means of certain arts and sciences, and illustrious speculations, according to every kind of virtue. For since the corruptible and the incorruptible, are by nature opposite, he has allotted the best thing of each species to the beginning and to the end. Heaven, as I before said, to the beginning, and man to the end.

XXVIII, And besides all this, another is also mentioned among the necessary causes. It was necessary that man should be the last of all created beings; in order that being so, and appearing suddenly, he might strike terror into the other animals. For it was fitting that they, as soon as they first saw him should admire and worship him, as their natural ruler and master; on which account, they all, as soon as they saw him,

became tame before him; even those, who by nature were most savage, becoming at once most manageable at the first sight of him; displaying their unbridled ferocity to one another, and being tame to man alone. For which reason the Father who made him to be a being dominant over them by nature not merely in fact, but also by express verbal appointment, established him as the king of all the animals, beneath the moon, whether terrestrial or aquatic, or such as traverse the air. For every mortal thing which lives in the three elements, land, water or air, did he put in subjection to him, excepting only the beings that are in heaven, as creatures who have a more divine portion. And what is apparent to our eyes is the most evident proof of this. For at times, innumerable herds of beasts are led about by one man, not armed, nor wearing iron, nor any defensive weapon, but clad only in a skin for a garment, and carrying a staff, for the purpose of making signs, and to lean upon also in his journeys if he become weary. And so the shepherd, and the goatherd, and the cowherd, lead numerous flocks of sheep, and goats, and herds of oxen; men neither vigorous, nor active in their bodies, so as to strike those who behold them with admiration because of their fiue appearance; and all the might and power of such numerous and well-armed beasts (for they have means of self-defence given them by nature), yet dread them as slaves do their master, and do all that is commanded them. Bulls are yoked to the plough to till the ground, and cutting deep furrows all day, sometimes even for a long space of time together, while some farmer is managing them. And rams being weighed down with heavy fleeces of wool, in the spring season, at the command of the shepherd, stand quietly, and lying down, without resistance, permit their wool to be shorn off, being accustomed naturally, like cities, to yield a yearly tribute to their sovereign. And moreover, that most spirited of animals, the horse, is easily guided after he has been bridled; in order that he may not become frisky, and shake off the rein; and he hollows his back in an admirable manner to receive his rider and to afford him a good seat, and then bearing him aloft, he gallops at a rapid pace, being eager to arrive at and carry him to the place to which he is urging him. And the rider without any toil, but in the most perfect quiet, makes a rapid journey, by using the body and feet of another animal.

XXIX. And any one who was inclined to dwell upon this subject might bring forward a great many other instances, to prove that there is no animal in the enjoyment of perfect liberty, and exempt from the dominion of man; but what has been already said is sufficient by way of example. We ought, however, not to be ignorant of this also, that it is no proof because man was the last created animal that he is the lowest in rank, and charioteers and pilots are witnesses of this; for the charioteers sit behind their beasts of burden, and are placed at,their backs, and yet when they have the reins in their hands, they guide them wherever they choose, and at one time they urge them on to a swift pace, and at another time they hold them back, if they are going on at a speed greater than is desirable. And pilots again, sitting in the hindmost part of the ship, that is the stern are, as one may say, the most important of all the people in the ship, inasmuch as they have the safety of the ship and of all those who are in it, in their hands. And so the Creator has made man to be as it were a charioteer and pilot over all other animals, in order that he may hold the reins and direct the course of every thing upon earth, having the superintendence of all animals and plants, as a sort of viceroy of the principal and mighty King.

XXX. 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

other proportion whatever; as are the numbers sixty-four, and seven hundred and twenty-nine; the one number of which is increased by doubling on from the unit, and the other by trebling. And it is not well to examine either species superficially, but the second has a most manifest pre-eminence. 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 sixtyfour as its square root, and sixteen as its cube root.

XXXI. 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

the three and the four. And the proportion of these numbers is a most musical one; for the number six bears to the number one a sixfold ratio, and the sixfold 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,

XXXII. 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 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

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 8 and 4 represent the sides containing the angle, and 5 the side subtonding it, we get 3x3 9 5x5=25.

4x4=16

25.