Philo of Alexandria's Interest in the Diatessaron (Philo's Understanding Certainly Influenced Clement) [Part Three]

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 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 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 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(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 (3x3)+(4x4) = 9+16= 25; 5x5= 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 the number three. Also, four is the number of a cube, by the addition of one to the number of a plane superficies, depth being added to the superficies. From which it is plain that the essence of the number seven is the foundation of geometry and trigonometry; and in a word, of all incorporeal and corporeal substances.

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. 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."

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, (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." Smith 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. 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.

And besides what has been already said, the growth of men from infancy to old age, when measured by the number seven, displays in a most evident manner its perfecting power; for in the first period of seven years, the putting forth of the teeth takes place. And at the end of the second period of the same length, he arrives at the age of puberty: at the end of the third period, the growth of the beard takes place. The fourth period sees him arrive at the fullness of his manly strength. The fifth seven years is the season for marriage. In the sixth period he arrives at the maturity of his understanding. The seventh period is that of the most rapid improvement and growth of both his intellectual and reasoning powers. The eighth is the sum of the perfection of both. In the ninth, his passions assume a mildness and gentleness, from being to a great degree tamed. In the tenth, the desirable end of life comes upon him, while his limbs and organic senses are still unimpaired: for excessive old age is apt to weaken and enfeeble them all. (104) And Solon, the Athenian lawgiver, described these different ages in the following elegiac verses:

In seven years from th' earliest breath,
The child puts forth his hedge of teeth;
When strengthened by a similar span,
He first displays some signs of man.
As in a third, his limbs increase,
A beard buds o'er his changing face.
When he has passed a fourth such time,
His strength and vigour's in its prime.
When five times seven years o'er his head
Have passed, the man should think to wed;
At forty two, the wisdom's clear
To shun vile deed of folly or fear:
While seven times seven years to sense
Add ready wit and eloquence.
And seven years further skill admit
To raise them to their perfect height.
When nine such periods have passed,
His powers, though milder grown, still last;
When God has granted ten times seven,
The aged man prepares for heaven.

Solon therefore thus computes the life of man by the aforesaid ten periods of seven years. But Hippocrates the physician says that there are Seven (it is hardly necessary to remind the reader of the description of the seven ages of man in Shakespeare. As You Like It, Act II. sc. 7) ages of man, infancy, childhood, boyhood, youth, manhood, middle age, old age; and that these too, are measured by periods of seven, though not in the same order. And he speaks thus; ``In the nature of man there are seven seasons, which men call ages; infancy, childhood, boyhood, and the rest. He is an infant till he reaches his seventh year, the age of the shedding of his teeth. He is a child till he arrives at the age of puberty, which takes place in fourteen years. He is a boy till his beard begins to grow, and that time is the end of a third period of seven years. He is a youth till the completion of the growth of his whole body, which coincides with the fourth seven years. Then he is a man till he reaches his forty-ninth year, or seven times seven periods. He is a middle aged man till he is fifty-six, or eight times seven years old; and after that he is an old man.

And it is also affirmed for the particular praise of the number seven, that it has a very admirable rank in nature, because it is composed of three and four. And if any one doubles the third number after the unit, he will find a square; and if he doubles the fourth number, he will find a cube. And if he doubles the seventh from both, he will both a cube and a square; therefore, the third number from the unit is a square in a double ratio. And the fourth number, eight, is a cube. And the seventh number, being sixty-four, is both a cube and a square at the same time; so that the seventh number is really a perfecting one, signifying both equalities, ùthe plane superficies by the square, according to the connection with the number three, and the solid by the cube according to its relationship to the number four; and of the numbers three and four, are composed the number seven.

But this number is not only a perfecter of things, but it is also, so to say, the most harmonious of numbers; and in a manner the source of that most beautiful diagram which describes all the harmonies, that of fourths, and that of fifths, and the diapason. It also comprises all the proportions, the arithmetical, the geometrical, and moreover the harmonic proportion. And the square consists of these numbers, six, eight, nine, and twelve; and eight bears to six the ratio of being one third greater, which is the diatessaron of harmony. And nine bears to six the ratio of being half as great again, which is the ratio of fifths. And twelve is to six, in a twofold proportion; and this is the same as the diapason. The number seven comprises also, as I have said, all the proportions of arithmetrical proportion, from the numbers six, and nine, and twelve; for as the number in the middle exceeds the first number by three, it is also exceeded by three by the last number. And geometrical proportion is according to these four numbers. For the same ratio that eight bears to six, that also does twelve bear to nine. And this is the ratio of thirds. Harmonic ratio consists of three numbers, six, and eight, and twelve. But there are two ways of judging of harmonic proportion. One when, whatever ratio the last number bears to the first, the excess by which the last number exceeds the middle one is the same as the excess by which the middle number exceeds the first. And any one may derive a most evident proof of this from the numbers before mentioned, six, and eight, and twelve: for the last number is double the first. And again, the excess of twelve over eight is double the excess of eight over six. For the number twelve exceeds eight by four, and eight exceeds six by two; and four is the double of two. And another test of harmonic proportion is, when the middle term exceeds and is exceeded by those on each side of it, by an equal portion; for eight being the middle term, exceeds the first term by a third part; for if six be subtracted from it, the remainder two is one third of the original number six: and it is exceeded by the last term in an equal proportion; for if eight be taken from twelve, the remainder four is one third of the whole number twelve.

Let this then be premised, as of necessity it must, respecting the honourable qualities which this diagram or square has, and the name to which it is entitled, and the number seven unfolds an equal number of ideas, and even more in the case of incorporeal things, which are perceptible only by the intellect; and its nature extends also over every visible essence, reaching to both heaven and earth, which are the boundaries of every thing. For what portion of all the things on earth is there which is not fond of seven; being subdued by an affection and longing for the seventh. Accordingly men say, that the heaven is girdled with seven circles, the names of which are as follows; the arctic, the antarctic, the summer tropic, the winter tropic, the equinoctial, the zodiac, and last of all the galaxy. For the horizon is something which affects ourselves, in proportion as any one has acute vision, or the contrary; our sensation cutting off at one time a lesser, and at another time a greater circumference. The planets too, and the corresponding host of fixed stars, are arrayed in seven divisions, displaying a very great sympathy with the air and the earth. For they turn the air towards the times, that are called the seasons of the year, causing in each of them innumerable changes by calm weather, and pleasant breezes, and clouds, and irresistible blasts of wind. And again, they make rivers to overflow and to subside, and turn plains into lakes; and again, on the contrary, they dry up the waters: they also cause the alterations of the seas, when they receded, and return with a reflux. For at times, when the tide recedes on a sudden, an extensive line of shore occupies what is usually a wide gulf of sea; and in a short time afterwards, the waters are brought back, and there appears a sea, sailed over, not by shallow boats, but by ships of exceeding great burden. And they also give increase and perfection to all the terrestrial animals and plants which produce fruit, endowing each with a nature to last a long time, so that new plants may flourish and come to maturity; ùthe old ones having passed away, in order to provide an abundant supply of necessary things.

Moreover, the constellation Ursa Major, which men call the guide of mariners, consists of seven stars, which the pilots keeping in view, steer in innumerable paths across the sea, directing their endeavours towards an incredible task, beyond the capacity of human intellect. For it is through conjectures, directed by the aforementioned stars, that they have discovered countries which were previously unknown; those who dwell on the continent having discovered islands, and islanders having found out continents. For it was fitting that the recesses both of earth and sea should be revealed to that God-loving animal, the race of mankind, by the purest of essences, namely heaven. And besides the stars above mentioned the band of the Pleiades is also made up of seven stars, the rising and occultation of which are the causes of great benefits to all men. For when they set, the furrows are ploughed up for the purpose of sowing; and when they are about to rise, they bring glad tidings of harvest; and after they have arisen, they awaken the rejoicing husbandman to the collection of their necessary food. And they with joy store up their food for their daily use. And the sun, the ruler of the day, making two equinoxes every year, both in spring and autumn. The spring equinox in the constellation of Aries, and the autumnal one in Libra, gives the most evident demonstration possible of the divine dignity of the number seven. For each of the equinoxes takes place in the seventh month, at which time men are expressly commanded by law to celebrate the greatest and most popular and comprehensive festivals; since it is owing to both these seasons, that all the fruits of the earth are engendered and brought to perfection; the fruit of corn, and all other things which are sown, being owing to the vernal equinox; and that of the vine, and of all the other plants which bear hard berries, of which there are great numbers, to the autumnal one.

And since all the things on the earth depend upon the heavenly bodies according to a certain natural sympathy, it is in heaven too that the ratio of the number seven began, and from thence it descended to us also, coming down to visit the race of mortal men. And so again, besides the dominant part of our mind, our soul is divided into seven divisions; there being five senses, and besides them the vocal organ, and after that the generative power. All which things, like the puppets in a raree show, which are moved by strings by the manager, are at one time quiet, and at another time in motion, each according to its suitable habits and capacities of motion. And in the same way, if any one were to set about investigating the different parts of the body, in both their interior and the exterior arrangement, he will in each case find seven divisions. Those which are visible are as follow; ùthe head, the chest, the belly, two arms, and two legs; the internal parts, or the entrails, as they are called, are the stomach, the heart, the lungs, the spleen, the liver, and the two kidneys. Again, the principal and dominant part in an animal is the head, and that has seven most necessary divisions: two eyes, an equal number of ears, two channels for the nostrils, and the mouth to make up seven, through which as Plato says, mortal things find their entrance, and immortal things their exit. For into the mouth do enter meat and drink, perishable food of a perishable body; but from out of it proceed wordsùthe immortal laws of an immortal soul, by means of which rational life is regulated.

Again, the things which are judged of by the best of the senses, sight, partake of number according to their kind. For the things which are seen are seven; body, distance, shape, magnitude, colour, motion, tranquillity, and besides these there is nothing. It also happens that all the changes of the voice amount to seven; the acute, the grave, the contracted, in the fourth place the aspirated sound, the fifth is the tone, the sixth the long, the seventh the short sound. There are also seven motions; the motion upwards, the motion downwards, that to the right, that to the left, the forward motion, the backward motion, and the rotatory motion, as is most especially shown by those who exhibit dances. It is affirmed also that the secretions of the body are performed in the aforesaid number of seven. For tears are poured out through the eyes, and the purifications of the head through the nostrils, and through the mouth the saliva which is spit out; there are, besides two other channels for the evacuation of the superfluities of the body, the one being placed in front and the other behind; the sixth mode of evacuation is the effusion of perspiration over the whole body, and the seventh that most natural exercise of the generative powers. Again, in the case of women, the flux called the catamenia, is usually carried on for seven days. Also, children in the womb receive life at the end of seven months, so that a very extraordinary thing happens: for children who are born at the end of the seventh month live, while those who are born at the expiration of the eighth month are altogether incapable of surviving. Again, the dangerous diseases of the body, especially when lasting fevers, arising from the distemperature of the powers within us, attack us, are usually decided about the seventh day. For that day determines the contest for life, allotting safety to some men, and death to others. [Philo of Alexandria On the Creation 89 - 125]