Text: VI. And first of all, I will speak of those which rather resemble heads of laws, of which in the first place one must at once admire the number, inasmuch as they are completed in the perfect number of the decade, which contains every variety of number, both those which are even, and those which are odd, and those which are even-odd; {1}{liddell and Scott explain this as meaning such even numbers as become odd when divided, as 2, 6, 10, 14, etc.} the even numbers being such as two, the odd numbers such as three, the even-odd such as five, it also comprehends all the varieties of the multiplication of numbers, and of those numbers which contain a whole number and a fraction, and of those which contain several fractional parts; (21) it comprehends likewise all the proportions; the arithmetical, which exceeds and it exceeded by an equal number: as in the case of the numbers one, and two, and three; and the geometrical, according to which, as the proportion of the first number is to the second, the same is the ratio of the second to the third, as is the case in the numbers one, two and four; and also in multiplication, which double, or treble, or in short multiply figures to any extent; also in those which are half as much again as the numbers first spoken of, or one third greater, and so on. It also contains the harmonic proportion, in accordance with which that number which is in the middle between two extremities, is exceeded by the one, and exceeds the other by an equal part; as is the case with the numbers three, four, and six. (22) The decade also contains the visible peculiar properties of the triangles, and squares, and other polygonal figures; also the peculiar properties of symphonic ratios, that of the diatessaron in proportion exceeding by one fourth, as is the ratio of four to three; that of fifths exceeding in the ratio of half as much again, as is the case with the proportion of three to two. Also, that of the diapason, where the proportion is precisely twofold, as is the ratio of two to one, or that of the double diapason, where the proportion is fourfold, as in the ratio of eight to two. (23) And it is in reference to this fact that the first philosophers appear to me to have affixed the names to things which they have given them. For they were wise men, and therefore they very speciously called the number ten the decade (teµn dekada), as being that which received every thing (hoµsanei dechada ousan), from receiving (tou dechesthai) and containing every kind of number, and ratio connected with number, and every proportion, and harmony, and symphony. VII. (24) Moreover, at all events, in addition to what has been already said, any one may reasonably admire the decade for the following reason, that it contains within itself a nature which is at the same time devoid of intervals and capable of containing them. Now that nature which has no connection with intervals is beheld in a point alone; but that which is capable of containing intervals is beheld under three appearances, a line, and a superficies, and a solid. (25) For that which is bounded by two points is a line; and that which has two dimensions or intervals is a superficies, the line being extended by the addition of breadth; and that which has three intervals is a solid, length and breadth having taken to themselves the addition of depth. And with these three nature is content; for she has not engendered more intervals or dimensions than these three. (26) And the archetypal numbers, which are the models of these three are, of the point the limit, of the line the number two, and of the superficies the number three, and of the solid the number four; the combination of which, that is to say of one, and two, and three, and four completes the decade, which displays other beauties also in addition to those which are visible. (27) For one may almost say that the whole infinity of numbers is measured by this one, because the boundaries which make it up are four, namely, one, two, three, and four; and an equal number of boundaries, corresponding to them in equal proportions, make up the number of a hundred out of decades; for ten, and twenty, and thirty, and forty produce a hundred. And in the same way one may produce the number of a thousand from hundreds, and that of a myriad from thousands. (28) And the unit, and the decade, and the century, and the thousand, are the four boundaries which generate the decade, which last number, besides what has been already said, displays also other differences of numbers, both the first, which is measured by the unit alone, of which an instance is found in the numbers three, or five, or seven; and the square which is the fourth power, which is an equally equal number. Also the cube, which is the eighth power, which is equally equal equally, and also the perfect number, the number six, which is made equal to its component parts, three, and two, and one. VIII. (29) But what is the use now of enumerating the excellencies of the decade, which are infinite in number; treating our most important task as one of no importance, which is, indeed, of itself most all-sufficient, and worthy material for the study of those who devote themselves to mathematics? The other points we must pass over for the present; but perhaps it may not be out of place to mention one by way of example; (30) for those who have devoted themselves to the doctrines of philosophy say that what are called the categories in nature are ten only in number, --quality, essence, quantity, relation, action, passion, possession, condition, and those two without which nothing can exist, time and place. (31) For there is nothing which is devoid of participation in these things; as, for instance, I partake of essence, borrowing of each one of the elements of which the whole world was made, that is to say, of earth and water, and air and fire, what is sufficient for my own existence. I also partake of quality, inasmuch as I am a man; and of quantity, inasmuch as I am a man of such and such a size. I also partake of relation, when any one is on my right hand or on my left. Again, I am in action when I rub or burn any thing. I am in passion when I am cut or rubbed by any one else. I am discerned as a possessor, when I am clothed or equipped with anything. And I am seen in condition, when sitting still or lying down. And I am altogether in time and place, since not one of all the categories just mentioned can exist without both these things. IX. (32) This, then, may be enough to say on these subjects; but it is necessary now to connect with these things what I am about to say, namely, that it was the Father of the universe who delivered these ten maxims, or oracles, or laws and enactments, as they truly are, to the whole assembled nation of men and women altogether. Did he then do so, uttering himself some kind of voice? Away! let not such an idea ever enter your mind; for God is not like a man, in need of a mouth, and of a tongue, and of a windpipe, (33) but as it seems to me, he at that time wrought a most conspicuous and evidently holy miracle, commanding an invisible sound to be created in the air, more marvellous than all the instruments that ever existed, attuned to perfect harmonies; and that not an inanimate one, nor yet, on the other hand, one that at all resembled any nature composed of soul and body; but rather it was a rational soul filled with clearness and distinctness, which fashioned the air and stretched it out and changed it into a kind of flaming fire, and so sounded forth so loud and articulate a voice like a breath passing through a trumpet, so that those who were at a great distance appeared to hear equally with those who were nearest to it. (34) For the voices of men, when they are spread over a very long distance, do naturally become weaker and weaker, so that those who are at a distance from them cannot arrive at a clear comprehension of them, but their understanding is gradually dimmed by the extension of the sound over a larger space, since the organs also by which it is extended are perishable. (35) But the power of God, breathing forth vigorously, aroused and excited a new kind of miraculous voice, and diffusing its sound in every direction, made the end more conspicuous at a distance than the beginning, implanting in the soul of each individual another hearing much superior to that which exists through the medium of the ears. For the one, being in some degree a slower kind of external sense, remains in a state of inactivity until it is struck by the air, and so put in motion. But the sense of the inspired mind outstrips that, going forth with the most rapid motion to meet what is said.

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