De Decalogo

for they would see that he, who had given them a sufficiency of the means of life was now also giving them a means which should contribute to their living well; accordingly, to live at all required meat and drink which they found, though they had never prepared them; and towards living well, and in accordance with nature and decorum, they required laws and enactments, by which they were likely to be improved in their minds.

These are the causes which may be advanced by probable conjecture, to explain the question which is raised on this point; for the true causes God alone knows. But having

Now those which he delivered in his own person by himself alone, are both laws in general, and also the heads of particular laws; and those which he promulgated by the agency of his prophet are all referred to those others;

and I will explain each kind as well as I can. 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; [*]( 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;

it comprehends likewise all the proportions; the arithmetical, which exceeds and is 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. [*]( Liddell and Scott explain this as meaning such even numbers as become odd when divided, as 2, 6, 10, 14, etc. )

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.

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 (τὴν δεκάδα), as being that which received every thing (ὡσανεὶ δεκάδα οὖσαν), from receiving (τοῦ δέχεσθαι) and containing every kind of number, and ratio connected with number, and every proportion, and harmony, and symphony.

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.

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.

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.

For one may almost say that the whole infinity of

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.

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;

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.

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

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,