V. (18) 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 said what is fitting concerning these matters, I shall now proceed in regular order to discuss the laws themselves with accuracy and precision: first of all of necessity, mentioning this point, that of his laws God himself, without having need of any one else, thought fit to promulgate some by himself alone, and some he promulgated by the agency of his prophet Moses, whom he selected, by reason of his pre-eminent excellence, out of all men, as the most suitable man to be the interpreter of his will. (19) 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; (20) and I will explain each kind as well as I can.

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.

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