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Concerning the Ten Commandments, which are the Heads of the Law (20-22)

urn:cts:greekLit:tlg0018.tlg023.1st1K-eng1:20-22
Refs {'start': {'reference': '20', 'human_reference': 'Section 20'}, 'end': {'reference': '22', 'human_reference': 'Section 22'}}
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and I will explain each kind as well as I can.

6
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; [*] 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. [*]

v.3.p.141

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.

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