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

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 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. 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 (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.

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 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. 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. [Philo Decalogue 20 - 28]