על עשרת הדברות ו׳On the Decalogue 6
א׳
1[20] I will deal with both to the best of my ability, taking those which are rather of the nature of summaries first.
ב׳
2Here our admiration is at once aroused by their number, which is neither more nor less than is the supremely perfect, Ten. Ten contains all different kinds of numbers, even as 2, odd as 3, and even-odd as 6, and all ratios, whether of a number to its multiples or fractional, when a number is either increased or diminished by some part of itself. So too it contains all the analogies or progressions,
ג׳
3[21] the arithmetical where each term in the series is greater than the one below and less than the one above by the same amount, as for example 1 2 3; the geometrical where the ratio of the second to the first term is the same as that of the third to the second, as with 1 2 4, and this is seen whether the ratio is double or treble or any multiple, or again fractional as 3 to 2, 4 to 3, and the like; once more the harmonic in which the middle term exceeds and is exceeded by the extremes on either side by the same fraction, as is the case with 3, 4, 6.
ד׳
4[22] Ten also contains the properties observed in triangles, quadrilaterals and other polygons, and also those of the concords, the fourth, fifth, octave and double octave intervals, where the ratios are respectively 1⅓, i.e. 4: 3, 1½, i.e. 3: 2, doubled, i.e. 2:1, fourfold, i.e. 8:2.
ה׳
5[23] Consequently it seems to me that those who first gave names to things did reasonably, wise men that they were, in giving it the name of decad, as being the dechad, or receiver, because it receives and has made room for every kind of number and numerical ratio and progressions and also concords and harmonies.