De Opificio Mundi

But there are two ways of judging of harmonic proportion. One when, whatever ratio the last number bears to the first, the excess by which the last number exceeds the middle one is the same as the excess by which the middle number exceeds the first. And any one may derive a most evident proof of this from the numbers before mentioned, six, and eight, and twelve: for the last number is double the first. And again, the excess of twelve over eight is double the excess of eight over six. For the number twelve exceeds eight by four, and eight exceeds six by two; and four is the double of two.

And another test of harmonic proportion is, when the middle term exceeds and is exceeded by those on each side of it, by an equal portion; for eight being the middle term, exceeds the first term by a third part; for if six be subtracted from it, the remainder two is one third of the original number six: and it is exceeded by the last term in an equal proportion; for if eight be taken from twelve, the remainder four is one third of the whole number twelve.

Let this then be premised, as of necessity it must, respecting the honourable qualities which this diagram or square has, and the name to which it is entitled, and the number seven unfolds an equal number of ideas, and even more in the case of incorporeal things, which are perceptible only by the intellect; and its nature extends also over every visible essence, reaching to both heaven and earth, which are the boundaries of every thing. For what portion of all the things on earth is there which is not fond of seven; being subdued by an affection and longing for the seventh.

Accordingly men say, that the heaven is girdled with seven circles, the names of which are as follows; the arctic, the antarctic, the summer tropic, the winter tropic, the equinoctial, the zodiac, and last of all the galaxy. For the horizon is something which affects ourselves, in proportion as any one has acute vision, or the contrary; our sensation cutting off at one time a lesser, and at