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 bound the infinity and unstable nature of matter by forms, and numbers and reasons, through which both the wholes and parts of all mortal natures are variegated with proper numbers. But it every where connects the precedaneous and more perfect genera of the Gods by the odd number, but the subordinate and secondary genera, by the even number. Thus for instance, in the intellectual orders, it produces the female and the prolific according to the even number, but the male and the paternal according to the odd number. But in the supermundane orders, it characterizes similitude and the immutable according to the odd number, but dissimilitude and a progression into secondary natures, according to the even number. For thus the Athenian guest also, orders that in sacred worship odd things should be distributed to the celestial, but even to the terrestrial powers. And according to each of these genera that which is of a more ruling nature must be referred to the odd number, but that which is subordinate, to the even number.

The nature of number, therefore, pervades from on high, as far as to the fast of things, adorning all things, and connecting them by appropriate forms. For how could a perfect number comprehend the period of the whole world, as the Muses in Plato assert that it does? Or how could numbers, some of which are productive of fertility, and others of sterility, comprehend the descents of souls? Or how could some of them define the ascents of souls in less, but others in greater periods, as Socrates says in the Phædrus, where he delivers to us restitutions consisting of three thousand and ten thousand years? Or how could time itself which is unically comprehensive of the psychical measures, proceed according to number, as Timæus says it does, unless divine number exists prior to all these, which imparts to all things a principal cause of order according to numbers? Since all things therefore subsist through numbers and forms, numbers are allotted a progression, from the intellectual summit. But forms have their generation from intelligible forms. For forms subsist primarily in the third triad of intelligibles. But numbers are primarily in the first triad of intellectuals; since also in the effects of these, every number indeed is form, but not every form is number.