Select Works of Plotinus — trans. Thomas Taylor

n this, that it is one simply, and that according to the one it is also at the same time all things. But the first is above the one and all things, being more simple than either of these.”

P. 558. There are apocatastatic periods of the stars and. spheres.

Of these periods of the stars, which are the causes of fertility and sterility in the sublunary region, Plato speaks in the 8th book of his Republic. And as what he says on this subject is no less obscure than important, I shall pre¬ sent the reader with the following attempt to elucidate his meaning, and to develope the mysteries of the geometric number, which he observes is the author of better and worse generations. The whole is extracted from the notes to my translation of the Republic.

In the first place, then, the passage respecting this num¬ ber is as follows : u It is indeed difficult for a city thus constituted to be changed ; but as every thing which is generated is obnoxious to corruption, neither will such a constitution as this remain for ever, but be dissolved. And its dissolution is this. Not only with respect to ter¬ restrial plants, but likewise in terrestrial animals, a fer¬ tility and sterility of soul as well as of body takes place.

p. 593

when the revolutions of the heavenly bodies complete the periphery of their respective orbits, which are shorter to the shorter-lived, and contrariwise to such as are the contrary. And with reference to the fertility and sterility of our race, although those are wise that you have edu¬ cated to be governors of cities, yet will they never by rea¬ son in conjunction with sense, observe the proper seasons, but overlook them, and sometimes generate children when they ought not. But the period to that which is divinely generated is that which the perfect number comprehends ; and to that which is generated by man, that period in which the augmentations surpassing and surpassed, when they shall have received three restitutions and four bound¬ aries of things assimilating and dissimilating, increasing and decreasing, shall render all things correspondent and effable ; of which the sesquitertian progeny, when con¬ joined with the pentad, and thrice increased, affords two harmonies. One of these, the equally equal, is a hun¬ dred times a hundred ; but the other, of equal length indeed, but more oblong, is of a hundred numbers from effable diameters of pentads, each being deficient by unity, and from two numbers that are ineffable, and from a hun¬ dred cubes of the triad.

a hun¬ dred times a hundred ; but the other, of equal length indeed, but more oblong, is of a hundred numbers from effable diameters of pentads, each being deficient by unity, and from two numbers that are ineffable, and from a hun¬ dred cubes of the triad. But the whole geometric number of this kind, is the author of better and worse generations ; of which when our governors being ignorant, join our couples together unseasonably, the children shall neither be of a good genius, nor fortunate/’

Plot.

2P oD4

In the second place, with respect to the meaning of what is here said by Plato, as to the periodical mutation of things in the sublunary region, it must be observed, that all the parts of the universe are unable to participate of the providence of divinity in a similar manner, but some of its parts enjoy this eternally, and others temporally ; some in a primary, and others in a secondary degree. For the universe being a perfect whole, must have a first, a middle, and a last part. But its first parts as having the most excellent subsistence, must always exist according to nature ; and its last parts must sometimes subsist ac¬ cording to, and sometimes contrary to nature. Hence the celestial bodies, which are the first parts of the universe, perpetually subsist according to nature, both the whole spheres, and the multitude co-ordinate to these w holes ; and the only alteration which they experience, is a muta¬ tion of figure, and variation of light at different periods. But in the sublunary region, while the spheres of the ele¬ ments remain on account of their subsistence as wholes, always according to nature, the parts of these wholes have sometimes a natural, and sometimes an unnatural subsist¬ ence ; for thus alone can the circle of generation unfold all the variety w'hich it contains.

The different periods in which these mutations happen, are called by Plato, with great propriety, periods of fertility and sterility. For in these periods, a fertility or sterility ofp. 595 men, animals, and plants, takes place ; so that in fertile periods, mankind will be both more numerous, and upon the whole, superior in mental and bodily endowments to the men of a barren period. And a similar reasoning must be extended to animals and plants. The so much celebrated heroic age, was the result of one of these fertile periods, in which men transcending the herd of mankind, both in practical and intellectual virtue, abounded on the earth.

. And a similar reasoning must be extended to animals and plants. The so much celebrated heroic age, was the result of one of these fertile periods, in which men transcending the herd of mankind, both in practical and intellectual virtue, abounded on the earth.

With respect to the epithet divinely generated , it is well observed by the Greek scholiast, t( that Plato does not mean by this either the whole world, though the epithet is primarily applicable to it, nor the celestial

\ regions only, nor the sublunary world, but every thing which is perpetually and circularly moved , whether in the heavens, or under the moon ; so far as it is corporeal calling it generated, (for no body is self-subsistent,) but so far as it is perpetually moved, divine . For it imitates the most divine of things, which possess an ever-vigilant life. But with respect to the perfect number mentioned here by Plato, we must not only direct our attention to a per¬ fect number in vulgar arithmetic, — for this is rather num¬ bered than number, tends to perfection and is never perfect, as being always in generation,— but we must survey the cause of this number, which is indeed intellec¬ tual, but comprehends the definite boundary of every

\ period of the world.”

596'

In the third place let us consider what Plato means by augmentations surpassing and surpassed ; things assimi¬ lating and dissimilating, increasing and decreasing, corre¬ spondent and effable.

Augmentations surpassing, are ratios of greater inequa¬ lity, viz. when the greater is compared to the less, and are multiples, super-particulars, super-partients, multiple su¬ per-particulars, and multiple super-partients. But mul¬ tiple ratio is, as we have elsewhere shown, when a greater quantity contains a less many times ; super-particular ratio is, when the greater contains the less quantity once, and some part of it besides ; and super-partient ratio is, when the greater contains the less quantity once, and certain parts of it likewise. Again, multiple super-parti¬ cular ratio is, when the greater contains the less many times, and some part of it besides ; and multiple superpartient ratio is, when the greater contains the less many times, and also some of its parts. But augmentations surpassed, are ratios of less inequality, viz. when the less is compared with the greater quantity ; as for instance, sub-multiples, sub-super-particulars, and sub-super-partients, and those which are composed from these three. Those numbers are called by Plato assimilating and dis¬ similating, which are denominated by arithmeticians simi¬ lar and dissimilar.