Concerning the procreation of the soul as discoursed in Timaeus (28-30)

Nor is the celestial nature privileged from this double society and communion. For sometimes it is seen to incline one way or the other, but it is set right again by the more powerful revolution of the Same, and governs

the world. Nay, there shall come a time, as it has happened already, when the world’s moving wisdom shall grow dull and drowsy, drowned in oblivion of its own duty; while that which is familiar and agreeable to the body from the beginning draws and winds back the right-hand motion of the universe, causing the wheels to go slow and heavy. Yet shall it not be able to dash in pieces the whole movement, for that the better part, rousing and recollecting herself and observing the pattern and exemplar of God, shall with his aid reduce all things again into their former order. Thus it is demonstrable by many proofs, that the soul was not altogether the workmanship of the Deity, but that having in itself a certain portion of innate evil, it was by him digested and beautified who limited infinity by unity, to the end it might be a substance within the compass of certain limits; intermixing order and mutation, variety and resemblance, by the force of the Same and the Other; and lastly working into all these, as far as it was possible, a mutual community and friendship by the assistance of numbers and harmony.

Concerning which things, although you have heard frequent discourses, and have likewise read several arguments and disputes committed to writing upon the same subjects, it will not be amiss for me also to give a short account, after a brief repetition of Plato’s own words. God, said he, in the first place withdrew one part from the whole; which done, he took away the double of that; then a third part, sesquialter in proportion to the second, and triple to the first; then a fourth part, double to the second; next a fifth part, being the triple of the third; then a sixth, eight times the first; and lastly a seventh, being twenty-seven times the first. This done, he filled up the duple and triple intervals, retrenching also from thence certain other particles, and placing them in the midst of those intervals; so that in every interval

there might be two medieties, the one exceeding and being exceeded by one and the same part of the extremes, the other exceeding and being exceeded by the same number. Now in regard that from these connections in the first spaces there arose the intervals of sesquialters, sesquiterces, and sesquioctaves, he filled up all the sesquiterce intervals with sesquioctaves, leaving a part of each, so that the interval left of the part might bear the numerical proportion of 256 to 243. [*]

Here the question will be first concerning the quantity, next concerning the order, and in the third place concerning the force and virtue of the numbers. As to the quantity, we are to consider which he takes in the double and triple intervals. As to the order, whether they are to be placed in one row, according to the direction of Theodorus, or (as Crantor will have them) in the form of a Λ, placing the unit at the top, and the duples and triples apart by themselves in two several files. Lastly, we are to examine of what use and virtue they are in the structure and composition of the soul.

As to the first, we shall relinquish the opinion of those who affirm that it is enough, in proportions, to consider the nature of the intervals, and of the medieties which fill up their vacancies; and that the demonstration can be made out for any numbers whatsoever that have spaces sufficient to receive the aforesaid proportions. For this being granted, it makes the demonstration obscure, without the help of schemes, and drives us from another theory, which carries with it a delight not unbecoming philosophy.

Beginning therefore from the unit, let us place the duples and triples apart; and there will be on the one side, 2, 4, 8; on the other 3, 9, 27; —seven numbers in all, proceeding forward by

multiplication four steps from the unit, which is assumed as the common base. ⋯ For not only here, but upon other occasions, the sympathy of the quaternary number with the septenary is apparent. There is this peculiar to that tetractys or quaternary number thirty six, so much celebrated by the Pythagoreans, which is more particularly worthy admiration,—that it is composed of the first four even numbers and the first four odd numbers; and it is the fourth connection made of numbers put together in order. The first connection is of one and two; the second of odd numbers. ⋯ For placing the unit, which is common to both, before, he first takes eight and then twenty-seven, as it were pointing out with the finger where to place each particular sort.

[These places are so depraved in the original, that the sense is lost.]

But it belongs to others to explain these things more accurately and distinctly; while we content ourselves with only what remains, as peculiarly proper to the subject in hand.