have reasoned upon certain principles, and that they have all had access to the same data whereon to ground their calculations. When, therefore, I find this same number 608 constantly occurring as a number in some way or other connected with their periods, I cannot help believing that it has been used by the persons formerly making the ancient calculations. Thus in this I find 608 years to form one boundary, or to come out as one number. Again, in the inquiry into the proper period from the foundation of Rome, on which the Ludi Sæculares ought to be celebrated in the time of Sylla, I find that the result of the very difficult calculations of one or some of the aruspices employed for the purpose of making the calculations, brings out the number 608 as one of the probable periods on which they ought to be celebrated; and, as I find several other such coincidences with this peculiar number, I cannot help thinking that they tend greatly to confirm my doctrines. It shews that this sacred number was in general use, and it justifies me in believing that it was often used in cases where the direct evidence of its use is only weak, but where analogy of reasoning would induce me to expect to find it.
It is impossible to read Stanley’s account of the doctrines of Pythagoras and not to see that, as a complete system, they were totally unknown to the persons who have left us the account of them. One says one thing, another says another. But it is evident, that much the greater part of what they say is opinion only; or what they had heard, as being the opinion of some one else. This state of uncertainty is the inevitable consequence of abstruse doctrines handed down by tradition. Then it follows, that evidence in these cases can amount at last only to probability, never to absolute demonstration. But when the probability is sufficiently strong, faith or belief will follow. And I think in reasoning, I have a right to take any asserted fact and reason upon it, depending for its reception by the reader, upon such evidence, positive, or circumstantial, or rational, as I shall be able to produce. Now I will produce an example of what I mean. We have every reason to believe, that Pythagoras travelled far to the East to acquire knowledge. In looking through the great mass of facts or doctrines charged to him, we find much oriental doctrine intermixed with truth and science, the same as we find at this day among the Brahmins: truth and science very much more correct than that which his successors (whose ignorance or uncertainty respecting him is admitted) knew or taught, mixed with an inconceivable mass of nonsense, of that description of nonsense, too, which his followers particularly patronized, and taught as sense and wisdom. Have we not, then, reason to make a selection, and give Pythagoras credit only for such parts as we find of the wise character to which I have alluded, and throw out all the remainder as the nonsense of his successors? What can be more striking than the fact of his teaching that the planets moved in curved orbits, a fact for the statement of which he got laughed at by his ignorant successors, but a fact which we now know to be well-founded!
All his doctrines, we are told by his followers, were founded on numbers, and they pretend to give us what was meant by these numbers, and choice nonsense they give us,—nonsense very unworthy of the man who taught the 47th proposition of Euclid, and the true planetary system. Then are we to believe them? I reply, no; we ought to believe only such parts as are analogous to the oriental systems, and to good sense. All the remainder must remain sub judice. I find very nearly the whole of the doctrine of numbers ascribed to him, by his successors, as nonsensical as their story of his golden thigh, so that I can give no credit to them; and, in consequence, I am obliged to have recourse to the East, and to suppose that when they repeat the admitted fact, that his doctrines were founded on numbers, the oriental numbers, on which the astronomical cycles and periods were founded, must chiefly be meant: such as the Zodiacal divisions, the Neros, the precessional year, &c. And this is confirmed when I read what has been extracted respecting Pythagoras from La Loubère, and when I find them stumbling on the cycle of the great Neros. If Pythagoras were not in some way or other connected with it, it seems surprising that this iden-
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