Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/28

 Moreover in the fourth Text; doth he not after some other Doctrines, prove it by another demonstration? Scilicet, That no transition is made but according to some defect (and so there is a transition or passing from the line to the superficies, because the line is defective in breadth) and that it is impossible for the perfect to want any thing, it being every way so; therefore there is no transition from the Solid or Body to any other magnitude. Now think you not that by all these places he hath sufficiently proved, how that there's no going beyond the three dimensions, Length, Breadth, and Thickness, and that therefore the body or solid, which hath them all, is perfect?

To tell you true, I think not my self bound by all these reasons to grant any more but onely this, That that which hath beginning, middle, and end, may, and ought to be called perfect: But that then, because beginning, middle, and end, are Three, the number Three is a perfect number, and hath a faculty of conferring Perfection on those things that have the same, I find no inducement to grant; neither do I understand, nor believe that, for example, of feet, the number three is more perfect then four or two, nor do I conceive the number four to be any imperfection to the Elements: and that they would be more perfect if they were three. Better therefore it had been to have left these subtleties to the Rhetoricians, and to have proved his intent, by necessary demonstration; for so it behoves to do in demonstrative sciences.

You seem to scorn these reasons, and yet it is all the Doctrine of the Pythagorians, who attribute so much to numbers; and you that be a Mathematician, and believe many opinions in the Pythagorick Philosophy, seem now to contemn their Mysteries.

That the Pythagorians had the science of numbers in high esteem, and that Plato himself admired humane understanding, and thought that it pertook of Divinity, for that it understood the nature of numbers, I know very well, nor should I be far from being of the same opinion: But that the Mysteries for which Pythagoras and his sect, had the Science of numbers in such veneration, are the follies that abound in the mouths and writings of the vulgar, I no waies credit: but rather because I know that they, to the end admirable things might not be exposed to the contempt, and scorne of the vulgar, censured as sacrilegious, the publishing of the abstruce properties of Numbers, and incommensurable and irrational quantities, by them investigated; and divulged, that he who discovered them, was tormented in the other World: I believe that some one of them to deter the common sort, and free himself from their inquisitiveness, told them that the mysteries of numbers were those trifles, which afterwards did so