Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/206

 ver so small, yet is it alwayes more than sufficient to reconduct the moveable to the circumference, from which it is distant but its least space, that is, nothing at all.

Your discourse, I must confess, is very accurate; and yet no less concluding than it is ingenuous; and it must be granted that to go about to handle natural questions, without Geometry, is to attempt an impossibility.

But Simplicius will not say so; and yet I do not think that he is one of those Peripateticks that disswade their Disciples from studying the Mathematicks, as Sciences that vitiate the reason, and render it lesse apt for contemplation.

I would not do so much wrong to Plato, but yet I may truly say with Aristotle, that he too much lost himself in, and too much doted upon that his Geometry: for that in conclusion these Mathematical subtilties Salviatus are true in abstract, but applied to sensible and Physical matter, they hold not good. For the Mathematicians will very well demonstrate for example, that Sphæra tangit planum in puncto; a position like to that in dispute, but when one cometh to the matter, things succeed quite another way. And so I may say of these angles of contact, and these proportions; which all evaporate into Air, when they are applied to things material and sensible.

You do not think then, that the tangent toucheth the superficies of the terrestrial Globe in one point only?

No, not in one sole point; but I believe that a right line goeth many tens and hundreds of yards touching the surface not onely of the Earth, but of the water, before it separate from the same.

But if I grant you this, do not you perceive that it maketh so much the more against your cause? For if it be supposed that the tangent was separated from the terrestrial superficies, yet it hath been however demonstrated that by reason of the great acuity of the angle of contingence (if happily it may be call'd an angle) the project would not separate from the same; how much lesse cause of separation would it have, if that angle should be wholly closed, and the superficies and the tangent become all one? Perceive you not that the Projection would do the same thing upon the surface of the Earth, which is asmuch as to say, it would do just nothing at all? You see then the power of truth, which while you strive to oppose it, your own assaults themselves uphold and defend it. But in regard that you have retracted this errour, I would be loth to leave you in that other which you hold, namely, that a material Sphere doth not touch a plain in one sole point: and I could wish some few hours conversation with some persons conversant in Geometry, might make you a little more intelligent