Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/210

 same in concrete, as they are imagined to be in abstract?

This I do affirm.

Then when ever in concrete you do apply a material Sphere to a material plane, you apply an imperfect Sphere to an imperfect plane, & these you say do not touch only in one point. But I must tell you, that even in abstract an immaterial Sphere, that is, not a perfect Sphere, may touch an immaterial plane, that is, not a perfect plane, not in one point, but with part of its superficies, so that hitherto that which falleth out in concrete, doth in like manner hold true in abstract. And it would be a new thing that the computations and rates made in abstract numbers, should not afterwards answer to the Coines of Gold and Silver, and to the merchandizes in concrete. But do you know Simplicius, how this commeth to passe? Like as to make that the computations agree with the Sugars, the Silks, the Wools, it is necessary that the accomptant reckon his tares of chests, bags, and such other things: So when the Geometricall Philosopher would observe in concrete the effects demonstrated in abstract, he must defalke the impediments of the matter, and if he know how to do that, I do assure you, the things shall jump no lesse exactly, than Arithmetical computations. The errours therefore lyeth neither in abstract, nor in concrete, nor in Geometry, nor in Physicks, but in the Calculator, that knoweth not how to adjust his accompts. Therefore if you had a perfect Sphere and plane, though they were material, you need not doubt but that they would touch onely in one point. And if such a Sphere was and is impossible to be procured, it was much besides the purpose to say, Quod Sphæra ænea non tangit in puncto. Furthermore, if I grant you Simplicius, that in matter a figure cannot be procured that is perfectly spherical, or perfectly level: Do you think there may be had two materiall bodies, whose superficies in some part, and in some sort are incurvated as irregularly as can be desired?

Of these I believe that there is no want.

If such there be, then they also will touch in one sole point; for this contact in but one point alone is not the sole and peculiar priviledge of the perfect Sphere and perfect plane. Nay, he that should prosecute this point with more subtil contemplations would finde that it is much harder to procure two bodies that touch with part of their snperficiessuperficies [sic], than with one point onely. For if two superficies be required to combine well together, it is necessary either, that they be both exactly plane, or that if one be convex, the other be concave; but in such a manner concave, that the concavity do exactly answer to the convexity of the other: the which conditions are much harder to be found, in regard of their too narrow determination, than those others, which in their casuall latitude are infinite.