Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/31

 And who saith that I cannot draw other lines? why may not I protract another line underneath, unto the point A, that may be perpendicular to the rest?

You can doubtless, at one and the same point, make no more than three right lines concurre, that constitute right angles between themselves.

I see what Simplicius means, namely, that should the said DA be prolonged downward, then by that means there might be drawn two others, but they would be the same with the first three, differing onely in this, that whereas now they onely touch, then they would intersect, but not produce new dimensions.

I will not say that this your argument may not be concludent; but yet this I say with Aristotle, that in things natural it is not alwaies necessary, to bring Mathematical demonstrations.

Grant that it were so where such proofs cannot be had, yet if this case admit of them, why do not you use them? But it would be good we spent no more words on this particular, for I think that Salviatus will yield, both to Aristotle, and you, without farther demonstration, that the World is a body, and perfect, yea most perfect, as being the greatest work of God.

So really it is, therefore leaving the general contemplation of the whole, let us descend to the consideration of its parts, which Aristotle, in his first division, makes two, and they very different and almost contrary to one another; namely the Coelestial, and Elementary: that ingenerable, incorruptible, unalterable, unpassible, &c. and this exposed to a continual alteration, mutation, &c. Which difference, as from its original principle, he derives from the diversity of local motions, and in this method he proceeds.

Leaving the sensible, if I may so speak, and retiring into the Ideal world, he begins Architectonically to consider that nature being the principle of motion, it followeth that natural bodies be indued with local motion. Next he declares local motion to be of three kinds, namely, circular, right, and mixt of right and circular: and the two first he calleth simple, for that of all lines the circular, and right are onely simple; and here somewhat restraining himself, he defineth anew, of simple motions, one to be circular, namely that which is made about the medium, and the other namely the right, upwards, and downwards; upwards, that which moveth from the medium; downwards, that which goeth towards the medium. And from hence he infers, as he may by and necessary consequence, that all simple motions are confined to these three kinds, namely, to the medium, from the medium, and about the medium; the which corresponds saith he, with what hath been said before of a body, that it also is perfected by three things, and so