Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/198

 of the circle, as a point that was distant from the contaction one palm, and the point that was distant half a palm, I likewise believe would fearse recede the fourth part of the distance of the second: so that within an inch or two of the contact, the separation of the Tangent from the circumference is scarse discernable.

So that the recession of the project from the circumference of the precedent circular motion is very small in the begining?

Almost insensible.

Now tell me a little; the project, which from the motion of the projicient receiveth an impetus of moving along the Tangent in a right line, and that would keep unto the same, did not its own weight depress it downwards, how long is it after the separation, ere it begin to decline downwards.

I believe that it beginneth presently; for it not having any thing to uphold it, its proper gravity cannot but operate.

So that, if that same stone, which being extruded from that wheel turn'd about very fast, had as great a natural propension of moving towards the centre of the said wheel, as it hath to move towards the centre of the Earth, it would be an easie matter for it to return unto the wheel, or rather not to depart from it; in regard that upon the begining of the separation, the recession being so small, by reason of the infinite acuteness of the angle of contact, every very little of inclination that draweth it back towards the centre of the wheel, would be sufficient to retain it upon the rim or circumference.

I question not, but that if one suppose that which neither is, nor can be, to wit, that the inclination of those grave bodies was to go towards the centre of the wheel, they would never come to be extruded or shaken off.

But I neither do, nor need to suppose that which is not; for I will not deny but that the stones are extruded. Yet I speak this by way of supposition, to the end that you might grant me the rest. Now fancy to your self, that the Earth is that great wheel, which moved with so great velocity is to extrude the stones. You could tell me very well even now, that the motion of projection ought to be by that right line which toucheth the Earth in the point of separation: and this Tangent, how doth it notably recede from the superficies of the Terrestrial Globe?

I believe, that in a thousand yards, it will not recede from the Earth an inch.

And did you not say, that the project being drawn by its own weight, declineth from the Tangent towards the centre of the Earth?