Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/200

 tion, from which ensueth the separation and elongation of the pen from the Earth?

I cannot tell.

How, do you not know that? The moveable is here the same, that is, the same pen; now how can the same moveable superate and exceed it self in motion?

I do not see how it can overcome or yield to it self in motion, unlesse by moving one while faster, and another while slower.

You see then, that you do know it. If therefore the projection of the pen ought to follow, and its motion by the tangent be to overcome its motion by the secant, what is it requisite that their velocities should be?

It is requisite that the motion by the tangent be greater than that other by the secant. But wretch that I am! Is it not only many thousand times greater than the descending motion of the pen, but than that of the stone? And yet like a simple fellow I had suffered my self to be perswaded, that stones could not be extruded by the revolution of the Earth. I do therefore revoke my former sentence, and say, that if the Earth should move, stones, Elephants, Towers, and whole Cities would of necessity be tost up into the Air; and because that that doth not evene, I conclude that the Earth doth not move.

Softly Simplicius, you go on so fast, that I begin to be more afraid for you, than for the pen. Rest a little, and observe what I am going to speap. If for the reteining of the stone or pen annexed to the Earths surface it were necessary that its motion of descent were greater, or as much as the motion made by the tangent; you would have had reason to say, that it ought of necessity to move as fast, or faster by the secant downwards, than by the tangent Eastwards: But did not you tell me even now, that a thousand yards of distance by the tangent from the contact, do remove hardly an inch from the circumference? It is not sufficient therefore that the motion by the tangent, which is the same with that of the diurnall Vertigo, (or hasty revolution) be simply more swift than the motion by the secant, which is the same with that of the pen in descending; but it is requisite that the same be so much more swift as that the time which sufficeth for the pen to move v. g. a thousand yards by the tangent, be insufficient for it to move one sole inch by the secant. The which I tell you shall never be, though you should make that motion never so swift, and this never so slow.

And why might not that by the tangent be so swift, as not to give the pen time to return to the surface of the Earth?

Try whether you can state the case in proper termes,