Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/153

 tarding, as being contrary to nature; and would be longer or shorter, according to the greater or less impulse, and according to the greater or less acclivity.

It seems, then, that hitherto you have explained to me the accidents of a moveable upon two different Planes; and that in the inclining plane, the grave moveable doth spontaneously descend, and goeth continually accelerating, and that to retain it in rest, force must be used therein: but that on the ascending plane, there is required a force to thrust it forward, and also to stay it in rest, and that the motion impressed goeth continually diminishing, till that in the end it cometh to nothing. You say yet farther, that in both the one and the other case, there do arise differences from the planes having a greater or less declivity or acclivity; so that the greater inclination is attended with the greater velocity; and contrariwise, upon the ascending plane, the same moveable thrown with the same force, moveth a greater distance, by how much the elevation is less. Now tell me, what would befall the same moveable upon a superficies that had neither acclivity nor declivity?

Here you must give me a little time to consider of an answer. There being no declivity, there can be no natural inclination to motion: and there being no acclivity, there can be no resistance to being moved; so that there would arise an indifference between propension and resistance of motion; therefore, methinks it ought naturally to stand still. But I had forgot my self: it was but even now that Sagredus gave me to understand that it would so do.

So I think, provided one did lay it down gently: but if it had an impetus given it towards any part, what would follow?

There would follow, that it should move towards that part.

But with what kind of motion? with the continually accelerated, as in declining planes; or with the successively retarded, as in those ascending.

I cannot tell how to discover any cause of acceleration, or retardation, there being no declivity or acclivity.

Well: but if there be no cause of retardation, much less ought there to be any cause of rest. How long therefore would you have the moveable to move?

As long as that superficies, neither inclined nor declined shall last.

Therefore if such a space were interminate, the motion upon the same would likewise have no termination, that is, would be perpetual.