Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/146

 But if it should happen that the Terrestrial Globe did move round, and consequently carry the Tower also along with it, and that the stone did then also grate and slide along the side of the Tower, what must its motion be then?

In this case we may rather say its motions: for it would have one wherewith to descend from the top of the Tower to the bottom, and should necessarily have another to follow the course of the said Tower.

So that its motion should be compounded of two, to wit, of that wherewith it measureth the Tower, and of that other wherewith it followeth the same: From which composition would follow, that the stone would no longer describe that simple right and perpendicular line, but one transverse, and perhaps not streight.

I can say nothing of its non-rectitude, but this I know very well, that it would of necessity be transverse, and different from the other directly perpendicular, which it doth describe, the Earth standing still.

You see then, that upon the meer observing the falling stone to glide along the Tower, you cannot certainly affirm that it describeth a line which is streight and perpendicular, unless you first suppose that the Earth standeth still.

True; for if the Earth should move, the stones motion would be transverse, and not perpendicular.

Behold then the Paralogism of Aristotle and Ptolomey to be evident and manifest, and discovered by you your self, wherein that is supposed for known, which is intended to be demonstrated.

How can that be? To me it appeareth that the Syllogism is rightly demonstrated without petitionem principii.

You shall see how it is; answer me a little. Doth he not lay down the conclusion as unknown?

Unknown; why otherwise the demonstrating it would be superfluous.

But the middle term, ought not that to be known?

Its necessary that it should; for otherwise it would be a proving ignotum per æquè ignotum.

Our conclusion which is to be proved, and which is unknown, is it not the stability of the Earth?

It is the same.

The middle term, which ought to be known, is it not the streight and perpendicular descent of the stone?

It is so.

But was it not just now concluded, that we can have no certain knowledg whether that same shall be direct and perpen-