Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/39

 I do not very well understand the question.

I will express it better by drawing a Figure: therefore I will suppose the line A B [in Fig. 3.] parallel to the Horizon, and upon the point B, I will erect a perpendicular B C; and after that I adde this slaunt line C A. Understanding now the line C A to be an inclining plain exquisitely polished, and hard, upon which descendeth a ball perfectly round and of very hard matter, and such another I suppose freely to descend by the perpendicular C B: will you now confess that the impetus of that which descends by the plain C A, being arrived to the point A, may be equal to the impetus acquired by the other in the point B, after the descent by the perpendicular C B?

I resolutely believe so: for in effect they have both the same proximity to the centre, and by that, which I have already granted, their impetuosities would be equally sufficient to re-carry them to the same height.

Tell me now what you believe the same ball would do put upon the Horizontal plane A B?

It would lie still, the said plane having no declination.

But on the inclining plane C A it would descend, but with a gentler motion than by the perpendicular C B?

I may confidently answer in the affirmative, it seeming to me necessary that the motion by the perpendicular C B should be more swift, than by the inclining plane CA; yet nevertheless, if this be, how can the Cadent by the inclination arrived to the point A, have as much impetus, that is, the same degree of velocity, that the Cadent by the perpendicular shall have in the point B? these two Propositions seem contradictory.

Then you would think it much more false, should I say, that the velocity of the Cadents by the perpendicular, and inclination, are absolutely equal: and yet this is a Proposition most true, as is also this that the Cadent moveth more swiftly by the perpendicular, than by the inclination.

These Propositions to my ears sound very harsh: and I believe to yours Simplicius?

I have the same sense of them.

I conceit you jest with me, pretending not to comprehend what you know better than my self: therefore tell me Simplicius, when you imagine a moveable more swift than another, what conceit do you fancy in your mind?

I fancie one to pass in the same time a greater space than the other, or to move equal spaces, but in lesser time.

Very well: and for moveables equally swift, what's your conceit of them?

I fancie that they pass equal spaces in equal times.