of the accelerated degrees of velocity, answering to the triangle ABC, hath passed in such a time such a space, it is very reasonable and probable, that making use of the uniform velocities answering to the parallelogram, it shall passe with an even motion in the same time a space double to that passed by the accelerate motion.
Sagr.I am entirely satisfied. And if you call this a probable Discourse, what shall the necessary demonstrations be? I wish that in the whole body of common Philosophy, I could find one that was but thus concludent.
In natural Sciences it is not necessary to seek Mathematicall evidence.Simpl.It is not necessary in natural Philosophy to seek exquisite Mathematical evidence.
Sagr.But this point of motion, is it not a natural question? and yet I cannot find that Aristotle hath demonstrated any the least accident of it. But let us no longer divert our intended Theme, nor do you fail, I pray you Salviatus, to tell me that which you hinted to me to be the cause of the Pendulum's quiescence, besides the resistance of the Medium ro penetration.
Salv.Tell me; of two penduli hanging at unequal distances, doth not that which is fastned to the longer threed make its vibrations more seldome?
The pendulum hanging at a longer threed, maketh its vibrations more seldome than the pendulum hanging at a shorter threed.Sagr.Yes, if they be moved to equall distances from their perpendicularity.
Salv.This greater or lesse elongation importeth nothing at all, for the same pendulum alwayes maketh its reciprocations in equall times, be they longer or shorter, that is, though the pendulum be little or much removed from its perpendicularity,The vibrations of the same pendulum are made with the same frequency, whether they be small or great. and if they are not absolutely equal, they are insensibly different, as experience may shew you: and though they were very unequal, yet would they not discountenance, but favour our cause. Therefore let us draw the perpendicular AB [in Fig. 9.] and hang from the point A, upon the threed AC, a plummet C, and another upon the same threed also, which let be E, and the threed AC, being removed from its perpendicularity, and then letting go the plummets C and E, they shall move by the arches CBD, EGF, and the plummet E, as hanging at a lesser distance, and withall, as (by what you said) lesse removed, will return back again faster, and make its vibrations more frequent than the plummet C, and therefore shall hinder the said plummet C, from running so much farther towards the term D, as it would do, if it were free: and thus the plummet E bringing unto it in every vibration continuall impediment,The cause which impedeth the pendulum, and reduceth it to rest. it shall finally reduce it to quiescence. Now the same threed, (raking away the middle plummet) is a composition of many grave penduli, that is, each of its parts is such a pendulum fastned neerer and neerer to the point A, and therefore dispo-sed
