Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/38

 shall be an easie task; for I reply, that the moveable passeth by the aforesaid degrees, but the passage is made without staying in any of them; so that the passage requiring but one sole instant of time, and every small time containing infinite instants, we shall not want enough of them to assign its own to each of the infinite degrees of tardity; although the time were never so short.

Hither to I apprehend you; nevertheless it is very much that that Ball shot from a Cannon (for such I conceive the cadent moveable) which yet we see to fall with such a precipice, that in less than ten pulses it will pass two hundred yards of altitude; should in its motion be found conjoyned with so small a degree of velocity, that, should it have continued to have moved at that rate without farther acceleration, it would not have past the same in a day.

You may say, nor yet in a year, nor in ten, no nor in a thousand; as I will endeavour to shew you, and also happily without your contradiction, to some sufficiently simple questions that I will propound to you. Therefore tell me if you make any question of granting that, that that ball in descending goeth increasing its impetus and velocity.

I am most certain it doth.

And if I should say that the impetus acquired in any place of its motion, is so much, that it would suffice to re-carry it to that place from which it came, would you grant it?

I should consent to it without contradiction, provided alwaies, that it might imploy without impediment its whole impetus in that sole work of re-conducting it self, or another equal to it, to that self-same height as it would do, in case the Earth were bored thorow the centre, and the Bullet fell a thousand yards from the said centre, for I verily believe it would pass beyond the centre, ascending as much as it had descended; and this I see plainly in the experiment of a plummet hanging at a line, which removed from the perpendicular, which is its state of rest, and afterwards let go, falleth towards the said perpendicular, and goes as far beyond it; or onely so much less, as the opposition of the air, and line, or other accidents have hindred it. The like I see in the water, which descending thorow a pipe, re-mounts as much as it had descended.

You argue very well. And for that I know you will not scruple to grant that the acquist of the impetus is by means of the receding from the term whence the moveable departed, and its approach to the centre, whither it motion tendeth; will you stick to yeeld, that two equal moveables, though descending by divers lines, without any impediment, acquire equal impetus, provided that the approaches to the centre be equal?