Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/205

 Page 180 but that the diminution of the same velocity, dependent on the diminution of the gravity of the moveable (which vvas the second cause) doth also observe the same proportion, doth not so plainly appear, And vvho shall assure us that it doth not proceed according to the proportion of the lines intercepted between the secant, and the circumference; or vvhether vvith a greater proportion?

I have assumed for a truth, that the velocities of moveables descending naturally, will follow the proportion of their gravities, with the favour of Simplicius, and of Aristotle, who doth in many places affirm the same, as a proposition manifest: You, in favour of my adversary, bring the same into question, and say that its possible that the velocity increaseth with greater proportion, yea and greater in infinitum than that of the gravity; so that all that hath been said falleth to the ground: For maintaining whereof, I say, that the proportion of the velocities is much lesse than that of the gravities; and thereby I do not onely support but confirme the premises. And for proof of this I appeal unto experience, which will shew us, that a grave body, howbeit thirty or fourty times bigger then another; as for example, a ball of lead, and another of sugar, will not move much more than twice as fast. Now if the projection would not be made, albeit the velocity of the cadent body should diminish according to the proportion of the gravity, much lesse would it be made so long as the velocity is but little diminished, by abating much from the gravity. But yet supposing that the velocity diminisheth with a proportion much greater than that wherewith the gravity decreaseth, nay though it were the self-same wherewith those parallels conteined between the tangent and circumference do decrease, yet cannot I see any necessity why I should grant the projection of matters of never so great levity; yea I farther averre, that there could no such projection follow, meaning alwayes of matters not properly and absolutely light, that is, void of all gravity, and that of their own natures move upwards, but that descend very slowly, and have very small gravity. And that which moveth me so to think is, that the diminution of gravity, made according to the proportion of the parallels between the tangent and the circumference, hath for its ultimate and highest term the nullity of weight, as those parallels have for their last term of their diminution the contact it self, which is an indivisible point: Now gravity never diminisheth so far as to its last term, for then the moveable would cease to be grave; but yet the space of the reversion of the project to the circumference is reduced to the ultimate minuity, which is when the moveable resteth upon the circumference in the very point of contact; so as that to return thither it hath no need of space: and therefore let the propension to the motion of descent be ne-