degrees. Which may the better be seen, by hanging two weights at two strings of equal length, and then removing them from perpendicularity, one a little way, and the other very far; the which being set at liberty, will go & return under the same times, the one by arches very small, & the other by very great ones, from whence followeth the conclusion of an admirable Problem;Admirable Problems of moveables descending by the Quadrant of a Circle, and of those descending by all the cords of the whole Circle. which is, That a Quadrant of a Circle being given (take a little diagram of the same, [in Fig. 3.]) as for instance: AB erect to the Horizon, so as that it rest upon the plain touching in the point B. and an Arch being made with a Hoop well plained and smoothed in the concave part, bending it according to the curvity of the Circumference ADB. So that a Bullet very round and smooth may freely run to and again within it (the rim of a Sieve is very proper for the experiment) I say, that the Bullet being put in any what ever place, neer or far from the lowest term B. As for instance, putting it in the point C, or here in D, or in E; and then let go, it will in equal times, or insensibly different arrive at the term B, departing from C, or from D, or from E, or from whatever other place; an accident truly wonderfull. We may add another accident no less strange than this, which is, That moreover by all the cords drawn from the point B to the points C, D, E; and to any other whatsoever, taken not onely in the Quadrant BA, but in all the whole circumference of the Circle the said moveable shall descend in times absolutely equal; insomuch that it shall be no longer in descending by the whole Diameter erect perpendicularly upon the point B, then it shall in descending by B. C. although it do sublend but one sole degree, or a lesser Arch. Let us add the other wonder, which is, That the motions of the falling bodies made by the Arches of the Quadrant AB; are made in shorter times than those that are made by the cords of those same Arches; so that the swiftest motion, and made by a moveable in the shortest time, to arrive from the point A, to the term B, shall be that which is made, not by the right line A, B, (although it be the shortest of all those that can de drawn between the points A. B.) but by the circumference ADB. And any point being taken in the said Arch; as for example: The point D. and two cords drawn A D, and D. B. the moveable departing from the qoint A, shall in a less time come to B, moving by the two cords A D and D B. than by the sole cord A, B. But the shortest of all the times shall be that of the fall by the Arch A D B. And the self same accidents are to be understood of all the other lesser Arches taken from the lowermost term B. upwards.
Sagr.No more, no more; for you so confund and fill me with Wonders, and distract my thoughts so many several wayes,that
