Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/43

 in as much more time as it was in coming by the inclining plane, it would pass double the space of the plane inclined: namely (for example) if the ball had past the plane D A in an hour, continuing to move uniformly with that degree of velocity which it is found to have in its arriving at the term A, it shall pass in an hour a space double the length D A; and because (as we have said) the degrees of velocity acquired in the points B and A, by the moveables that depart from any point taken in the perpendicular C B, and that descend, the one by the inclined plane, the other by the said perpendicular, are always equal: therefore the cadent by the perpendicular may depart from a term so near to B, that the degree of velocity acquired in B, would not suffice (still maintaining the same) to conduct the moveable by a space double the length of the plane inclined in a year, nor in ten, no nor in a hundred. We may therefore conclude, that if it be true, that according to the ordinary course of nature a moveable, all external and accidental impediments removed, moves upon an inclining plane with greater and greater tardity, according as the inclination shall be less; so that in the end the tardity comes to be infinite, which is, when the inclination concludeth in, and joyneth to the horizontal plane; and if it be true likewise, that the degree of velocity acquired in some point of the inclined plane, is equal to that degree of velocity which is found to be in the moveable that descends by the perpendicular, in the point cut by a parallel to the Horizon, which passeth by that point of the inclining plane; it must of necessity be granted, that the cadent departing from rest, passeth thorow all the infinite degrees of tardity, and that consequently, to acquire a determinate degree of velocity, it is necessary that it move first by right lines, descending by a short or long space, according as the velocity to be acquired, ought to be either less or greater, and according as the plane on which it descendeth is more or less inclined; so that a plane may be given with so small inclination, that to acquire in it the assigned degree of velocity, it must first move in a very great space, and take a very long time; whereupon in the horizontal plane, any how little soever velocity, would never be naturally acquired, since that the moveable in this case will never move: but the motion by the horizontal line, which is neither declined or inclined, is a circular motion about the centre: therefore the circular motion is never acquired naturally, without the right motion precede it; but being once acquired, it will continue perpetually with uniform velocity. I could with other discourses evince and demonstrate the same truth, but I will not by so great a digression interrupt our principal argument: but rather will return to it upon some other occasion; especially since we not assumed the