Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/170

 composition of the two motions do go alwayes receding with greater and greater proportion from the circumference of that circle, which the centre of the stones gravity would have designed, if it had alwayes staid upon the Tower; it followeth of necessity that this recession at the first be but little, yea very small, yea, more, as small as can be imagined, seeing that the descending grave body departing from rest, that is, from the privation of motion, towards the bottom and entring into the right motion downwards, it must needs passe through all the degrees of tardity, that are betwixt rest, and any assigned velocity; the which degrees are infinite; as already hath been at large discoursed and proved.

It being supposed therefore, that the progresse of the acceleration being after this manner, and it being moreover true, that the descending grave body goeth to terminate in the centre of the Earth, it is necessary that the line of its mixt motion be such, that it go continually receding with greater and greater proportion from the top of the Tower, or to speak more properly, from the circumference of the circle described by the top of the Tower, by means of the Earths conversion; but that such recessions be lesser and lesser in infinitum; by how much the moveable finds it self to be lesse and lesse removed from the first term where it rested. Moreover it is necessary, that this line of the compounded motion do go to terminate in the centre of the Earth. Now having presupposed these two things, I come to describe about the centre A [in Fig. 1. of this second Dialogue;] with the semidiameter A B, the circle B I, representing to me the Terrestrial Globe, and prolonging the semidiameter A B to C, I have described the height of the Tower B C; the which being carried about by the Earth along the circumference B I, describeth with its top the arch C D: Dividing, in the next place, the line C A in the middle at E; upon the centre E, at the distance E C, I describe the semicircle C I A: In which, I now affirm, that it is very probable that a stone falling from the top of the Tower C, doth move, with a motion mixt of the circular, which is in common, and of its peculiar right motion. If therefore in the circumference C D, certain equal parts C F, F G, G H, H L, be marked, and from the points F, G, H, L, right lines be drawn towards the centre A, the parts of them intercepted between the two circumferences C D and B I, shall represent unto us the same Tower C B, transported by the Terrestrial Globe towards D I; in which lines the points where they come to be intersected by the arch of the semicircle C I, are the places by which from time to time the falling stone doth passe; which points go continually with greater and greater proportion receding from the top of the