Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/280

 hath deribed ince the time that it touched the globe, (which curvilinear path we may call the cycloid or epicycloid) will be to double the vered ine of half the arc which ince that time has touched the globe in paing over it, at the um of the diameters of the globe and the wheel, to the emidiameter of the globe.

If a wheel tand upon the inide of a concave globe at right angles thereto, and revolving about its own axis go forward in one of the great circles of the globe, the length of the curvilinear path which any point, given in the perimeter of the wheel, hath decribed ince it touched the globe, will be to the double of the vered ine of half the arc which in all that time has touched the globe in paing over it, as the difference of the diameter of the globe and the wheel, to the emidiameter of the globe.

Let ABL (PL 19. Fig. 1.2.) be the globe, C its centre. BPV the wheel initing thereon, E the centre of the wheel, B the point of contact, and P the given point in the perimeter of the