hath deſribed ſince the time that it touched the globe, (which curvilinear path we may call the cycloid or epicycloid) will be to double the verſed ſine of half the arc which ſince that time has touched the globe in paſſing over it, at the ſum of the diameters of the globe and the wheel, to the ſemidiameter of the globe.
Proposition XLIX. Theorem XVII.
If a wheel ſtand upon the inſide 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 deſcribed ſince it touched the globe, will be to the double of the verſed ſine of half the arc which in all that time has touched the globe in paſſing over it, as the difference of the diameter of the globe and the wheel, to the ſemidiameter of the globe.
Let ABL (PL 19. Fig. 1.2.) be the globe, C its centre. BPV the wheel inſiſting thereon, E the centre of the wheel, B the point of contact, and P the given point in the perimeter of the
