wheel. Imagine this wheel to proceed in the great circle ABL from A through B towards L. and in its progreſs to revolve in ſuch a manner that the arcs AB, PB may be always equal the one to the other, and the given point P in the perimeter of the wheel may deſcribe in the mean time the curvilinear path AP. Let AP be the whole curvilinear path deſcribed ſince the wheel touched the globe in A, and the length of this path AP will be to twice the verſed line of the arc PB, as 2 CE to CB. For let the right line CE (produced if need be) meet the wheel in V, and join CP, BP, EP, VP; produce CP, and let fall thereon the perpendicular VF. Let PH, VH, meeting in H, touch the circle in P and K and let PH cut VF in G, and to VP let fall the perpendiculars GI, HK. From the centre C with any interval let there be deſcribed the circle nom, cutting the right line CP in n, the perimeter of the wheel BP in o, and the curvilinear path AP in m; and from the centre V with the interval Va let there be deſcribed a circle cutting VP produced in q.
Becauſe the wheel in its progreſs always revolves about the point of contact B, it is manifeſt that the right line BP is perpendicular to that curve line AP which the point P of the wheel deſcribes, and therefore that the right line VP will touch this curve in the point P. Let the radius of the circle nom be gradually increaſed or diminiſhed ſo that at laſt it become equal to the diſtance CP; and by reaſon of the ſimilitude of the evaneſcent figure Pnomq, and the figure PFGVI, the ultimate ratio of the evaneſcent lineolæ Pm, Pn, Po, Pq, that is, the ratio of the momentary mutations
