CHAP. IV.] 



MELOID AND APIOID. 



103 



let RN be the tangent to the meloid, it must cut the circle (3.16), 

 and therefore cuts the meloid. 



Fig. 9, Meloid. 



Case 2. When the curve is convex towards B, draw a circle V as 

 before. Draw CT a tangent to the circle ; it is also a tangent to the 

 meloid. For suppose a circle S drawn touching the curve internally, 

 it must touch V and also CT, and any other line would cut S. QED. 



Scholium (see Figs. 8 and 9). Let M be the point. Join AM, 

 BM, cut off ME, so that AM : ME : : power of B : power of A. Join 

 AE, bisect AME by MH, make XH perpendicular, make XMH = 

 XHM, XM is a tangent. 



PROPOSITION 9 THEOREM. 



If lines be drawn from the foci to any point in a meloid or apioid, 

 the sines of the angles which they make with the perpendicular to the 

 tangent are to one another as the powers of 



