156 



Dr Taylor, Geometrical Notes on Theorems 



The point h is an intersection of consecutive normals, the 

 position of H when P, p coincide. 



Making AN, An, AI equal, we get 



AK = SAN + 2a ; hK = AN. PN/a ; 



and for the equation to the evolute, the locus of h, 



27ay 2 = 4 (x - 2a) 3 . 



To find /* produce the axis outwards to B so that 



27 27 



BZ = — lat. rect. = —r a, 

 16 4 



Then draw ZL at right angles to the axis to meet the circle 

 on BK as diameter, and inflect Zh to HK parallel to BL. 



Having given his constructions without proof at the end of 

 prop. 39 in his Serenus De Sect. Goni, Halley concludes, 



" Horum omnium demon ftrationem, cum in nimiam excrefceret 

 molem, totamque fere folidam Geometriam poftularet, in prse- 

 fentia omittendam cenfeo. Ex iis tamen quae in quinto Conicorum 

 [Apollonii] habentur, et quae in Philofoph, Tranfact. Num. 188 & 

 190 tradidimus, non multo opere comprobari poterunt." 



B. 



Fr£gier. 

 A chord PQ of a conic which subtends a right angle at 



o 



a fixed point on the curve passes through a fixed point on the 

 normal at 0. 



