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, A I equal, we get 
AK = 3AN + 2a; hK = AN.PN/a ; 
and for the equation to the evolute, the locus of h, 
27 ay 2 = 4 (oc — 2a) 3 . 
To find h produce the axis outwards to B so that 
27 27 
BZ — — lat. rect. = — - a. 
lo 4 
Then draw ZL at right angles to the axis to meet the circle 
on BK as diameter, and inflect Zli to HK parallel to BL. 
Having given his constructions without proof at the end of 
prop. 39 in his Serenus De Sect. Coni , Halley concludes, 
“ Horum omnium demonftrationem, cum in nimiam excrefceret 
molem, totamque fere folidam Geometriam poftularet, in prae- 
fentia omittendam cenfeo. Ex iis tamen quae in quinto Conicoru 
[Apollonii] habentur, et qua? in Philo/oph. Tran/act. Num. 188 
190 tradidimus, non multo opere comprobari poterunt.” 
B. 
Fr^gier. 
1 A chord PQ of a conic which subtends a right angle at 
a fixed point 0 on the curve passes through a fixed point on the 
normal at 0. 
£>3 
