A history of Greek mathematics - Wilbourhall.org

:
THE CONICS, BOOK V 165
greater or less than NG according as OP is or is not intermediate
between the two normals (V. 51, 52).
The proofs are of course long and complicated.
y is determined in this way
The length
(1) In the case of the parabola, measure MH towards the
vertex equal to \p, and divide AH atiV^so that HN X
= 2N X
A.
The length y is then taken such that
y:P 1
N 1
= N 1
H:HM,
where Pji^ is the ordinate passing through JV^ ;
(2) In the case of the hyperbola and ellipse, we have
AM>\p, so that GA \AM