OM : AK = BB' : AB' = y : y',
and, by multiplication,
OM : OQ' = y2 : y'2,
or
x : x' = y2 : y'2;
whence
The abscissas of two points on a parabola are to each other as the squares of the corresponding coördinates, a diameter and the tangent to the curve at the extremity of the diameter being the axes of reference.
The last equation may be written
y2 = 2px,
where 2p stands for y'2 : x'.