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'.