The property is that if any quadrilateral, ABCD, skew or otherwise, have its sides AB, DC divided in E, F so that
AE : EB = DF : FC = AD : BO
then the direction of the line EF shall bisect the angle between the directions of BC, AD.
This extension of Euclid's VI. 3 follows immediately from the proposition that if AE : EB = DF : FC, then all such lines as EF are parallel to one plane, namely, the plane parallel to BC, AD; and that they each cut similar lines drawn with reference to BC, AD.