Recall: Four points on a line l are harmonically related if the line
is determined by a pair of points from the intersection of lines in a complete
quadrangle and the intersection of that line with the other two sides of
the complete quandrangle.
[In the figure: The line XZ would determined two other points, XZ#AD=R and XZ#BC=S, so that the points XRZS are harmonically related.] This is denoted H(XZ,RS). Four points on a line that are harmonically related: It has already been demonstrated that if H(AB,CD) then H(BA,CD), and conversely if H(BA,CD) then H(AB,CD). This is the meaning of saying "H(AB,CD) is equivalent to H(BA,CD)". Similarly H(AB,CD) is equiv. to H(AB,DC) and H(BA,DC). |