Definition:Cross-Ratio of Lines through Origin/Also presented as

Cross-Ratio of Lines through Origin: Also presented as

Some sources present the cross-ratio of lines through the origin as:

$\tuple {\lambda \mu, \lambda', \mu'} := \dfrac {\lambda - \lambda'} {\lambda - \mu'} / \dfrac {\mu - \lambda'} {\mu - \mu'}$

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {II}$. The Straight Line: $20$. Condition that the two pairs of lines through the origin, $y = \lambda x$, $y = \mu x$ and $y = \lambda' x$, $y = \mu' x$ should be apolar