Clark Kimberling, Ceva collineations,
Forum Geometricorum 7 (2007) 67--72.
Abstract: Suppose L_1 and L_2 are lines. There exists a unique
point U such that if X in L_1, then X^{-1}© U in L_2, where X^{-1} denotes
the isogonal conjugate of X and X^{-1}© U is the X^{-1}-Ceva
conjugate of U. The mapping X -> X^{-1}©
U is the U-Ceva collineation. It maps every line onto a line and in particular
maps L_1 onto L_2. Examples are given involving the line at infinity, the
Euler line, and the Brocard axis. Collineations map cubics to cubics, and
images of selected cubics under certain U-Ceva collineations are briefly
considered.
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