The Methods of Plane Projective Geometry Based on the Use of General Homogeneous Coordinates

algebraic arbitrary assume called Chap chapter chord circle coincide collinear common concurrent condition conic conjugate with respect Consider conversely coordinates correspondence cross-ratio cuts defined definition degenerate determined distinct drawn dual elements envelope equal equation examples expressed fixed point follows four four points further given conic given line given points gives rise harmonic conjugate Hence homogeneous ILLUSTRATION infinite inscribed involution lies line joining locus meet meets the conic Note obtain opposite P₁ pairs parameter passes pencil plane point of intersection polar pole position projective properties Prove range ratios reader relation respect result roots self-corresponding points self-polar separate Show sides similarly straight line Suppose taken tangents theorem touches triangle ABC triangle of reference uniquely values vanish variable vertices zero