The Principles of Projective Geometry

A₁ ABCD anharmonic ratio axis of perspective B₁ Brianchon's theorem C₁ Carnot's theorem centre of perspective Ceva's Theorem coincide common conjugates concurrent conic touching conjugate lines conjugate points conjugate rays connectors construct correlative corresponding points corresponding rays curve diameter double contact double points envelope figure fixed lines fixed points four points G points given conic given line given point harmonic conjugates Hence hexagon imaginary inscribed involution determined involution pencil line at infinity lines joining locus meet the conic opposite sides pair of lines pairs of conjugate pairs of corresponding pairs of points parabola parallel Pascal lines Pascal's theorem perpendicular plane perspective points at infinity points of intersection polar pole projective ranges proved quadrangle quadrilateral radical axis range described real points right angles self-corresponding points straight line subtend system of conics tangents three pairs triangle ABC vanishing line vertex vertices