Syllabus
Projective line and plane, geometric point, homogeneous coordinates, projective extension of the affine line, affine plane, proper and improper points. Cross ratio, harmonic quadruple. Projectivity on the line, in the plane. The duality principle.
Projectivity and perspectivity of linear systems. Constructions of projectivities, perspectivities, direction line, direction point, Pappos theorem. Fixed points of a projectivity on a line. Involution. Complete quadripoint, quadrilateral.
Projective construction of conics. Construction of a tangent line, of tangent points. Construction of a projetivity on a conic. Involution on a conic.
Affine classification of regular conics, special constructions for hyperbola, parabola, ellipse. Perpendicularity, circle, constructions with an auxiliary circle.
Pascal and Brianchon theorems.
Pole and polar, conjugated poles and polars. Conjugated diameteres, foci.
Annotation
Construction of projective plane and projective extension of Euclidean plane. Description of conics and construction of conics from given elements.