All the propositions in projective geometry occur in dual pairs which have the property that, starting from either proposition of a pair, the other can be immediately inferred by interchanging the parts played by the words "point" and "line." The principle was enunciated by Gergonne (1825-1826; Cremona 1960, p. x). A similar duality exists for reciprocation as first enunciated by Poncelet (1817-1818; Casey 1893; Lachlan 1893; Cremona 1960, p. x). Examples of dual geometric objects include Brianchon's theorem and Pascal's theorem, the 15 Plücker lines and 15 Salmon points, the 20 Cayley lines and 20 Steiner points, the 60 Pascal lines and 60 Kirkman points, dual polyhedra, and dual tessellations.

Brianchon's theorem | conservation of number principle | continuity principle | Desargues' theorem | duality law | dual polyhedron | Pappus's hexagon theorem | Pascal's theorem | projective geometry | reciprocal | reciprocation | self-dual