Here are presented a number of papers on projective (incidence) geometry following the presentation of the book The Geometry of Incidence by Harold L. Dorwart, Prentice-Hall (1966). At some point, I hope to present a proof of the harmonic ratio and a discussion of the finite projective plane.
Projective Geometry 1: Theorem of Pappus and Introduction to the Series. After presenting the necessary mathematics to understand the nature of the theorems and their proofs as they will be presented in this series (employing the Gibbs's vector algebra), the proof of Pappas's Hexagonal theorem is presented.
Projective Geometry 2: Dorwart's Introduction of Line Coordinates. Here we examine the introduction of line coordinates by Harold L. Dorwart from his book (pp. 37--38). Athough Dorwart uses line coordinates in his proofs of some theorems in his book, I will not explicitly use them beyond this paper. But as the solved problems in this paper reveal, line coordinates do have a useful place in cartesian geometry.
Projective Geometry 3: Dorwart's Proof of the Theorem of Pappus. This paper reviews a proof of Pappus's hexagonal theorem using homogeneous coordinates, as presented in his book, pp. 82--84.
Projective Geometry 4: Desargues's Theorem with Coordinate-Free Proof. We prove Desargues's Theorem using the coordinate-free form of Gibbs's vector algebra. The proof proceeds in two steps. First, we find an expression that would prove collinearity if a certain condition holds, and then we use the various constraints to find the missing pieces to the proof.
Projective Geometry 5: Desargues's Theorem with Analytic Proof Adapted from Dorwart. We prove Desargues's Theorem using a version of Harold L. Dorwart's proof from his book, The Geometry of Incidence, pp. 95--98.
Projective Geometry 6: Pappus Two Concurrences Problem and Grassmann-Plucker Relations. This paper proves the Pappus Two Concurrences lemma, and Grassmann-Plucker relations and related lemmas, in coordinate-free vector formalism.
Projective Geometry 7: Pascal's Theorem with Analytic Proof Adapted from Dorwart. Pascal's Theorem with Analytic Proof Adapted from Dorwart.
Projective Geometry / The Cross Ratio: This proof uses simple Euclidean geometry.
Papers on the stereographic projection:
Projective Geometry / Stereographic projection of a circle onto a line.
Projective Geometry / Stereographic projection of Riemann sphere in 3D.