Even though the idea of “points at infinity” is helpful for visualizing things, within projective geometry itself, this is not a natural distinction: any projective point is as good as any other one.

In analogy with our presentation of affine geometry, we will define projective spaces, projective subspaces, projective frames, and projective maps. The analogy will fade away when we …

The construction of projective geometry can be pursued synthetically by altering the axioms of Euclidean geometry. In particular, projective geometry arises only from incidence axioms; no …

The purpose of these notes is to introduce projective geometry, and to establish some basic facts about projective curves. Everything said here is contained in the long appendix of the book by …

Projective Geometry concerns itself principally with the study of descriptive properties of figures, although it will be found that the applications to engineering are mostly metrical. 3. Projection …

Desargues' Projective Geometry1 Mathematics behind Alberti's Veil: Family of lines (light rays) through a point (eye) plus a plane (veil). Recall Pappus' Theorem: A1; A2; A3; collinear; B1; …

Proof By composing projective transformations and their inverses, it's enough to show that if L is the line aX + bY + cZ = 0, then there is a projective transformation taking L to the line X = 0.