Editing Poncelet–Steiner theorem (section)

=== Projective geometry, as it relates to the Poncelet-Steiner Theorem ===
{{main|Projective geometry}}

'''Projective geometry''' is the study of the geometric properties that are [[invariant_(mathematics)|invariant]] under [[projective transformations]]. Though a distinct topic in its own right, many of the concepts of projective geometry are applied here to Steiner constructions. Jean-Victor Poncelet was a major contributor to the subject when he postulated the theorem of this article, which Jakob Steiner later proved. Many of the related concepts developed in projective geometry include but are not limited to: [[concurrent lines|concurrence]], "points at infinity", [[perspective_(geometry)|perspective]] and [[perspectivity]], [[projectivity]], ratios and [[cross-ratio]]s, conjugates, stable or fixed points of involutions, invariants, [[Duality_(projective_geometry)|duality]], homogeneity and homography, linear transformations, [[projective harmonic conjugates|projective harmonics]], [[Pencil_(geometry)|pencils]] (of lines or of circles), and others. A thorough treatment of Steiner constructions and their proofs require a background in projective geometry, though the subject of projective geometry is not restricted to straightedge-only constructions.