History — Thales in space
The improper pencil of parallel planes is exactly the tool of Thales’ theorem in space (which is met in the chapter on synthetic geometry): a pencil of parallel planes cut by two transversals determines proportional corresponding segments. In this modern reading, Thales’ theorem is “given by the structure of the pencil” of parallel planes.
Links
Topics: Analytic geometry in space
Concepts: Pencil of planes
Skills: Analytic geometry
People: Thales