On diagrams accompanying reductio ad absurdum proofs in Euclid's Elements book I. Reviewing Hartshorne and Manders
Abstract
Exploring selected reductio ad absurdum proofs in Book 1 of the Elements, we show they include figures that are not constructed. It is squarely at odds with Hartshorne's claim that "in Euclid's geometry, only those geometrical figures exist that can be constructed with ruler and compass". We also present diagrams questioning Manders' distinction between exact and co-exact attributes of a diagram, specifically, a model of semi-Euclidean geometry which satisfies straightness of lines and equality of angles and does not satisfy the parallel postulate.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.