2022/06/24 by Piotr Błaszczyk, Błaszczyk, Piotr, Anna Petiurenko +1
Computer Science · Mathematics · #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Mathematics and Applications #Mathematics, Computing, and Information Processing
paper · pdf · doi:10.48550/arxiv.2206.12213
openalex publication_date 2022/06/24 · openalex created_date 2022/06/29 · openalex updated_date 2026/07/28
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.