Interpreting Euclid

Autor: Piotr Błaszczyk, Anna Petiurenko

This book offers a comprehensive reinterpretation of Euclid’s Elements (Books I–VI) through the lens of modern geometry, with particular attention to the influence of Hilbert’s Grundlagen der Geometrie . It examines how twentieth-century formal systems – such as those of Hilbert, Borsuk and Szmielew, and Tarski – function not as direct representations of Euclid’s original work, but as historically situated interpretations shaped by metamathematical concerns. Combining historical analysis with contemporary developments, the book discusses topics ranging from proportion theory and the foundations of geometry to mechanical proofs and non-Euclidean models. By highlighting the conceptual differences between ancient and modern approaches, it provides both a technical and philosophical contribution to the understanding of Euclid’s geometry and its legacy.