BOOK
From Affine to Euclidean Geometry: An Axiomatic Approach
This monograph, originally published in Polish, provides a rigorous and fully formalized treatment of the foundations of geometry using first-order logic. The book traces a mathematical "odyssey," developing Euclidean geometry through the lens of affine geometry. It focuses on the deep connections between synthetic and analytic plane geometry, illustrating how algebraic laws like Pappus' law correlate with geometric properties. Completed and translated by the author's colleague, Maria Moszyńska, after Szmielew's death, the text is regarded as a masterwork of simplicity, precision, and beauty, suitable for graduate-level courses in the foundations of mathematics.
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