Euclid Book 1 Props VI-VIII - A Foundation for Geometry - Sociology and Pure Maths - N J Wildberger

Euclid Book 1 Props VI-VIII - A Foundation for Geometry - Sociology and Pure Maths - N J Wildberger

Explore Propositions VI to VIII of Book 1 in Euclid's Elements, examining the first instances of proofs by contradiction in mathematics. Delve into the logical foundations of geometry, questioning the suitability of Euclid's work for modern times. Analyze each proposition in detail, including the proof that equal angles in a triangle are subtended by equal sides, the impossibility of constructing certain equal line segments, and the congruence of triangles with equal sides and bases. Critically evaluate the logical issues present in these proofs and consider alternative foundations for modern geometry. Gain insights into the historical development of mathematical reasoning and its relevance to contemporary mathematical practice.