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

This course examines Euclid’s Book 1 Propositions VI–VIII, focusing on triangle properties, geometric constructions, and proofs by contradiction. It also considers whether Euclid’s Elements provides a suitable logical foundation for modern geometry.

Syllabus

Intro
Elements Book 1 Prop 6 - If two angles of a triangle are equal, then the sides subtending the equal angles will be equal.
Elements Book 1 Prop 7 - On the same Right Line cannot be constructed two Right Lines equal to two other Right Lines at different points on the same side, and having the same Ends which the first Right Line has.
Elements Book 1 Prop 8 - If two Triangles have two Sides of the one equal to two Sides of the other, each to each, and the Bases equal, then the Angles contained under the equal Sides will be equal.
Logical Issues
Q: If Euclid's Elements are not really a proper logical foundation for geometry - then what is?