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

Insights into Mathematics via YouTube

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Overview

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This course explores Propositions VI to VIII of Book 1 of Euclid's Elements, focusing on proofs by contradiction in mathematics and questioning the suitability of Euclid as a foundation for modern geometry. The course discusses logical issues and explores alternatives to Euclid's Elements as a logical foundation for geometry. The intended audience for this course includes individuals interested in the historical foundations of mathematics and the evolution of geometric principles. The teaching method involves analyzing Euclid's propositions and engaging in critical discussions about the relevance of historical mathematical foundations in modern times.

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?

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Insights into Mathematics

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