Explore a critical review of Euclid's Book 1 Propositions I-V in this insightful video lecture. Delve into the foundations of modern pure mathematics by examining these early propositions from Euclid's Elements. Gain an understanding of the logical orientation of mathematics through careful analysis of constructions using straight-edge and compass, as well as theoretical results like the side-angle-side congruence condition. Investigate the role of angle in Euclidean geometry and question the logical validity of Euclid's work as a foundation for modern geometry. Consider whether Euclid's approach was more aligned with applied mathematics. Suitable for those interested in the history and philosophy of mathematics, as well as the logical underpinnings of geometric reasoning.
Euclid Book 1 Props I - V - A Critical Review - Sociology and Pure Mathematics - N J Wildberger
Insights into Mathematics via YouTube
Overview
Syllabus
Intro
Elements Book 1 Prop 1 - To describe and Equilateral Triangle upon a given finite Right Line.
Elements Book 1 Prop 2 - At a given Point, to put a Right Line equal to a Right Line given.
Elements Book 1 Prop 3 - Two unequal Right Lines being given, to cut off a Part from the great Equal to the lesser.
Elements Book 1 Prop 4 - Theorem
Elements Book 1 Prop 5 - Theorem - The Angles at the Base of an Isosceles Triangle are equal between themselves; and if the equal Sides be produced, the Angles under the base shall be equal between themselves.
Problems logic with Euclid so far
Conclusion
Taught by
Insights into Mathematics
