The golden thread in Euclid
The primary thread: 15 VIPs (* = construction)
We follow the theory of Herz-Fischler.
- Book I
- Prop. 42*: Make parallelogram = triangle
- Prop. 45*: Make parallelogram = rectangle
- Prop. 47 : Pythagorean theorem
- Book II
- Prop. 06 : Rectangle + square = square (solve quadratic eqn, a lemma)
- Prop. 11*: DEMR (the golden section)
- Prop. 14*: Square = rectangle
- Book III
- Prop. 32 : Two lines through/touching a circle
- Prop. 36 : Two lines through/touching a circle
- Prop. 37 : Two lines through/touching a circle
- Book IV
- Prop. 10*: The magic triangle
- Prop. 11*: Pentagon in a circle
- Book VI
- Prop. 29*: Parallelogram = parallelogram + rectangle
- Prop. 30*: DEMR
- Book XIII
- Prop. 06 : DEMR = two apotomes
- Prop. 17*: Make a dodecahedron
Bibliography
Herz-Fischler, Roger,
A Mathematical History of Division in Extreme
and Mean Ratio,
Waterloo: Wilfred Laurier University Press, 1987.
Ralph H. Abraham, 06 May 1996.