Euclid's Extreme and Mean Proportion Construction

GeoGebra Commands & Parameters

1. Circle(A_1, A_2) → c_1
2. Line(A_1, C_1) → a_1
3. Point(c_1) → D
4. OrthogonalLine(D, a_1) → b_1
5. Intersect(c_1, a_1, 1) → A
6. Intersect(a_1, b_1) → C
7. Segment(A, C) → a
8. Segment(D, C) → b
9. Intersect(c_1, a_1, 2) → B
10. Segment(C, B) → c
11. Polygon(B, A, 4) → poly1, e, f, g, h, H_1, G
12. Midpoint(A, H_1) → E
13. Segment(E, B) → i
14. Circle(E, B) → k
15. OrthogonalLine(A, a) → j
16. Intersect(k, j, 2) → F
17. Polygon(F, A, 4) → poly2, l, m, n, p, M, H
18. Segment(D, B) → q
19. Segment(D, A) → r
20. Segment(A, B) → s
21. Segment(A, M) → t
22. Distance(A, B) → AB
23. Distance(A, M) → AM
24. Segment(C, A) → d
25. Circle(A_{3}, A_{4}) → c_{2}
26. Line(A_{3}, C_{2}) → a_{2}
27. Point(c_{2}) → D_{1}
28. OrthogonalLine(D_{1}, a_{2}) → b_{2}
29. Intersect(c_{2}, a_{2}, 1) → A_{5}
30. Intersect(a_{2}, b_{2}) → C_{3}
31. Segment(A_{5}, C_{3}) → a_{3}
32. Segment(D_{1}, C_{3}) → b_{3}
33. Intersect(c_{2}, a_{2}, 2) → B_{1}
34. Segment(C_{3}, B_{1}) → c_{3}
35. Polygon(B_{1}, A_{5}, 4) → poly1_{1}, e_{1}, f_{1}, g_{1}, h_{1}, H_{2}, G_{1}
36. Midpoint(A_{5}, H_{2}) → E_{1}
37. Segment(E_{1}, B_{1}) → i_{1}
38. Circle(E_{1}, B_{1}) → k_{1}
39. OrthogonalLine(A_{5}, a_{3}) → j_{1}
40. Intersect(k_{1}, j_{1}, 2) → F_{1}
41. Polygon(F_{1}, A_{5}, 4) → poly2_{1}, l_{1}, m_{1}, n_{1}, p_{1}, M_{1}, H_{3}
42. Segment(D_{1}, B_{1}) → q_{1}
43. Segment(D_{1}, A_{5}) → r_{1}
44. Segment(A_{5}, B_{1}) → s_{1}
45. Segment(A_{5}, M_{1}) → t_{1}
46. Distance(A_{5}, B_{1}) → AB_{1}
47. Distance(A_{5}, M_{1}) → AM_{1}
48. Segment(C_{3}, A_{5}) → d_{1}