Proposition:
[i]Every procedure that can be carried out with a compass and straightedge can be done with a compass alone.[/i]
This is problem #33 in Heinrich Dörrie's [i]100 Great Problems of Elementary Mathematics.[/i]
Dorrie divides the problem into two basic constructions, from which any other can be built:
[list=1]
[*] Find the intersection of two straight lines
[b]a) Add (or subtract) two line segments[/b]
b) Complete a ratio comparison: Given m, n and q, solve for x in
[i]m/n = x/q[/i]
c) Intersect two lines
[/list]
II) Find the intersection of a straight line and a circle.
The solution presented is due to Mascheroni.
