A Method of Trisecting Angles

Folks, as promised, here is the method for dividing any angle into three equal parts. That's how it looks to me anyway, and until someone demonstrates that the sections are not equal (rather than simply pointing to the damn proof and saying, "Look, it's impossible!") I will trust my eyes on this one. Try it yourself and see...

Trisection of angle using only compass and straightedge.

1-Draw arbitrary angle A-O-A' (no greater than 180°. If greater than 180°, bisect, work as follows, then rejoin.)

2-Draw bisector, B, of angle through O.

3-Draw arbitrary-sized circle P; on bisector B, with center P, and tangent to inside of angle A-O-A':

4-Draw parallels, C and D, to bisector B, and tangent to circle P'

5-Draw parallels, E and E'; through point P, to angle A-O-A'

6-Draw parallels, F and F'; to angle A-O-A'; tangent to circle P'

7-Draw line, from intersection of lines F and C at G, connecting with intersection of lines D and F^' at H, crossing B at J.

8-Draw circle O' with center at O, through J and new points K, L, M, N.

9-Draw circles J, L, and M' around points J, L, and M, same size as circle P:

10-Draw trisector X-O, from O, tangent to both circles J'and L'.

11-Draw trisector Y-O, from O, tangent to both circles J'and M'.

12-One may also draw hexsectors Z and Z' through points L and M from O. Line D-O is also a hexsector.

I have found it possible to extend this method, enabling one to 5-sect an angle (pentasect, for word techies), 7-sect, or any odd-numbered division of an angle.

It seems evident to me that by measuring with compass, the angles are indeed equally 1/3 the original angle. Still, a proper mathematical proof is required. As mentioned earlier, this would entail an investigation into Wantzel's proof to determine where he went wrong. (Readers can download that paper here.)

Alfred King Aldin. "A Pythagoreanism." Philosophic Research and Analysis, Fall 1971, pp. 6-7.
(This is an obscure journal coming out of Boulder, Colorado, and is has been defunct for some time now. He also published a response to readers in the issue of Late Winter 1973.)

M.L. Wantzel (1837). "Recherches sur les moyens de reconnaître si un Problème de Géométrie peut se résoudre avec la règle et le compas". Journal de Mathématiques Pures et Appliquées 1 (2): 366–372.
(Yes, dear research students, I copied that link right off Wikipedia! And I enjoyed it!)

(Image scanned and posted on the Internet with evil delight from Mr. Aldin's original article.)