The Lost Chord
Chords are the lines that segment the circle. All of the regular polygons can be drawn from a fixed point with a piece of string. A piece of string is a cord. This is a journal of one method of finding the Chords or the perimeter length of each segment of the regular polygons.
There is nothing mystical about these symbols. The magic is the geometry itself, for within these simple figures is the power to shape the world.
LINE
CROSS
LINE the First Chord. The line is the radius of the circle. If one end of a cord or piece of string is held to a fixed point, the other end will swing 360°.Dead Center is found by affixing the cord to any point on the perimeter of the circle and making an identical circle. The space formed is the Vesica Pisces.
CROSS, the Second Chord. The cross is the line, height of the circles, drawn through the points where the circles cross within the Vesica Pisces.
TRIANGLE
SQUARE
TRIANGLE, the Third Chord. The equilateral triangle can be drawn by placing a circle within the Vesica Pisces. The top and bottom of the circle are the guides for sides of the triangle.
SQUARE, the Fourth Chord. The chord of the square is the radius of the circle. The chords of the square are the perimeters of the quadrants.
PENTAGON
HEXAGON
PENTAGON, the Fifth Chord. CA = AB. BC = the length of the Fifth Chord.
HEXAGON, the Sixth Chord. The chord of the hexagon is a quarter segment of the diamond or rhombus within the Vesica Pisces.
DIAGRAM 1
DIAGRAM 2
- Diagram 1
- Draw the Pentagon Figure, CA = AB.
- Draw in the line from B to C.
- Draw a line from D to E that is the same length as the line from O to B.
- Then, find a point (F) that is equal distance from OBE.
- Drawing a circle around the points OBE is an easy way to do this.
- The circle center is the Point (F).
- Mark the Point with a small dot and hide/delete (purple) guide lines.
- Diagram 2
- Draw a straight line from E to the line between B and C.
- Draw a line from O, through Point F, to G.
- Draw a line from O to E.
- Draw a line from B to G.
HEPTAGON
HEPTAGRAM
HEPTAGON, the Seventh Chord. The length of the Seventh Chord is along the line from O to E where that line intersects the side of the the small circle (shown in green) in the center of the irregular pentagram. The length of the Chord touches the small circle at the point where the small circle touches the irregular pentagram itself. (shown as black line in figure HEPTAGON on the left)
OCTAGON
OCTAGRAM
OCTAGON, the Eighth Chord. The length of Eighth Chord is the length of the line OG, intersecting mid-top cross section of the irregular pentagram on line BC (shown as black line in figure OCTAGON on the left).
ENNEAGON
ENNEAGRAM
ENNEAGON, the Ninth Chord. Draw a circle within the irregular pentagram as shown. The length of the Ninth Chord is the length from O to the center of the circle (shown as black line in figure ENNEAGON on the left).
DECAGON
DECAGRAM
DECAGON, the Tenth Chord. The length of the Tenth Chord is the measure from OB and also, DE. It is shown in as a black line in the figure, DEGAGON on the left in both places.
HENDECAGON
HENDECAGRAM
HENDECAGON, the Eleventh Chord. The length of the Eleventh Chord is the measure from OG to the line from B to C (shown as a black line in the figure HENDECAGON on the left.
DODECAGON
DODECAGRAM
DODECAGON, the Twelfth Chord. The length of the Twelfth Chord is the line from B to the center of the small circle in the middle of the irregular pentagram.(shown as a black line in the figure DODECAGON on the left.