2) Open compasses to chosen radius (the above table will give you a few ideas).
3) Choose a point on the horizon line and insert point of compass.
4) With lead touching paper, swing compasses around in a circle. This is the first circle. The circle is symbolic of Heaven and Unity.
5) Move compasses. Insert point of compasses where right hand side of circle cuts the horizon line. Swing compasses to draw large arc.
6) Repeat step 5 for the left hand side of the circle.
7) Draw intersecting arcs above and below the initial circle. Keeping the same radius, insert the point of the compasses where the right hand circle cuts the first circle (above the horizon). Draw a small arc. Repeat at the intersecting point below the horizon. Repeat on the left hand side of the circle.
8) Align the ruler with the points where the arcs intersect and the centre of the circle. Draw the vertical axis.
9) With the radius of the compasses unaltered, insert the point of the compasses where the first circle cuts the vertical axis above the horizon. Draw a large arc.
10) Repeat at the intersection of the first circle and the vertical axis, below the horizon.
The above diagram is fundamental. It is symbolic of the movement from point, to line, to plane (surface). The four petalled flower unfolds from Unity, as life unfolds from the Word of God. The five circles together from a quatrefoil, which is frequently seen in miniatures of Christ and the four Evangelists.
If you join the tips of the four petals, you draw a square. From this first square, which is symbolic of the earth, all other shapes and proportions can be developed.
diagram by the author :Diane George
The diagonal of the initial square is √2 in length.
To construct a rectangle that measures √2 (the square root of 2) along its longest side:-
1) Place the point of the compasses at the lower left corner of the square.
2) Extend the arm of the compasses to the upper right corner of the square.
3) Swing an arc (green) so that it crosses the horizon line.
4) Without moving the point of the compasses, open the arm to where the arc crosses the horizon line.
5) Move the compasses & put the point in the upper left corner of the square.
6) Draw a small arc so that it crosses the uppermost horizontal line.
7) Join the two points to complete the rectangle.
The diagonal of this new rectangle measures root 3 (√[√2 x √2] + [1 x 1] = √(2+1) = √3)
Repeat the above steps to draw a rectangle that measures the square root of 3 along its longest side (blue), extending the arm of the compasses to the upper right corner of the root 2 rectangle.
To draw a rectangle that measures Φ (phi), the Golden Mean, along its longest side:-
1) Mark a point exactly halfway along the upper and lower sides of the square and draw in the vertical.
2) Place the point of the compasses where the vertical cuts the lower side of the square.
3) Extend the arm of the compasses to the upper right corner of the square.
4) Swing an arc down so that it cuts the horizon (orange).
5) Without moving the point of the compasses, open the arm to where the arc crosses the horizon line.
6) Move the compasses & put the point where the vertical cuts the upper side of the square.
7) Draw a small arc so that it crosses the uppermost horizontal line.
8) Join the two points to complete the rectangle.
It's worth practising these fundamental rectangles. They occur again and again in illuminated manuscripts. Either the outer, bounding rectangle will be one of these figures, or features within the illumination will take their proportions and siting from these, or both.
Other important geometric figures that crop up time and again are:-
table by author: Diane George
diagrams by Diane George