Geometric Design Principles
If you have ever read much about the vesica, you probably know that it generates equilateral triangles, and hexagons that have sides equal to the radius of the circles. It also generates a rhombus made of two equilateral triangles. If our radius is one, the axes of rhombus are 1 and 1.732 (the square root of 3). If you have studied this much at all you will have seen that a good whole number approximation of the sqrt of 3 is 256/153.
 If we multiply these numbers by 4 we get 1060 the number of the name of Apollo, and 612 the number of the name of Zeus. If we make the long axis 612, the short axis becomes 353 the number of the name of Hermes. It has already been pointed out that the circles cross at 30 and 60 degrees, and that 31 degrees latitude is six seventh the equator. In real world terms, this means that in a circle that has a radius of 153, 265 is just a little long of 6/7's of the diameter of that circle. The larger red circles below are 6/7 the larger circles. The smaller red circles are 1/7 the diameter of the larger black circles.
 C = 2 Pi R, and R = 153, C = 961.33. C/7 = 137.33. (C/7) x 6 =824. (6/7C)/3.1416 = 262.3. The number you get if you use the tangent of 59 degrees is 255, but you can't see the difference on the side of a building. Below you can see that six points of the sri yantra touch the outer circle while eight touch the red inner circle. The two long parallel lines are each one seventh from the equator. This is the 51.4 degree triangle.
 On page 81 of Old Way of Seeing, Jonathan Hale inserts a discussion of regulating lines into his section on the vesica. You will remember that the Milan Cathedral plan shows us the rhombus used for regualting lines for that building.
 On page 81, Hale is looking at the facade of the Notre Dame Cathedral in Paris, specifically the left protal on the west side of the building. He notes that the angle that is over the doorway is 49.4 degrees, that it has a slope of 7 over 6. (An isoceles triangle seven tall with a base of 12.) He recommends that the same angles were used to regulate the face of the building. Notice that he speaks of more than system of regulating lines, and that he doesn't center on the rose window? Below the cathedral image you can see a better depiction of regulating lines. You might go back a couple of pages and look at the grid lawlwer uses.
 He fails to tie in the vesica but reminds us that ratios that expressed 'certain spiritual qualities' were built into the cathedrals; that in the Gothic cosmology, which derived from a far more ancient system, every number had a meaning. Seven, he says, was the number of the Virgin while six represented perfection and time. I offer this interpretation.
 Above the Notre Dame facade. See more related images.
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