Doubling the Circle
John Michell suggests that this (on the left below) is the template for St Mary's Chapel at Glastonbury, as well as for the Stonehenge and other structures. It consists of a circle inscribed in a triangle and a hexagram that are inscribed in another circle. The implication is that there is another hexagon inside the central circle and another one outside of the outer one, ad infinitum.
Adding another hexagram in the center would give us the figures of Metatron's Cube and the Tree of Life, seen on the last page, but Michell never mentions the name Metatron's Cube, and never fully explores the development of this figure.
I call this geometric exercise 'doubling the circle', because by adding two more circles to the first image (above right) you can prove that the outer circle is twice as large as the inner one, since a vesica made of three over-lapping circles 1 unit wide is 2 units wide. [Remember that the vesica consists of equal circles whose centers are on the circumference of another circle, causing an overlap one radius wide.]
The Vesica Piscis
The vesica piscis produces a series of ever increasing (or decreasing, depending on how you look at it) circles, hexagrams, triangles and rectangles, each twice as large as the next one (like the fractals seen earlier). The image on the left below has three 'levels' of circles showing that the outer circle is four small circles tall. [This is the image that illustrates what was said on the previous page about using circles to prove distances in the 'idealized' DC map.]
Overlaying the figure on the left onto the eagle on the Great Seal so that the top small circle matches the circle around the field of stars (which are themselves arranged like the Star of David) produces the image in the middle above. The image on the left below shows how two vesica (3 circles) define twin equilateral triangles, hexagons and hexagrams, while the image on the right shows how this was adapted to the other side of the Great Seal. [Note how the base of the blue triangle and base of the pyramid coincide.]
The vesica is the template for the Great Seal, the cathedral plan and the DC map.
Triangulum and Quadratum
Let's look closely at the inner circle in the Milan Cathedral plan as viewed by Caesarino. Inscribed within that circle we find an equal-armed cross and a diagonal square (both in red), a hexagon and a triangle formed by the diagonals of the hexagon.
[Notice how the rhombus generates a cross with arms that are un-equal. Draftsmen use two different triangles, one is a 45-45-90 triangle that is one quarter of the diagonal square, while the other is a 30-60-90 triangle that is one quarter of a rhombus. Half a diagonal square is still a 45-45-90 triangle, while half a rhombus is an equilateral traingle.]
We now know that the triangle and hexagon derive from the vesica, and are associated with the ad triangulum spoken of earlier. The ad quadratum is based on a diagonal square which results from a circle and a cross. The top of the triangle from the left image and the bottom of the square from the right image, when overlapped, produce the Masonic Compass and Square, which represent the ad triangulum and ad quadratum as symbols of the double soul of the Universe.
When Striling suggests that the Milan Cathedral was designed using a cross and rhombus (or vesica), he was referring to the quadratum and triangulum design forms which Masons represent by the square and compass and which designers represent by a triangle and a square. In the DC map, the quadratum is represented by the othogonal street grid and the oblique square that constituted the district originally. The District of Columbia is shaped like a diagonal square.
Below we add two more large circles to the image above which produces a large Star of David and the rectangular grid. Extending the lines of the hexagon in the middle circle produces the isometric grid (in red). Where those lines cross the big triangle marks the top points of the pentagram. The vesica generates the equilateral triangle, the rhombus, the Star of David, Metatron's Cube and the Tree of Life.
The ideal template for the DC map
Remember that the ideal template was shortened about 75% to produce the DC plan, meaning that the map image was reduced in height until what was an equilateral triangle now has ~52 degree base angles, accomodating the pyramid cross-section and producing a shortened pentagram and hexagram. The Wash Mmt is south and east of where it 'should' be because it was moved in order to mimic the position of he Queen's Chamber in the cross-section.
In adition to that, the Capitol Building was located north of it's ideal position for topographic reasons expalined above, which throws off everything south of the WH. So, if we move the CB south a little bit and realign the elements of the map that relate to the it, then increase the height of the triangle in the DC map, we will get the above figure in the western half of the map.
Here is an image of the template for all of the map. In this image and the one above, the CB and East Cap St have been moved south, straightening Penn, NY, and Maryland Ave's, and relocating Virginia Ave. Mass Ave is straightened by moving Lincoln Square the same distance east of the CB that the WH is west of it.