David Fideler reports that the length of the stylobate is 353.8 Greek feet long. 353 is the number of the name of Apollo's brother Hermes. Three times 353.8 is 1061 the number of the name of Apollo. Hermes name is 1/4 the sqaure root of 2, 1.4142. While all of this is true, Fideler's image doesn't give you any clues as to the actual design of the building; the positions of regulating lines, and why things were placed where they were.

For my analysis, I am going to rotate his image to the right, since the worshipper is supposed to approach the holy place from the west, as if the god is coming at you from the east; an obvious allusion to the rising of the sun, stars and planets. I am also going to include all the steps for reasons that will instantly become clear.

Regulating lines derive from geometric figures by projecting the sides or diagonals, and are used to place elements in a design. Floor plans are generally quadratic (derived from squares) while elevation plans are triangulum forms. We can expect squares to figure big time in the design, as Fideler has intuited. Including the stairs gives us two squares and a center line that locates four columns.

Diagonals of those squares locate centers of two circles and the positions of several more columns. One circle centers on the cella (on the right). Note especially that where the circles cross determines the location of the top step (red rectangle). The red rectangle is 6/7's as wide as the blue one is. If the blue line is the pole and the center line is the equator, then the red line is 59 degrees.

Where the diagonals of the square cross the circles is 45 degrees.The inner blue rectangle marks that, and is located in the center of the columns. This rectangle is 5/7's the width of the outer blue one.

Two more circles produce horizontal lines. This is 30 degrees, and half way from the center line to the perimeter.

The red circles below are half as wides as the blue ones. The inner rectangle is one circle tall and three wide.

Here adding another circle all round shows that the outside perimeter is a rectangle measuring 2x4 circle widths. As you can see this matches the set up at the Hebrew Tabernacle where the court was 50x100 (1:2) and the Tabernacle itself was 30x10 (3:1).

Here we use the diagonals of the square and more circles to establish a 3x5 rectangle. Continuing this process yields 4x6, 5x7, 6x8, 7x9, and 8x10 rectangles. You will recall that the Temple and the Tabernacle were both 1x3 (10x30 and 20x60), that the court around the Tabernacle was 2x4 (50x100), and that the Ark of the Covenant was 3x5 (1.5X2.5). The end of Noah's Ark was 30x50, as was the side of the Altar in front on the Taberbnacle (3x5). The end of the Temple and Tabernacle were 4x6 (20x30, 10x15). 6x8 is the 3-4-5 triangle.

In this image we see that HPH Bromwell uses the diagonals of the 1x2 rectangle to establish a larger rectangle with the same proportion. Although he has the same square as above, he does not use it to project his regulating lines. He has abandoned the idea that the central rectangle should be 1:3. His is a pure quadratic form that uses only squares and double squares and their diagonals.

Continue to How and Why this Works, a discussion of real world applications of geometry.

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