Miletus- Market Gate – Geometries of Creation

Make a square whose edges align with the axes of the central quatri-style block, and set it on the podium; its top edge will align with the column bases of the upper story. Call its side length 1.000.

The distance between the inner column axes is then .500.
Inscribe a circle in the square, along with its diagonals; this locates the base of the lower columns at height .147 and the lip of the lower cornice at height .854.
Unfold the diagonals of the square to find the base of the upper entablature at height 1.414.
Inscribe an octagon around the circle, and draw rays to its corners; their intersection with the circle falls at height .694, establishing the top of the column shafts.

From the point where this horizontal intersects the vertical axes of the inner columns, drop diagonals outwards until they hit the baseline; these intersection points will lie 1.889 units apart, locating the axes of the columns just framing the lateral entries.
The upper ray/circle intersections in the original red square fall at height .962, locating the top edge of the main story entablature.
A key punctuation point on the upper entablature, where it steps out to full width, falls at height 1.500.
The center axes of the lateral entries can be found 1.445 units apart, i.e. halfway between 1.000 and 1.889 found for the previously established interaxial spans.

A square of this height locates another big punctuation point on the upper entablature.
To get the axes of the outermost columns, swing a big arc from the lower corner of the red square through the point on the lateral entry axis at height 1.500; these arcs will hit the baseline 2.870 units apart.

To get the axes of the penultimate column pair, swing an arc from the same center through the point where the column axis framing the lateral entry hits the crucial story division at height .854; these new arcs will hit the baseline 2.351 units apart.
To get the bottom of the lower column bases, extend the rays of octagonal symmetry until they intersect the vertical axes of the columns framing the lateral entries; these intersections fall at height .109.

The tops of the column shafts in the lower zone appear to fall at height .333, or one third, which can be found by intersecting the half-diagonal of the red square with the diagonal of the square’s lower quadrant.
To get the top of the main capitals, begin by subdividing the interval between the two inner major column sets, and then swing an arc tangent to this line until it intersects the diagonal of the red square, which will happen at height .765.
The top of the main entablature falls at height .914, aligned with the corner of a great octagon of height 2.000 concentric with the red square of height 1.000.
The tops of the shafts in the upper wall niches fall at height 1.250, as the diagonals from height 1.000 indicate.
The tops of the lateral pediments seem to have inner tips at height 1.618, i.e. The Golden Section of the original square.
The top of the main central pediment falls at height 1.750, as the diagonals from height 1.500 indicate, and the raking angle of its sides can be found by connecting this vertex to the points at height 1.500 on the entry axes.
Voila…
This is the Market Gate from Miletus, Turkey. The source image is Figure 3 from PHOTOGRAMMETRIC RECORDING AND EVALUATION OF THE MARKET GATE OF MILETUS FOR ARCHITECTURAL HERITAGE CONSERVATION, by T. Vögtle, K. Ringle, M. Nutto, H.-P. Bähr, M. Pfanner, F. Zens, M. Maischberger, from Proceedings of the XIXthe International Symposium, CIPA 2003: new perspectives to save cultural heritage: Antalya (Turkey), 30 September-04 October, 2003.